Particle Image Pattern Research Articles

Particle image velocimetry (PIV) uncertainty quantification using moment of correlation (MC) plane

We present a new uncertainty estimation method for particle image velocimetry (PIV), that uses the correlation plane as a model for the probability density function (PDF) of displacements and calculates the second order moment of the correlation (MC). The cross-correlation between particle image patterns is the summation of all particle matches convolved with the apparent particle image diameter. MC uses this property to estimate the PIV uncertainty from the shape of the cross-correlation plane. In this new approach, the generalized cross-correlation (GCC) plane corresponding to a PIV measurement is obtained by removing the particle image diameter contribution. The GCC primary peak represents a discretization of the displacement PDF, from which the standard uncertainty is obtained by convolving the GCC plane with a Gaussian function. Then a Gaussian least-squares-fit is applied to the peak region, accounting for the stretching and rotation of the peak, due to the local velocity gradients and the effect of the convolved Gaussian. The MC method was tested with simulated image sets and the predicted uncertainties show good sensitivity to the error sources and agreement with the expected RMS error. Subsequently, the method was demonstrated in three PIV challenge cases and two experimental datasets and was compared with the published image matching (IM) and correlation statistics (CS) techniques. Results show that the MC method has a better response to spatial variation in RMS error and the predicted uncertainty is in good agreement with the expected standard uncertainty. The uncertainty prediction was also explored as a function of PIV interrogation window size. Overall, the MC method performance establishes itself as a valid uncertainty estimation tool for planar PIV.

Image-based characterization of the pulp flows

Material flow characterization is important in the process industries and its further automation. In this study, close-to-laminar pulp suspension flows are analyzed based on double-exposure images captured in laboratory conditions. The correlation-based methods including autocorrelation and the particle image pattern technique were studied. During the experiments, synthetic and real test data with manual ground truth were used. The particle image pattern matching method showed better performance achieving the accuracy of 90.0% for the real data set with linear motion of the suspension and 79.2% for the data set with flow distortions.

Particle image pattern mutual information and uncertainty estimation for particle image velocimetry

In this work we introduce a new measure for particle image velocimetry (PIV) cross-correlation quality and establish analytically its connection to the basic PIV theory. This metric, which we term ‘mutual information’ (MI), can be used to estimate the number of correlated particles and connect to the PIV measurement uncertainty quantification. In PIV the number of particles in common between two consecutive frames forms the basis of the cross-correlation operation that yields the velocity measurement. Since the particle image pattern intensity distribution within each image represents the available signal, the inherent number of common particle pairs between the cross-correlated images, which can be thought of as the amount of mutual information, governs the potential accuracy of the PIV measurement. The number of common particle pairs between the images can be expressed by the product of the image density NI, and the fraction of particles that leave the frame due to in-plane and out-of-plane motion FI and FO, respectively. It has previously been shown that this parameter, NIFIFO, directly relates to the validity of a PIV measurement. However, in real experiments, NIFIFO is unknown and difficult to calculate. Here we propose to overcome this limitation by introducing a new metric (MI), which directly computes the apparent amount of common information contained in the particle patterns of two consecutive images without prior knowledge of the particle field. Both theoretical derivation and experimental results are provided to show that MI and NIFIFO represent the same characteristics of a PIV measurement. Subsequently, MI is used to develop a model for PIV uncertainty estimation. This metric and the corresponding uncertainty model presented herein are applied to both standard and a filtered phase-only (robust phase correlation) correlation methods. These advancements lead to robust uncertainty estimation models, which are tested against both synthetic benchmark data as well as real experimental measurements. For all cases considered here, and uncertainties demonstrated coverage factors approximately equal to the theoretically expected values of 68.5% and 95%, which reflect 1σ and 2σ levels in a normal distribution model respectively.

