Modeling and correction of peak-locking in digital PIV

The systematic tendency of PIV evaluations to bias towards integral pixel values is known as peak-locking. These errors, although small, significantly affect the statistics extracted from such measurements. In this paper, the process by which such errors accrue is modeled, and a scheme for the removal of the same is suggested. Specifically, the modeling process considers FFT PIV with discrete window offset. The results are applied to actual situations and the results are found to be encouraging. The process is computationally inexpensive, and can be applied as a post processing technique to existing data to correct peak-locking.     

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     

Accuracy and time performance of different schemes of the local field correction PIV technique

Local field correction particle image velocimetry (LFC-PIV) has become an established alternative among high-resolution PIV techniques. Previous works by the authors introduced its implementation by means of simple algorithms. In these works the initial limitation of the method, which was related to the mean distance between particles, was removed. Comparison with other contemporary high-resolution techniques indicates that it offers advantages in robustness and accuracy. The trade-off for this better performance is a heavier computing load. Until now, the computing time that this load requires has not been characterized in detail, since this computing time could be substantially reduced by accepting a reduction in accuracy. This paper focuses on the characterization of the trade-off between time and accuracy, thus offering a new perspective to PIV. In this field, LFC-PIV offers a wide range of possibilities that are described in the paper. Several alternative schemes for LFC-PIV are tested, together with an analysis of the influence of the number of iterations. Performance figures for both accuracy and expended time are given. Metrological evaluation is carried out over synthetic images. A test of coherence between these results and the performance on real images is also presented. The paper shows that even for a limited number of iterations this technique offers advantages.     

A simple model for the effect of peak-locking on the accuracy of boundary layer turbulence statistics in digital PIV

A simple model was constructed to study the effect of peak-locking on the accuracy of particle image velocimetry (PIV) turbulence statistics. A crucial parameter is the ratio between the root-mean-square (rms) velocity and the discretization velocity, which reflects the number of peaks distributed over the velocity probability density functions. When the ratio of the discretization velocity, which is set by the PIV setup parameters, to the rms, given by the flow, is larger than two, the maximum errors introduced in the mean and rms values become significant (larger than 1%). The errors introduced also depend on the amplitude, or severity, of the peak-locking, and whether the mean displacement corresponds to an integer or a fractional number of pixels. The peak-locking affects the statistical moments of different order in such a way that the errors are phase shifted. The proposed model can be used to predict errors in the turbulence statistics in a laboratory PIV experiment. According to our model predictions, the most significant influence of peak-locking in a boundary layer type of flow is an overall underestimation of the wall-normal rms. Our predictions are in good agreement with our experimental results from turbulent boundary layers and the recent experimental results from a turbulent channel flow by Christensen (Exp Fluids 36:484–497, 2004) for a case of moderate peak-locking.

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On the accuracy of velocity and vorticity measurements with PIV

A number of numerical techniques aimed at improving the accuracy of measurements using the correlation approach in Particle Image Velocimetry, PIV, are proposed and investigated. In this approach the velocity (displacement) is found as the location of a peak in the correlation map. Based on an experimental model the best performing peak finding approaches are selected among different strategies. Second, an algorithm is proposed which minimizes errors on the estimates of vorticity using velocity distributions obtained by means of PIV. The proposed methods are experimentally validated against a flow with known properties. Work supported by NASA Ames Research Center     

The fully digital evaluation of photographic PIV recordings

The performance of a purely digital evaluation system for photographic PIV recordings is described. High resolution digital images are obtained from the 35 mm negatives using a commonly available slide scanner. Together with the continually improving capabilities of standard computers, this evaluation system is a cost effective alternative to the traditional analog optical/digital (Young's fringe method) and purely optical PIV interrogation systems. Compared to the optical systems the fully digital evaluation can provide a higher spatial resolution while maintaining a similar measurement uncertainty. Using actual PIV recordings absolute measurement uncertainties are obtained and further predictions toward optimal displacement data recovery are made with the aid of Monte-Carlo simulations. Measurement uncertainties are minimized for particle image diameters on the order of 2 pixels while the reduction of the image depth (i.e. bits/pixel) has little effect. The overall performance of the described digital evaluation is compared to two types of optical evaluation systems.Affiliated with DNW-NWB, DLR-Braunschweig.     

