Analysis of weighting windows for image deformation methods in PIV

The use of a weighting window (WW) in the evaluation of the cross-correlation coefficient and in the iterative procedure of image deformation method for particle image velocimetry (PIV) applications can be used to both stabilise the process and to increase the spatial resolution. The choice of the WW is a parameter that influences the complete PIV algorithm. Aim of this paper is to examine the influence of this aspect on both the accuracy and spatial resolution of the PIV algorithm. Results show an overall accordance between the theoretical approach and the simulation both with synthetic and real images. The choice of the combination of WW influences significantly the spatial resolution and accuracy of the PIV algorithm.

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An application of Gappy POD

An iterative procedure, based on the proper orthogonal decomposition (POD), first proposed by Everson and Sirovich (J Opt Soc Am A 12(8):1657–1664, 1995) is applied to marred particle image velocimetry (PIV) data of shallow rectangular cavity flow at Mach 0.19, 0.28, 0.38, and 0.55. The procedure estimates the POD modes while simultaneously estimating the missing vectors in the PIV data. The results demonstrate that the absolute difference between the repaired vectors and the original PIV data approaches the experimental uncertainty as the number of included POD modes is increased. The estimation of the dominant POD modes is also shown to converge by examining the subspace spanned by the POD eigenfunctions.

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Selective seeding for micro-PIV

A novel seeding method for microscale particle image velocimetry (micro-PIV) is presented. The method relies on selective seeding of a thin fluid layer within an otherwise particle-free flow. In analogy to the laser sheet in macroscale PIV, the generated particle sheet defines both the depth and the position of the measurement plane, independent of the details of the optical setup. Selectively seeded micro-PIV is applied to measure the instantaneous velocity field in a microchannel with a depth-wise resolution 20% below the estimated optical measurement depth of the micro-PIV system. In principle, a measurement depth corresponding to the diameter of the tracer particles may be achieved.

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Variational optical flow estimation for particle image velocimetry

We introduce a novel class of algorithms for evaluating PIV image pairs. The mathematical basis is a continuous variational formulation for globally estimating the optical flow vector fields over the whole image. This class of approaches has been known in the field of image processing and computer vision for more than two decades but apparently has not been applied to PIV image pairs so far. We pay particular attention to a multi-scale representation of the image data so as to cope with the quite specific signal structure of particle image pairs. The experimental evaluation shows that a prototypical variational approach competes in noisy real-world scenarios with three alternative approaches especially designed for PIV-sequence evaluation. We outline the potential of the variational method for further developments.The publications of the CVGPR Group are listed under .

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Analysis of velocity interpolation schemes for image deformation methods in PIV

The spatial resolution of PIV can be increased significantly by using an image deformation method (IDM) and very small grid distance (i.e. the final distance between vectors), therefore, also increasing the processing time. By using an interpolation scheme with a good spectral response, in the dense predictor step of the algorithm, it is possible to increase the grid distance without decreasing the spatial resolution therefore decreasing the total processing time.

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Analysis of interpolation schemes for image deformation methods in PIV

Abstract   Image deformation methods in particle image velocimetry are becoming more and more accepted by the scientific community but some aspects have not been thoroughly investigated neither theoretically nor with the aid of simulations. A fundamental step in this type of algorithm is reconstruction of the deformed images that requires the use of an interpolation scheme. The aim of this paper is to examine the influence of this aspect on the accuracy of the PIV algorithm. The performance assessment has been conducted using synthetic images and the results show that both the systematic and total errors are strongly influenced by the interpolation scheme used in the reconstruction of the deformed images. Time performances and the influence of particle diameter are also analysed.

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Spatial resolution of PIV for the measurement of turbulence

Recent technological advancements have made the use of particle image velocimetry (PIV) more widespread for studying turbulent flows over a wide range of scales. Although PIV does not threaten to make obsolete more mature techniques, such as hot-wire anemometry (HWA), it is justifiably becoming an increasingly important tool for turbulence research. This paper assesses the ability of PIV to resolve all relevant scales in a classical turbulent flow, namely grid turbulence, via a comparison with theoretical predictions as well as HWA measurements. Particular attention is given to the statistical convergence of mean turbulent quantities and the spatial resolution of PIV. An analytical method is developed to quantify and correct for the effect of the finite spatial resolution of PIV measurements. While the present uncorrected PIV results largely underestimate the mean turbulent kinetic energy and energy dissipation rate, the corrected measurements agree to a close approximation with the HWA data. The transport equation for the second-order structure function in grid turbulence is used to establish the range of scales affected by the limited resolution. The results show that PIV, due to the geometry of its sensing domain, must meet slightly more stringent requirements in terms of resolution, compared with HWA, in order to provide reliable measurements in turbulence.