Measurement of fluid rotation, dilation, and displacement in particle image velocimetry using a Fourier–Mellin cross-correlation

Traditional particle image velocimetry (PIV) uses discrete Cartesian cross correlations (CCs) to estimate the displacements of groups of tracer particles within small subregions of sequentially captured images. However, these CCs fail in regions with large velocity gradients or high rates of rotation. In this paper, we propose a new PIV correlation method based on the Fourier–Mellin transformation (FMT) that enables direct measurement of the rotation and dilation of particle image patterns. In previously unresolvable regions of large rotation, our algorithm significantly improves the velocity estimates compared to traditional correlations by aligning the rotated and stretched particle patterns prior to performing Cartesian correlations to estimate their displacements. Our algorithm, which we term Fourier–Mellin correlation (FMC), reliably measures particle pattern displacement between pairs of interrogation regions with up to ±180° of angular misalignment, compared to 6–8° for traditional correlations, and dilation/compression factors of 0.5–2.0, compared to 0.9–1.1 for a single iteration of traditional correlations.We apply our FMC algorithm to synthetic computer-generated PIV images with known velocity and vorticity fields, and to an experimentally measured flow field. Our results show that combining FMC with discrete window offset (DWO) or iterative image deformation (IID) algorithms decreases the mean and variance of displacement and vorticity errors compared to traditional correlations, and that FMC accelerates the convergence of IID.

Particle image velocimetry correlation signal-to-noise ratio metrics and measurement uncertainty quantification

In particle image velocimetry (PIV) the measurement signal is contained in the recorded intensity of the particle image pattern superimposed on a variety of noise sources. The signal-to-noise-ratio (SNR) strength governs the resulting PIV cross correlation and ultimately the accuracy and uncertainty of the resulting PIV measurement. Hence we posit that correlation SNR metrics calculated from the correlation plane can be used to quantify the quality of the correlation and the resulting uncertainty of an individual measurement. In this paper we extend the original work by Charonko and Vlachos and present a framework for evaluating the correlation SNR using a set of different metrics, which in turn are used to develop models for uncertainty estimation. Several corrections have been applied in this work. The SNR metrics and corresponding models presented herein are expanded to be applicable to both standard and filtered correlations by applying a subtraction of the minimum correlation value to remove the effect of the background image noise. In addition, the notion of a ‘valid’ measurement is redefined with respect to the correlation peak width in order to be consistent with uncertainty quantification principles and distinct from an ‘outlier’ measurement. Finally the type and significance of the error distribution function is investigated. These advancements lead to more robust and reliable uncertainty estimation models compared with the original work by Charonko and Vlachos. The models are tested against both synthetic benchmark data as well as experimental measurements. In this work, uncertainties are estimated at the 68.5% confidence level while uncertainties are estimated at 95% confidence level. For all cases the resulting calculated coverage factors approximate the expected theoretical confidence intervals, thus demonstrating the applicability of these new models for estimation of uncertainty for individual PIV measurements.

In vitro shear stress measurements using particle image velocimetry in a family of carotid artery models: effect of stenosis severity, plaque eccentricity, and ulceration.

Atherosclerotic disease, and the subsequent complications of thrombosis and plaque rupture, has been associated with local shear stress. In the diseased carotid artery, local variations in shear stress are induced by various geometrical features of the stenotic plaque. Greater stenosis severity, plaque eccentricity (symmetry) and plaque ulceration have been associated with increased risk of cerebrovascular events based on clinical trial studies. Using particle image velocimetry, the levels and patterns of shear stress (derived from both laminar and turbulent phases) were studied for a family of eight matched-geometry models incorporating independently varied plaque features – i.e. stenosis severity up to 70%, one of two forms of plaque eccentricity, and the presence of plaque ulceration). The level of laminar (ensemble-averaged) shear stress increased with increasing stenosis severity resulting in 2–16 Pa for free shear stress (FSS) and approximately double (4–36 Pa) for wall shear stress (WSS). Independent of stenosis severity, marked differences were found in the distribution and extent of shear stress between the concentric and eccentric plaque formations. The maximum WSS, found at the apex of the stenosis, decayed significantly steeper along the outer wall of an eccentric model compared to the concentric counterpart, with a 70% eccentric stenosis having 249% steeper decay coinciding with the large outer-wall recirculation zone. The presence of ulceration (in a 50% eccentric plaque) resulted in both elevated FSS and WSS levels that were sustained longer (∼20 ms) through the systolic phase compared to the non-ulcerated counterpart model, among other notable differences. Reynolds (turbulent) shear stress, elevated around the point of distal jet detachment, became prominent during the systolic deceleration phase and was widely distributed over the large recirculation zone in the eccentric stenoses.

