A hybrid digital particle tracking velocimetry technique

A novel approach to digital particle tracking velocimetry (DPTV) based on cross-correlation digital particle image velocimetry (DPIV) is presented that eliminates the need to interpolate the randomly located velocity vectors (typical of tracking techniques) and results in significantly improved resolution and accuracy. In particular, this approach allows for the direct measurement of mean squared fluctuating gradients, and thus several important components of the turbulent dissipation. The effect of various parameters (seeding density, particle diameter, dynamic range, out-of-plane motion, and gradient strength) on accuracy for both DPTV and DPIV are investigated using a Monte Carlo simulation and optimal values are reported. Validation results are presented from the comparison of measurements by the DPTV technique in a turbulent flat plate boundary layer to laser Doppler anemometer (LDA) measurements in the same flow as well as direct numerical simulation (DNS) data. The DPIV analysis of the images used for the DPTV validation is included for comparison. Received: 29 August 1994/Accepted: 31 May 1996     

Development and validation of echo PIV

The combination of ultrasound echo images with digital particle image velocimetry (DPIV) methods has resulted in a two-dimensional, two-component velocity field measurement technique appropriate for opaque flow conditions including blood flow in clinical applications. Advanced PIV processing algorithms including an iterative scheme and window offsetting were used to increase the spatial resolution of the velocity measurement to a maximum of 1.8 mm×3.1 mm. Velocity validation tests in fully developed laminar pipe flow showed good agreement with both optical PIV measurements and the expected parabolic profile. A dynamic range of 1 to 60 cm/s has been obtained to date.     

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

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

Digital particle image velocimetry

Digital particle image velocimetry (DPIV) is the digital counterpart of conventional laser speckle velocitmetry (LSV) and particle image velocimetry (PIV) techniques. In this novel, two-dimensional technique, digitally recorded video images are analyzed computationally, removing both the photographic and opto-mechanical processing steps inherent to PIV and LSV. The directional ambiguity generally associated with PIV and LSV is resolved by implementing local spatial cross-correlations between two sequential single-exposed particle images. The images are recorded at video rate (30 Hz or slower) which currently limits the application of the technique to low speed flows until digital, high resolution video systems with higher framing rates become more economically feasible. Sequential imaging makes it possible to study unsteady phenomena like the temporal evolution of a vortex ring described in this paper. The spatial velocity measurements are compared with data obtained by direct measurement of the separation of individual particle pairs. Recovered velocity data are used to compute the spatial and temporal vorticity distribution and the circulation of the vortex ring.     

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     

Phase correlation processing for DPIV measurements

A novel digital particle image velocimetry (DPIV) correlation method is presented, the Gaussian transformed phase correlation (GTPC) estimator, using nonlinear filtering techniques coupled with the phase-transform (PHAT) generalized cross-correlation filter. The use of spatial windowing is shown to be ideally suited for the use of phase correlation estimators, due to their invariance to the loss of correlation effects. Error analysis demonstrates the increased valid vector detection and measurement accuracy of the windowed GTPC over the traditional Fourier based estimator in a series of uniform displacement Monte Carlo simulations. Analysis of the GTPC performance in the PIV standard image sets shows error reductions on the order of 15–45% over the range of simulations. Experimental DPIV images from a turbulent rib roughened channel flow are used to validate the use of the GTPC, which shows a strong reduction in peak locking effects, background noise errors, and erroneous vectors. Together, these results demonstrate the coupled benefits provided by the use of advanced filtering techniques applied to the phase correlation estimator. With the correct implementation of these filters, the GTPC is able to provide substantial improvements to the robustness of DPIV estimation.     

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     

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 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.     

