Stereoscopic PIV on multiple color-coded light sheets and its application to axial flow in flapping robotic insect wings

Non-scanning volume flow measurement techniques such as 3D-PTV, holographic and tomographic particle image velocimetry (PIV) permit reconstructions of all three components (3C) of velocity and vorticity vectors in a fluid volume (3D). In this study, we present a novel 3D3C technique termed Multiple-Color-Plane Stereo Particle-Image-Velocimetry (color PIV), which allows instantaneous measurements of 3C velocity vectors in six parallel, colored light sheets. We generated the light sheets by passing white light of two strobes through dichroic color filters and imaged the slices by two 3CCD color cameras in Stereo-PIV configuration. The stereo-color images were processed by custom software routines that sorted each colored fluid particle into one of six gray-scale images according to its hue, saturation, and luminance. We used conventional Stereo PIV cross-correlation algorithms to compute a 3D planar vector field for each light sheet and subsequently interpolated a volume flow map from the six vector fields. As a first application, we quantified the wake and axial flow in the vortical structures of a robotic insect (fruit fly) model wing. In contrast to previous findings, the measured data indicate strong axial flow components on the upper wing surface, including axial flow in the leading-edge vortex core. Collectively, color PIV is robust against mechanical misalignments, avoids laser safety issues, and computes instantaneous 3D vector fields in a fraction of the time typical for other 3D systems. Color PIV might thus be of value for volume measurements of highly unsteady flows.     

Stereoscopic micro particle image velocimetry

A stereoscopic micro-PIV (stereo-μPIV) system for the simultaneous measurement of all three components of the velocity vector in a measurement plane (2D–3C) in a closed microchannel has been developed and first test measurements were performed on the 3D laminar flow in a T-shaped micromixer. Stereomicroscopy is used to capture PIV images of the flow in a microchannel from two different angles. Stereoscopic viewing is achieved by the use of a large diameter stereo objective lens with two off-axis beam paths. Additional floating lenses in the beam paths in the microscope body allow a magnification up to 23×. The stereo-PIV images are captured simultaneously by two CCD cameras. Due to the very small confinement, a standard calibration procedure for the stereoscopic imaging by means of a calibration target is not feasible, and therefore stereo-μPIV measurements in closed microchannels require a calibration based on the self-calibration of the tracer particle images. In order to include the effects of different refractive indices (of the fluid in the microchannel, the entrance window and the surrounding air) a three-media-model is included in the triangulation procedure of the self-calibration. Test measurement in both an aligned and a tilted channel serve as an accuracy assessment of the proposed method. This shows that the stereo-μPIV results have an RMS error of less than 10% of the expected value of the in-plane velocity component. First measurements in the mixing region of a T-shaped micromixer at Re = 120 show that 3D flow in a microchannel with dimensions of 800 × 200 μm² can be measured with a spatial resolution of 44 × 44 × 15 μm³. The stationary flow in the 200 μm deep channel was scanned in multiple planes at 22 μm separation, providing a full 3D measurement of the averaged velocity distribution in the mixing region of the T-mixer. A limitation is that this approach requires a stereo-objective that typically has a low NA (0.14–0.28) and large depth-of-focus as opposed to high NA lenses (up to 0.95 without immersion) for standard μPIV.     

Hummingbirds generate bilateral vortex loops during hovering: evidence from flow visualization

This article derives a method to estimate and correct the bias error of the shift vector’s absolute length in the presence of curved streamlines. The main idea is to identify the most likely streamline with constant curvature from the second-order shift vector and its gradient. The work establishes a theoretical framework including the systematic errors of the first-order and second-order shift vector’s absolute value and angle. Synthetic images of a stationary vortex are used to validate the proposed method. The curvature-correction is also applied to a synthetic flow field with non-constant curvature to demonstrate its potential for more realistic flow fields. The results reveal that second-order accurate vector fields suffer from a biased shift vector length depending on the streamline’s curvature and on the shift vector length. The bias error is negligible for vector fields with a shift vector length below the streamline curvature radius. For large shift vectors or strong curvatures, the bias error can be significantly reduced with the developed method. The approach is very general and can be applied to any vector field obtained from window-correlation particle image velocimetry (PIV), single-pixel ensemble-correlation PIV, particle tracking velocimetry or optical flow methods. It also works for all 3D extensions of the techniques, such as 3D-PTV or tomographic PIV.     

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.     

Tomographic PIV measurements in a turbulent lifted jet flame

Measurements of instantaneous volumetric flow fields are required for an improved understanding of turbulent flames. In non-reacting flows, tomographic particle image velocimetry (TPIV) is an established method for three-dimensional (3D) flow measurements. In flames, the reconstruction of the particles location becomes challenging due to a locally varying index of refraction causing beam-steering. This work presents TPIV measurements within a turbulent lifted non-premixed methane jet flame. Solid seeding particles were used to provide the 3D flow field in the vicinity of the flame base, including unburned and burned regions. Four cameras were arranged in a horizontal plane around the jet flame. Following an iterative volumetric self-calibration procedure, the remaining disparity caused by the flame was less than 0.2 pixels. Comparisons with conventional two-component PIV in terms of mean and rms values provided additional confidence in the TPIV measurements.     