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Microscale Synthetic Schlieren

We develop the axisymmetric Synthetic Schlieren technique to study the wake of a microscale sphere settling through a density stratification. A video-microscope was used to magnify and image apparent displacements of a micron-sized random-dot pattern. Due to the nature of the wake, density gradient perturbations in the horizontal greatly exceed those in the vertical, requiring modification of previously developed axisymmetric techniques. We present results for 780 and 383 μm spheres, and describe the limiting role of noise in the system for a 157 μm sphere. This technique can be instrumental in understanding a range of ecological and environmental oceanic processes on the microscale.

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A real-time model-based approach for the reconstruction of fluid flows induced by microorganisms

An experiment on living microorganisms is conducted to gain insight into their motion and fluid exchange characteristics. Biocompatible microscopic particle image velocimetry (PIV)-systems are used to capture images of seeded particles in the induced fluid flows. To enhance the abilities of these devices we present a model-based approach for the reconstruction of admissible flow fields from captured images. A priori knowledge of the physical model of the flow is used to iteratively refine a predicted flow field. A physics-based filter operation generates a velocity field that is consistent with the model of incompressible laminar flows described by the Navier–Stokes equations. Interactive steering of the reconstruction process is achieved by exploiting programmable graphics hardware as a co-processor for numerical computations. To validate our method, we estimate velocity vector fields from synthetic image pairs of flow scenarios for which ground truth velocity fields exist and real-world image sequences of the flow induced by sessile microorganisms.

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XPIV–Multi-plane stereoscopic particle image velocimetry

We introduce the three-dimensional measurement technique (XPIV) based on a Particle Image Velocimetry (PIV) system. The technique provides three-dimensional and statistically significant velocity data. The main principle of the technique lies in the combination of defocus, stereoscopic and multi-plane illumination concepts. Preliminary results of the turbulent boundary layer in a flume are presented. The quality of the velocity data is evaluated by using the velocity profiles and relative turbulent intensity of the boundary layer. The analysis indicates that the XPIV is a reliable experimental tool for three-dimensional fluid velocity measurements.More information at:

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Turbulence statistics from optical whole-field measurements in particle-laden turbulence

Obtaining turbulence statistics in particle-laden flows using optical whole-field measurements is complicated due to the inevitable data loss. The effects of this data loss are first studied using synthetic data and it is shown that the interpolation of missing data leads to biased results for the turbulence spectrum and its derived quantities. It is also shown that the use of overlapping interrogation regions in images with a low image density can lead to biased results due to oversampling. The slotting method is introduced for the processing of particle image velocimetry (PIV) data fields with missing data. Next to this, it is extended to handle unstructured data. Using experimental data obtained by a dual-camera PIV/PTV (particle tracking velocimetry) system in particle-laden grid turbulence, the performance of the new approach is studied. Some preliminary two-phase results are presented to indicate the significant improvement in the statistics, as well as to demonstrate the unique capabilities of the system.An erratum to this article can be found at

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Near-wall hindered Brownian diffusion of nanoparticles examined by three-dimensional ratiometric total internal reflection fluorescence microscopy (3-D R-TIRFM)

A three-dimensional nanoparticle tracking technique using ratiometric total internal reflection fluorescence microscopy (R-TIRFM) is presented to experimentally examine the classic theory on the near-wall hindered Brownian diffusive motion. An evanescent wave field from the total internal reflection of a 488-nm bandwidth argon-ion laser is used to provide a thin illumination field on the order of a few hundred nanometers from the wall. Fluorescence-coated polystyrene spheres of 200±20 nm diameter (specific gravity=1.05) are used as tracers and a novel ratiometric analysis of their images allows the determination of fully three-dimensional particle locations and velocities. The experimental results show good agreement with the lateral hindrance theory, but show discrepancies from the normal hindrance theory. It is conjectured that the discrepancies can be attributed to the additional hindering effects, including electrostatic and electro-osmotic interactions between the negatively charged tracer particles and the glass surface.