Turbulent flow around a surface-mounted obstacle using 2D-3C DPIV

The mean turbulent flow structure around a cube mounted on the surface of an open-surface water channel was studied using a two-dimensional implementation of digital particle image velocimetry (DPIV). The out-of-plane velocity component was obtained by the use of the concept of continuity applied to two-dimensional velocity fields recorded in parallel planes. Various methods were used for the identification and localization of large-scale vortical structures in the three-dimensional flow around the surface-mounted obstacle. The results show the feasibility of its application to three-dimensional PIV data and the superior performance of recent identification techniques (namely swirling strength and normalized angular momentum), over the classical vorticity-based criterion.     

In vitro post-stenotic flow quantification and validation using echo particle image velocimetry (Echo PIV)

Echo particle image velocimetry (Echo PIV) presents itself as an attractive in vivo flow quantification technique to traditional approaches. Promising results have been acquired; however, limited quantification and validation is available for post-stenotic flows. We focus here on the comprehensive evaluation of in vitro downstream stenotic flow quantified by Echo PIV and validated in relation to digital particle image velocimetry (DPIV). A Newtonian blood analog was circulated through a closed flow loop and quantified immediately downstream of a 50 % axisymmetric blockage at two Reynolds numbers (Re) using time-averaged Echo PIV and DPIV. Centerline velocities were in good agreement at all Re; however, Echo PIV measurements presented with elevated standard deviation (SD) at all measurements points. SD was improved using increased line density (LD); however, frame rate or field of view (FOV) is compromised. Radial velocity profiles showed close agreement with DPIV with the largest disparity in the shear layer and near-wall recirculation. Downstream recirculation zones were resolved by Echo PIV at both Re; however, magnitude and spatial coverage was reduced compared to DPIV that coincided with reduced contrast agent penetration beyond the shear layer. Our findings support the use of increased LD at a cost to FOV and highlight reduced microbubble penetration beyond the shear layer. High local SD at near-wall measurements suggests that further refinement is required before proceeding to in vivo quantification studies of wall shear stress in complex flow environments.     

Digital particle velocimetry technique for free-surface boundary layer measurements: Application to vortex pair interactions

A variation of the digital particle image velocimetry (DPIV) technique was developed for the measurement of velocity at a free surface for low Froude number flows. The two-step process involves first determining the location of the free surface in the digital images of the seeded flow using the fast Fourier transform-based method of surface elevation mapping (SEM), which takes advantage of total internal reflection at the interface. The boundary-fitted DPIV code positions the interrogation windows below the computed location of the interface to allow for extrapolation of interfacial velocities. This technique was designed specifically to handle large surface-parallel vorticity which can occur when the Reynolds number is large and surface-active materials are present. The SEM technique was verified on capillary-gravity waves and the full boundary-fitted DPIV technique was applied to the interaction of vortex pairs with a free surface covered by an insoluble monolayer. The local rise and fall of the free surface as well as the passage and return of a contamination front was clearly observed in the DPIV data. Received: 20 June 1999/Accepted: 27 November 2000     

Simultaneous velocimetry/accelerometry measurements in a turbulent two-phase pipe flow

A two-color digital particle image velocimetry and accelerometry (DPIV and DPIA) measurement technique is described that records the velocity and acceleration fields of both the solid and liquid phases simultaneously. Measurements were taken at turbulent conditions of a vertical pipe flow using glass spheres as the solid phase and fluorescent particles to indicate fluid phase motion. Nd-YAG pulse lasers acted as illumination sources and images were recorded by two monochrome CCD cameras. The two-color aspect of the technique was realized by placing optical filters in front of the cameras to discriminate between the phases. Cross-correlations and auto-correlations were applied to determine velocity and acceleration fields of the two phases. Results showing some of the capabilities of the technique as applied to a two-phase pipe flow experiment are provided. For the condition studied, it was found that there was turbulence suppression due to the solid phase and that the statistics associated with the acceleration probability distribution were different for the solid and fluid phases.     

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.     