Stereo-PIV using self-calibration on particle images

A stereo-PIV (stereo particle image velocimetry) calibration procedure has been developed based on fitting a camera pinhole model to the two cameras using single or multiple views of a 3D calibration plate. A disparity vector map is computed on the real particle images by cross-correlation of the images from cameras 1 and 2 to determine if the calibration plate coincides with the light sheet. From the disparity vectors, the true position of the light sheet in space is fitted and the mapping functions are corrected accordingly. It is shown that it is possible to derive accurate mapping functions, even if the calibration plate is quite far away from the light sheet, making the calibration procedure much easier. A modified 3-media camera pinhole model has been implemented to account for index-of-refraction changes along the optical path. It is then possible to calibrate outside closed flow cells and self-calibrate onto the recordings. This method allows stereo-PIV measurements to be taken inside closed measurement volumes, which was not previously possible. From the computed correlation maps, the position and thickness of the two laser light sheets can be derived to determine the thickness, degree of overlap and the flatness of the two sheets.     

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.     

Tomographic particle image velocimetry

This paper describes the principles of a novel 3D PIV system based on the illumination, recording and reconstruction of tracer particles within a 3D measurement volume. The technique makes use of several simultaneous views of the illuminated particles and their 3D reconstruction as a light intensity distribution by means of optical tomography. The technique is therefore referred to as tomographic particle image velocimetry (tomographic-PIV). The reconstruction is performed with the MART algorithm, yielding a 3D array of light intensity discretized over voxels. The reconstructed tomogram pair is then analyzed by means of 3D cross-correlation with an iterative multigrid volume deformation technique, returning the three-component velocity vector distribution over the measurement volume. The principles and details of the tomographic algorithm are discussed and a parametric study is carried out by means of a computer-simulated tomographic-PIV procedure. The study focuses on the accuracy of the light intensity field reconstruction process. The simulation also identifies the most important parameters governing the experimental method and the tomographic algorithm parameters, showing their effect on the reconstruction accuracy. A computer simulated experiment of a 3D particle motion field describing a vortex ring demonstrates the capability and potential of the proposed system with four cameras. The capability of the technique in real experimental conditions is assessed with the measurement of the turbulent flow in the near wake of a circular cylinder at Reynolds 2,700.     

Quantification of dispersed phase concentration using light sheet imaging methods

With the prevalence of particle image velocimetry (PIV) as a quantitative tool for fluid mechanics diagnostics, its application for analyzing complicated multiphase flows has been steadily increasing over the last several decades. While the primary issue in using PIV for multiphase flows is in separating the information of the phases for independent analysis with a minimum of spurious “cross-talk,” an equally crucial but often overlooked point is in the accurate quantitative measurement of the dispersed phase concentration. Accurate concentration measurement is important due to the fact that the dispersed phase is often heterogeneously distributed in both space and time, either due to a non-uniformity of the source of particulates (such as a spray nozzle or sediment boundary) or due to inertial migration of the particles even from originally homogeneous spatial distributions. In the current work, we examine the effects of light sheet profile distortion and attenuation by tracer seeding particles, as well as reflected light from local wall boundaries on the effective light sheet thickness. The effective thickness is critical for concentration measurements, as it dictates the dispersed phase detection volume. A direct calibration method is demonstrated to measure the effective light sheet thickness in a water/glass bead system, which shows that systematic bias errors on the order of 30% can result if the reflective bed condition is not accounted for, and the errors can be as high as 50% or more if a single-point measure of the sheet width is used.     

Three-dimensional PIV measurement of flow around an arbitrarily moving body

A three-dimensional (3D) particle image velocimetry measurement technique capable of simultaneously monitoring 3D fluid flows and the structure of an arbitrarily moving surface embedded in the flow was proposed with a heavy emphasis on image processing methods. The costs associated with the experimental apparatus were reduced by recording the surface and the trace particles at one image plane without the use of additional cameras or illumination devices. An optimal exposure time for surface and particle imaging was identified using red fluorescent tracer particles in conjunction with a long-pass glass filter. The particle image and surface image were then separated using an image separation process that relied on the feature scaling differences between the particles and the surface texture. A feature detection process and a matching process facilitated estimation of the 3D surface points, and the 3D surface structure was modeled by Delaunay triangulation. The particle volume reconstruction algorithm constrained the voxels inside the surface structure to zero values to minimize ghost particle generation. Volume self-calibration was employed to improve the reconstruction quality and the triangulation accuracy. To conserve computing resources in the presence of numerous zero voxels, the MLOS-SMART reconstruction and the direct non-zero voxel cross-correlation method were applied. Three-dimensional experiments that modeled the flows around an eccentric rotating cylinder and a flapping flag were conducted to validate the present technique.     