Optimization of particle image distortion for PIV measurements

In this study, a jump matching correlation scheme is proposed. For the multi-grid, iterative particle image distortion analysis, the coarse grid solutions are not obtained from coarse pixel image constructed by binning small pixels to large pixel, but by jumping the interrogation window the number of pixels specified during the particle image matching process. With the jump matching scheme applied and particle image interpolated, the central difference particle image pattern matching and image distortion analysis are easily linked together to resolve flow fields from coarsest grid to super-resolution grid. Optimization of particle image distortion is achieved by averaging a forward and a backward image distortion correlation for every iteration process. The proposed method is first verified by standard particle images of impinging jet flow that has exact solution available, and then applied to analyze uniform flow past two side-by-side circular cylinders. Satisfactory results are obtained from the jump matching scheme proposed.

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.

Evaluation of aero-optical distortion effects in PIV

Aero-optical distortion effects on the accuracy of particle image velocimetry (PIV) are investigated. When the illuminated particles are observed through a medium that is optically inhomogeneous due to flow compressibility, the resulting particle image pattern is subjected to deformation and blur. In relation to PIV two forms of error can be identified: position error and velocity error. In this paper a model is presented that describes these errors and particle image blur in relation to the refractive index field of the flow. In the case of 2D flows the model equations can be simplified and, furthermore, the background oriented schlieren technique (BOS) can be applied as a means to assess and correct for the optical error in PIV. The model describing the optical distortion is validated by both computer simulation and real experiments of 2D flows. Two flow features are considered: one with optical distortion normal to the velocity (shear layer) and one with optical distortion in the direction of the flow (expansion fan). Both simulation and experiments demonstrate that the major source for the velocity error is the second derivative of the refractive index in the direction of the velocity vector. The aero-optical distortion effect is less critical for shearing interfaces in comparison with compression/expansion fronts, the most critical case being represented by shock waves. Based on the results from the simulated experiments, it is concluded that for the 2D flow case the BOS method allows a measurement of the mean velocity error in PIV and can reduce it to a large extent.

On errors of digital particle image velocimetry

The goal of the present study is to quantify and reduce, when possible, errors in two-dimensional digital particle image velocimetry (DPIV). Two major errors, namely the mean bias and root-mean-square (RMS) errors, have been studied. One fundamental source of these errors arises from the implementation of cross correlation (CC). Other major sources of these errors arise from the peak-finding scheme, which locates the correlation peak with a sub-pixel accuracy, and noise within the particle images. Two processing techniques are used to extract the particle displacements. First, a CC method utilizing the FFT algorithm for fast processing is implemented. Second, a particle image pattern matching (PIPM) technique, usually requiring a direct computation and therefore more time consuming, is used. Using DPIV on simulated images, both the mean-bias and RMS errors have been found to be of the order of 0.1 pixels for CC. The errors of PIPM are about an order of magnitude less than those of CC. In the present paper the authors introduce a peak-normalization method which reduces the error level of CC to that of PIPM without adding much computational effort. A peak-compensation technique is also introduced to make the mean-bias error negligible in comparison with the RMS error. Noise in an image suppresses the mean-bias error but, on the other hand, significantly amplifies the RMS error. A digital video signal usually has a lower noise level than that of an analogue one and therefore provides a smaller error in DPIV.

Limitation and improvement of PIV

Limitation and improvement of PIV

Deformed particle image pattern matching in Particle Image Velocimetry

The deformation of particle image patterns due to velocity gradients causes errors of velocity measurements and false velocity detections in PIV (Particle Image Velocimetry). A novel technique to overcome those limitations inherent in the conventional PIV by correcting the particle image pattern according to the local velocity gradients in two dimensional flows, i.e. ∂u/∂x, ∂u/∂y, ∂v/∂x and ∂v/∂y, is proposed and successfully applied to a water flow downstream of a backward facing step.

Three-dimensional particle imaging with a single camera

A new approach to the instantaneous three-dimensional mapping of flow fields is introduced. A single camera system uses defocusing in conjunction with a mask (three pin holes) embedded in the camera lens to decode three-dimensional point sources of light (i.e., illuminated particles) on a single image. The sizes and locations of the particle image patterns on the image plane relate directly to the three-dimensional positions of the individual particles. Using sequential images, particles may be tracked in space and time, yielding whole-field velocity information. Calibration of the system is straightforward, whereas the self-similarity of the particle image patterns can be used in automating the data-extraction process. The described technique was used to obtain particle trajectories in the flow field of a vortex ring impinging on a wall.