On the uncertainty of digital PIV and PTV near walls

The reliable measurement of mean flow properties near walls and interfaces between different fluids or fluid and gas phases is a very important task, as well as a challenging problem, in many fields of science and technology. Due to the decreasing concentration of tracer particles and the strong flow gradients, these velocity measurements are usually biased. To investigate the reason and the effect of the bias errors systematically, a detailed theoretical analysis was performed using window-correlation, singe-pixel ensemble-correlation and particle tracking evaluation methods. The different findings were validated experimentally for microscopic, long-range microscopic and large field imaging conditions. It is shown that for constant flow gradients and homogeneous particle image density, the bias errors are usually averaged out. This legitimates the use of these techniques far away from walls or interfaces. However, for inhomogeneous seeding and/or nonconstant flow gradients, only PTV image analysis techniques give reliable results. This implies that for wall distances below half an interrogation window dimension, the singe-pixel ensemble-correlation or PTV evaluation should always be applied. For distances smaller than the particle image diameter, only PTV yields reliable results.     

Evaluation and correction of perspective errors in endoscopic PIV

Results are presented from a single and dual lens endoscopic PIV imaging system with a view to application of PIV where optical access is restricted, such as internal combustion engines and other internal flows. PIV images taken from the single lens system were processed using cross-correlation and a quadratic distortion-mapping function. The dual lens images were processed using cross-correlation, a cubic mapping function, and standard stereoscopic relationships. Comparisons between the single and dual lens systems show the single lens system to have in-plane errors, caused by perspective effects, of an order of magnitude greater than the stereoscopic dual lens endoscopic PIV system. The stereo arrangement is recommended wherever quantitative velocimetry is required, and may also prove useful in general endoscopic inspection where dimensional measurements are to be estimated.     

Improvement of measurement accuracy in micro PIV by image overlapping

Micro PIV uses volume illumination; therefore, the velocity measured at the focal plane is a weighted average of the velocities within the measurement volume. The contribution of out-of-focus particles to the PIV correlation can generate significant measurement errors particularly in near wall regions. We present a new application of image overlapping, which is shown to be very effective in improving the accuracy of time-averaged velocity measurements by effectively reducing the measurement depth. The performance of image overlapping and correlation averaging were studied using synthetic and experimental images of micro channel flow, both with and without image pre-processing. The results show that for flows without particle clumping, image overlapping provides the best measurement accuracy without any need for image pre-processing. For flows with particle clumping, image overlapping combined with band-pass filtering provides the best measurement accuracy. When overlapped images are saturated with particles due to a large number of image pairs, image overlapping measurement still does not show any visible pixel-locking effect. Image overlapping was found to have comparable or slightly reduced pixel-locking effects compared to correlation averaging. In addition, image overlapping utilizes significantly fewer computational resources than the other techniques.     

An advection-based model to increase the temporal resolution of PIV time series

A numerical implementation of the advection equation is proposed to increase the temporal resolution of PIV time series. The method is based on the principle that velocity fluctuations are transported passively, similar to Taylor’s hypothesis of frozen turbulence. In the present work, the advection model is extended to unsteady three-dimensional flows. The main objective of the method is that of lowering the requirement on the PIV repetition rate from the Eulerian frequency toward the Lagrangian one. The local trajectory of the fluid parcel is obtained by forward projection of the instantaneous velocity at the preceding time instant and backward projection from the subsequent time step. The trajectories are approximated by the instantaneous streamlines, which yields accurate results when the amplitude of velocity fluctuations is small with respect to the convective motion. The verification is performed with two experiments conducted at temporal resolutions significantly higher than that dictated by Nyquist criterion. The flow past the trailing edge of a NACA0012 airfoil closely approximates frozen turbulence, where the largest ratio between the Lagrangian and Eulerian temporal scales is expected. An order of magnitude reduction of the needed acquisition frequency is demonstrated by the velocity spectra of super-sampled series. The application to three-dimensional data is made with time-resolved tomographic PIV measurements of a transitional jet. Here, the 3D advection equation is implemented to estimate the fluid trajectories. The reduction in the minimum sampling rate by the use of super-sampling in this case is less, due to the fact that vortices occurring in the jet shear layer are not well approximated by sole advection at large time separation. Both cases reveal that the current requirements for time-resolved PIV experiments can be revised when information is poured from space to time. An additional favorable effect is observed by the analysis in the frequency domain whereby the spectrum becomes significantly less prone to aliasing error for the super-sampled data series.     

Target-free Stereo PIV: a novel technique with inherent error estimation and improved accuracy

A novel, accurate and simple stereo particle image velocimetry (SPIV) technique utilising three cameras is presented. The key feature of the new technique is that there is no need of a separate calibration phase. The calibration data are measured concurrently with the PIV data by a third paraxial camera. This has the benefit of improving ease of use and reducing the time taken to obtain data. This third camera also provides useful velocity information, considerably improving the accuracy of the resolved 3D vectors. The additional redundancy provided by this third perspective in the stereo reconstruction equations suggests a least-squares approach to their solution. The least-squares process further improves the utility of the technique by means of the reconstruction residual. Detailed error analysis shows that this residual is an accurate predictor of resolved vector errors. The new technique is rigorously validated using both pure translation and rotation test cases. However, while this kind of validation is standard, it is shown that such validation is substantially flawed. The case of the well-known confined vortex breakdown flow is offered as an alternative validation. This flow is readily evaluated using CFD methods, allowing a detailed comparison of the data and evaluation of PIV errors in their entirety for this technique.     