Eulerian and Lagrangian views of a turbulent boundary layer flow using time-resolved tomographic PIV

Coherent structures and their time evolution in the logarithmic region of a turbulent boundary layer investigated by means of 3D space–time correlations and time-dependent conditional averaging techniques are the focuses of the present paper. Experiments have been performed in the water tunnel at TU Delft measuring the particle motion within a volume of a turbulent boundary layer flow along a flat plate at a free-stream velocity of 0.53 m/s at Re _θ = 2,460 based on momentum thickness by using time-resolved tomographic particle image velocimetry (PIV) at 1 kHz sampling rate and particle tracking velocimetry (PTV). The obtained data enable an investigation into the flow structures in a 3D Eulerian reference frame within time durations corresponding to 28 δ/U. An analysis of the time evolution of conditional averages of vorticity components representing inclined hairpin-like legs and of Q2- and Q4-events has been performed, which gives evidence to rethink the early stages of the classical hairpin development model for high Reynolds number TBLs. Furthermore, a PTV algorithm has been applied on the time sequences of reconstructed 3D particle image distributions identifying thousands of particle trajectories that enable the calculation of probability distributions of the three components of Lagrangian accelerations.     

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:

A scanning PIV method for fine-scale turbulence measurements

A hybrid technique is presented that combines scanning PIV with tomographic reconstruction to make spatially and temporally resolved measurements of the fine-scale motions in turbulent flows. The technique uses one or two high-speed cameras to record particle images as a laser sheet is rapidly traversed across a measurement volume. This is combined with a fast method for tomographic reconstruction of the particle field for use in conjunction with PIV cross-correlation. The method was tested numerically using DNS data and with experiments in a large mixing tank that produces axisymmetric homogeneous turbulence at \(R_\lambda \simeq 219\) . A parametric investigation identifies the important parameters for a scanning PIV set-up and provides guidance to the interested experimentalist in achieving the best accuracy. Optimal sheet spacings and thicknesses are reported, and it was found that accurate results could be obtained at quite low scanning speeds. The two-camera method is the most robust to noise, permitting accurate measurements of the velocity gradients and direct determination of the dissipation rate.     

PIV for granular flows

 Particle image velocimetry (PIV) has been adapted for use in measuring particle displacement and velocity fields in granular flows. “Seeding” is achieved by using light and dark particles. The granular flow adjacent to a clear bounding wall is illuminated with a strobe, and the recorded images are analyzed using standard PIV techniques. The application is demonstrated by measuring convection rolls in a granular bed undergoing vertical oscillations. The PIV measured displacement is consistent with displacement of a marked layer of particles. Received: 29 January 1998/Accepted: 8 April 1999     

The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer

To investigate the accuracy of tomographic particle image velocimetry (Tomo-PIV) for turbulent boundary layer measurements, a series of synthetic image-based simulations and practical experiments are performed on a high Reynolds number turbulent boundary layer at Re_θ = 7,800. Two different approaches to Tomo-PIV are examined using a full-volume slab measurement and a thin-volume “fat” light sheet approach. Tomographic reconstruction is performed using both the standard MART technique and the more efficient MLOS-SMART approach, showing a 10-time increase in processing speed. Random and bias errors are quantified under the influence of the near-wall velocity gradient, reconstruction method, ghost particles, seeding density and volume thickness, using synthetic images. Experimental Tomo-PIV results are compared with hot-wire measurements and errors are examined in terms of the measured mean and fluctuating profiles, probability density functions of the fluctuations, distributions of fluctuating divergence through the volume and velocity power spectra. Velocity gradients have a large effect on errors near the wall and also increase the errors associated with ghost particles, which convect at mean velocities through the volume thickness. Tomo-PIV provides accurate experimental measurements at low wave numbers; however, reconstruction introduces high noise levels that reduces the effective spatial resolution. A thinner volume is shown to provide a higher measurement accuracy at the expense of the measurement domain, albeit still at a lower effective spatial resolution than planar and Stereo-PIV.     

A calibration procedure for millimeter-scale stereomicroscopic particle image velocimetry

A stereomicroscopic particle image velocimetry (SμPIV) system has been developed for millimeter scale flows. The SμPIV system is based on an off-the-shelf stereomicroscope, with magnification between 0.69× and 30×, and a field of view between 7.5 × 6 mm and 250 × 200 μm. Custom calibration targets were devised using printed circuit board technology, and applied at a magnification factor of 1.74, with a field of view of 4.75 × 3.8 mm. Measurement errors were assessed by moving a test block with fixed particles. Total system uncertainty in test block displacement transverse to the optical axis was 0.5% of the field of view, and 3% of the depth of field for motion along the optical axis. Approximately 20% of this uncertainty was due to the calibration target quality and test block procedures.     

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.