Effect of resolution on the speed and accuracy of particle image velocimetry interrogation

Particle image velocimetry incorporates a process by which an image of a flow field, bearing double images of seeding particles, is analyzed in small regions called “interrogation spots.” Each spot is imaged onto a photodetector array whose digitized output is evaluated computationally using the auto-correlation technique. This paper examines the effects of resolving the spot using arrays of various resolutions, motivated primarily by a gain in speed. For this purpose, two specially created test photographs representing (i) uniform flow and (ii) solid body rotation, were interrogated using array sizes ranging from 32 × 32 to 256 × 256. Each reduction in resolution by a factor of two gains a factor of four in interrogation speed, but this benefit is counteracted by a loss in accuracy. The particle image diameter strongly influences accuracy through two distinct error mechanisms. When the particle image is small compared to the pixel size, mean bias error becomes significant due to finite numerical resolution of the correlation function. Conversely, when the particle image is large, random error due to irregularities in the electronic images predominates. The optimum image size, therefore, lies not at either extreme but at an intermediate value such that the particle image is small in an absolute sense, and yet large relative to the pixel size. A version of this paper was presented at the 12th Symposium on Turbulence, University of Missouri-Rolla, 24–26 September 1990     

Measurement of mixing processes with combined digital particle image velocimetry and planar laser induced fluorescence

A combined digital particle image velocimetry (DPIV) and planar laser induced fluorescence (PLIF) approach was developed to measure both the time mean and turbulent mass transport in mixing processes. The system couples the two well-known techniques to enable synchronized planar measurements of flow velocities and concentrations in a study area. The potential interference effect between the seeding particles for DPIV and the fluorescent dye excitation for PLIF was carefully investigated. The performance of the system was verified with the experimental results of a turbulent round jet discharging into a stagnant environment. Comparison between the measurements obtained in the present study with the large body of existing information on pure jets is satisfactory. The key advantage of the shorter duration required with this approach compared to point-based techniques is highlighted.     

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     

Stereoscopic particle image velocimetry measurements of the flow around a surface-mounted block

The advantages of 3D measurement techniques and the accuracy of the backward projection algorithm are discussed. The 3D calibration reconstruction used is based on an analytical relation between real and image co-ordinates. The accuracy of the stereoscopic particle image velocimetry (PIV) system is assessed by taking measurements of the flow in angular displacement configuration with prisms. A comparison is made with 2D PIV measurements and the accuracy of this stereo PIV algorithm is evaluated. By using this 3D measurement technique, the topology and the main 3D features of the flow around a surface-mounted block are investigated.     

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

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

Large-scale tomographic particle image velocimetry using helium-filled soap bubbles

To measure large-scale flow structures in air, a tomographic particle image velocimetry (tomographic PIV) system for measurement volumes of the order of one cubic metre is developed, which employs helium-filled soap bubbles (HFSBs) as tracer particles. The technique has several specific characteristics compared to most conventional tomographic PIV systems, which are usually applied to small measurement volumes. One of them is spot lights on the HFSB tracers, which slightly change their position, when the direction of observation is altered. Further issues are the large particle to voxel ratio and the short focal length of the used camera lenses, which result in a noticeable variation of the magnification factor in volume depth direction. Taking the specific characteristics of the HFSBs into account, the feasibility of our large-scale tomographic PIV system is demonstrated by showing that the calibration errors can be reduced down to 0.1 pixels as required. Further, an accurate and fast implementation of the multiplicative algebraic reconstruction technique, which calculates the weighting coefficients when needed instead of storing them, is discussed. The tomographic PIV system is applied to measure forced convection in a convection cell at a Reynolds number of 530 based on the inlet channel height and the mean inlet velocity. The size of the measurement volume and the interrogation volumes amount to 750 mm × 450 mm × 165 mm and 48 mm × 48 mm × 24 mm, respectively. Validation of the tomographic PIV technique employing HFSBs is further provided by comparing profiles of the mean velocity and of the root mean square velocity fluctuations to respective planar PIV data.