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A study of a 3-D double backward-facing step

An investigation of the flow over a three-dimensional (3-D) double backward-facing step is presented using a combination of both quantitative measurements from a particle image velocimetry (PIV) system and qualitative oil-flow visualizations. The arrangement of the PIV instrument allows for snap-shots of the (x, y) and (y, z) planes at various axial and spanwise positions. The measurements illustrate characteristics that are found in both two-dimensional (2-D) backward-facing steps and 3-D flows around wall mounted cubes. In particular, the development of a horseshoe vortex is found after each step alongside other vortical motions introduced by the geometry of the model. Large turbulence levels are found to be confined to a region in the center of the backstep; their mean square levels being much larger than what has been observed in 2-D backward-facing steps. The large turbulent fluctuations are attributed to a quasi-periodic shedding of the horseshoe vortex as it continuously draws energy from the spiral nodes of separation, which form to create the base of the horseshoe vortex. A combination of effects including the shedding of the first horseshoe vortex, the horizontal entrainment of air and the presence of two counter rotating vortices initiated at reattachment, are shown to cause the steering vector of the flow to jettison away from the surface in the first redeveloping region and along the center at z/h = 0. Oil-flow visualizations confirm these observations.

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Assessment of camera models for use in planar velocimetry calibration

The performance of three implementations of pinhole-based camera models for use in common light-sheet imaging arrangements is investigated on the background of application to particle image velocimetry (PIV) and Doppler global velocimetry (DGV). Calibration data obtained from translated planar calibration targets was found to yield camera attitude within 0.1° on four different test cases with object distance varying as little as 2% depending on the choice of camera model. Camera calibration using data from a single image of coplanar points is considered a viable alternative to manual triangulation of camera positions but is restricted to off-normal viewing directions.

Analysis of the wake–mixing-layer interaction using multiple plane PIV and 3D classical POD

The strong interaction between turbulent structures arising from a plane mixing layer impinging on a circular cylinder is studied. This complex flow has been investigated by a set-up called dual-plane PIV that uses two 2D PIV (two-dimensional particle image velocimetry) planes acquired simultaneously. This approach allowed us to apply a 3D-POD (three-dimensional proper orthogonal decomposition) treatment. The first POD modes show the main footprint of the flow configuration, which comprises oblique structures associated with the action of the mixing layer on the near wake. The present study suggests, by analogy, that this phenomenon behaves like the dislocation observed in uniform wake flows.

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Spatial resolution of the Stereo PIV technique

A theoretical analysis of the spatial resolution in terms of modulation transfer function of the Stereo PIV technique with and without the correction of the misalignment error is performed, and the results show that some wavelengths of the flow field can be significantly dephased and modulated. A performance assessment has been conducted with both synthetic and real images and shows a good agreement with the theoretical analysis. The reconstruction of the three-dimensional displacement field is achieved using both the methods proposed by Soloff et al. (Meas Sci Technol 8:1441–1454, 1997) and by Willert (Meas Sci Technol 8:1465–1479, 1997).

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Double-pulse planar-LIF investigations using fluorescence motion analysis for mixture formation investigation

A concept for dynamic mixture formation investigations of fuel/air mixtures is presented which can equally be applied to several other laser induced fluorescence (LIF) applications. Double-pulse LIF imaging was used to gain insight into dynamic mixture formation processes. The setup consists of a modified standard PIV setup. The "fuel/air ratio measurement by laser induced fluorescence (FARLIF)" approach is used for a quantification of the LIF images in order to obtain pairs of 2D fuel/air ratio maps. Two different evaluation concepts for LIF double pulse images are discussed. The first is based on the calculation of the temporal derivative field of the fuel/air ratio distribution. The result gives insight into the dynamic mixing process, showing where and how the mixture is changing locally. The second concept uses optical flow methods in order to estimate the motion of fluorescence (i.e., mixture) structures to gain insight into the dynamics, showing the distortion and the motion of the inhomogeneous mixture field. For this "fluorescence motion analysis" (FMA) two different evaluation approaches—the "variational gradient based approach" and the "variational cross correlation based approach"—are presented. For the validation of both, synthetic LIF image pairs with predefined motion fields were generated. Both methods were applied and the results compared with the known original motion field. This validation shows that FMA yields reliable results even for image pairs with low signal/noise ratio. Here, the "variational gradient based approach" turned out to be the better choice so far. Finally, the experimental combination of double-pulse FARLIF imaging with FMA and simultaneous PIV measurement is demonstrated. The comparison of the FMA motion field and the flow velocity field captured by PIV shows that both results basically reflect complementary information of the flow field. It is shown that the motion field of the fluorescence structures does not (necessarily) need to represent the actual flow velocity and that the flow velocity field alone can not illustrate the structure motion in any case. Therefore, the simultaneous measurement of both gives the deepest insight into the dynamic mixture formation process. The examined concepts and evaluation approaches of this paper can easily be adapted to various other planar LIF methods (with the LIF signal representing, e.g., species concentration, temperature, density etc.) broadening the insight for a wide range of different dynamic processes.

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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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