Analysis of interpolation schemes for image deformation methods in PIV: effect of noise on the accuracy and spatial resolution

As testified by a previous article (Astarita and Cardone in Exp Fluids 38:233–243, 2005), a critical point that can influence significantly the accuracy of image deformation methods (IDM) for particle image velocimetry (PIV) is the interpolation scheme (IS) used in the reconstruction of deformed images. In the cited paper the effect of noise has been neglected and for this reason in this follow-up paper the influence of the IS, in the presence of noise, on both accuracy and spatial resolution is studied. Performance assessment is conducted using synthetic images with particles of Gaussian shape and with constant and sinusoidal displacement fields. Both the local and the top hat moving average approaches are investigated and the modulation transfer function, the total and bias errors have been used to evaluate the performances of IDMs for PIV applications. The results show that, when a high noise level is present in the images, the influence of the IS is less relevant than what was shown by Astarita and Cardone (Exp Fluids 38:233–243, 2005).     

Limitations of accuracy in PIV due to individual variations of particle image intensities

The effect of independent variations of the intensity of individual tracer particles between consecutive images on the accuracy of common displacement estimation methods in particle image velocimetry (PIV) is investigated. Such variations can be observed, e.g., in flows with components perpendicular to the illumination sheet, leading to out-of-plane displacements of the tracer particles. The achievable accuracy of PIV measurements is shown to be limited by this effect alone to be of the order of 0.1 pixel, yielding a basic limitation of the PIV technique.

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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     

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     

Limits and accuracy of the Stereo-LFC PIV technique and its application to flows of industrial interest

Particle image velocimetry with local field correction (LFC PIV) has been tested in the past to obtain two components of velocity in a two dimensional domain (2D2C). When compared to conventional correlation based algorithms, this advanced technique has shown improvements in three important aspects: robustness, resolution and ability to cope with large displacements gradients. A further step in the development of PIV algorithms consists in the combination of LFC with the stereo technique, which is able to obtain three components of velocity in a plane (2D3C PIV). In this work this combination is implemented and its performance is evaluated carrying out the following two different tasks:

Characterization of the tip clearance flow in an axial compressor using 3-D digital PIV

The accurate characterization and simulation of rotor tip clearance flows has received much attention in recent years due to their impact on compressor performance and stability. At NASA Glenn the first known three dimensional digital particle image velocimetry (DPIV) measurements of the tip region of a low speed compressor rotor have been acquired to characterize the behavior of the rotor tip clearance flow. The measurements were acquired phase-locked to the rotor position so that changes in the tip clearance vortex position relative to the rotor blade can be seen. The DPIV technique allows the magnitude and relative contributions of both the asynchronous motions of a coherent structure and the temporal unsteadiness to be evaluated. Comparison of measurements taken at the peak efficiency and at near stall operating conditions characterizes the mean position of the clearance vortex and the changes in the unsteady behavior of the vortex with blade loading. Comparisons of the 3-D DPIV measurements at the compressor design point to a 3D steady N-S solution are also done to assess the fidelity of steady, single-passage simulations to model an unsteady flow field.     

Volumetric correlation PIV: a new technique for 3D velocity vector field measurement

A method is proposed that allows three-dimensional (3D) two-component measurements to be made by means of particle image velocimetry (PIV) in any volume illuminated over a finite thickness. The method is based on decomposing the cross-correlation function into various contributions at different depths. Because the technique is based on 3D decomposition of the correlation function and not reconstruction of particle images, there is no limit to particle seeding density as experienced by 3D particle tracking algorithms such as defocusing PIV and tomographic PIV. Correlations from different depths are differentiated by the variation in point spread function of the lens used to image the measurement volume over that range of depths. A number of examples are demonstrated by use of synthetic images which simulate micro-PIV (μPIV) experiments. These examples vary from the trivial case of Couette flow (linear variation of one velocity component over depth) to a general case where both velocity components vary by different complex functions over the depth. A final validation—the measurement of a parabolic velocity profile over the depth of a microchannel flow—is presented. The same method could also be applied using a thick light sheet in macro-scale PIV and in a stereo configuration for 3D three-component PIV.