An efficient simultaneous reconstruction technique for tomographic particle image velocimetry

To date, Tomo-PIV has involved the use of the multiplicative algebraic reconstruction technique (MART), where the intensity of each 3D voxel is iteratively corrected to satisfy one recorded projection, or pixel intensity, at a time. This results in reconstruction times of multiple hours for each velocity field and requires considerable computer memory in order to store the associated weighting coefficients and intensity values for each point in the volume. In this paper, a rapid and less memory intensive reconstruction algorithm is presented based on a multiplicative line-of-sight (MLOS) estimation that determines possible particle locations in the volume, followed by simultaneous iterative correction. Reconstructions of simulated images are presented for two simultaneous algorithms (SART and SMART) as well as the now standard MART algorithm, which indicate that the same accuracy as MART can be achieved 5.5 times faster or 77 times faster with 15 times less memory if the processing and storage of the weighting matrix is considered. Application of MLOS-SMART and MART to a turbulent boundary layer at Re _θ = 2200 using a 4 camera Tomo-PIV system with a volume of 1,000 × 1,000 × 160 voxels is discussed. Results indicate improvements in reconstruction speed of 15 times that of MART with precalculated weighting matrix, or 65 times if calculation of the weighting matrix is considered. Furthermore the memory needed to store a large weighting matrix and volume intensity is reduced by almost 40 times in this case.     

Stereoscopic particle image velocimetry

Stereoscopic particle image velocimetry (PIV) employs two cameras to record simultaneous but distinct off-axis views of the same region of interest (illuminated plane within a flow seeded with tracer particles). Sufficient information is contained in the two views to extract the out-of-plane motion of particles, and also to eliminate perspective error which can contaminate the in-plane measurement. This review discusses the principle of stereoscopic PIV, the different stereoscopic configurations that have been used, the relative error in the out-of-plane to the in-plane measurement, and the relative merits of calibration-based methods for reconstructing the three-dimensional displacement vector in comparison to geometric reconstruction. It appears that the current trend amongst practitioners of stereoscopic PIV is to use digital cameras to record the two views in the angular displacement configuration while incorporating the Scheimpflug condition. The use of calibration methods has also gained prominence over geometric reconstruction. Received: 15 April 1999/Accepted: 1 February 2000     

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.     

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.     

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.     

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.     

Hybrid stereoscopic particle image velocimetry

 The technical aspects of a photographic stereo camera for three-dimensional particle image velocimetry are described herein. The hybrid concept of the camera combines advantages of the angular displacement and the translation method. The camera uses two CCD sensors in order to adjust the lens distances and angles to meet the Scheimpflug criterion and two coupled rotating mirrors for image shifting. An application to a jet flow with an exit velocity of 33 m/s demonstrates the succesfull optimization of the recording process. Received: 27 September 1996/Accepted: 6 March 1997     

Use of holography in particle image velocimetry measurements of a swirling flow

 Particle Image Velocimetry (PIV) is now a well established experimental technique to measure two components of the velocity in a planar region of a flow field. This paper shows how its proven capabilities can be further extended by using holographic recording to register the particle displacements. Among other unique characteristics, holography enables the acquisition of multiple images on a single plate, and the recording of three dimensional images. These features are used to circumvent some of the limitations of conventional PIV. Some of these possibilities are demonstrated in this study by applying the technique to a high Reynolds number swirling flow using a lens-less off-axis orthogonal recording geometry. Received: 25 February 1998/ Accepted: 2 September 1998     

Deep field noise in holographic particle image velocimetry (HPIV): numerical and experimental particle image field modelling

 Holographic recording overcomes the limits in 2-D particle image velocimetry (PIV) to cover a 3-D flow field volume. Interrogation by focusing on single planes in a reconstructed particle field is disturbed by noise from out-of-focus particles. A numerical simulation models image reconstruction and shows how validation rates depend on aperture and volume depth. An experimental model environment of scattering particles in moveable plastic slices gives support to the numerical results. Simulations and tests are carried out for interrogation by autocorrelation and crosscorrelation techniques and furnish guidelines for system design. Received: 27 December 1996 / Accepted: 14 August 1997     

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     

Microscopic particle image velocimetry measurements of transition to turbulence in microscale capillaries

The character of transitional capillary flow is investigated using pressure-drop measurements and instantaneous velocity fields acquired by microscopic PIV in the streamwise–wall-normal plane of a 536 μm capillary over the Reynolds-number range 1,800 ≤ Re ≤ 3,400 in increments of 100. The pressure-drop measurements reveal a deviation from laminar behavior at Re = 1,900 with the differences between the measured and the predicted laminar-flow pressure drop increasing with increasing Re. These observations are consistent with the characteristics of the mean velocity profiles which begin to deviate from the parabolic laminar profile at Re = 1,900, interpreted as the onset of transition, by becoming increasingly flatter and fuller with increasing Re. A fully-turbulent state is attained at Re ≅ 3,400 where the mean velocity profile collapses onto the mean profile of fully-developed turbulent pipe flow from an existing direct numerical simulation at Re = 5,300. Examination of the instantaneous velocity fields acquired by micro-PIV in the range 1,900 ≤ Re < 3,400 reveal that transitional flows at the microscale are composed of a subset of velocity fields illustrating a purely laminar behavior and a subset of fields that capture significant departure from laminar behavior. The fraction of velocity fields displaying non-laminar behavior increases with increasing Re, consistent with past observations of a growing number of intermittent turbulent spots bounded by nominally laminar flow in macroscale pipe flow with increasing Re. Instantaneous velocity fields that are non-laminar in character consistently contain multiple spanwise vortices that appear to streamwise-align to form larger-scale interfaces that incline slightly away from the wall. The characteristics of these “trains” of vortices are reminiscent of the spatial features of hairpin-like vortices and hairpin vortex packets often observed in fully-turbulent wall-bounded flow at both the macro- and micro-scales. Finally, single-point statistics computed from the non-laminar subsets at each transitional Re, including root-mean-square velocities and the Reynolds shear stress, reveal a gradual and smooth maturation of the patches of disordered motion toward a fully-turbulent state with increasing Re.     

Stereoscopic particle image velocimetry measurements of the flow around a Rushton turbine

 The principles of stereoscopic particle image velocimetry (PIV), including distortion compensation, were applied to the turbulent flow in a vessel stirred by a Rushton turbine. An angular offset configuration was used and tilt-axis lens mounts were incorporated in order to satisfy the Scheimpflug condition, significantly reducing the ordinarily large depth of field requirements of such configurations. A distortion compensation procedure, or in situ calibration, was utilized in place of the ray tracing, or mechanical registration, used in previous studies. The calibration procedure was validated using two tests, one a rigid translation of a speckle target, the other the viscous flow between two concentric cylinders. The results of the tests suggest the success with which the distortion compensation procedure may be applied to real fluid flows. Phase-locked instantaneous data were ensemble averaged and interpolated in order to obtain mean 3-D velocity fields on a cylindrical shell enclosing the turbine blade. From these fields, the tip vortex pairs and the radial jet documented in previous studies of mixer flows were easily identified. Received: 5 February 1999/Accepted: 1 December 1999     

Investigation of thermal convection in water columns using particle image velocimetry

Particle image velocity measurements were applied on thermally driven convection at low Rayleigh numbers. In a model experiment using a water column heated from bottom and cooled from above, the velocity field was studied at different vertical temperature gradients. In the testing facility with high aspect ratio (about 19) representing a 1-m-long column with 5?cm diameter, occurrence of free convection was verified for destabilizing temperature gradients of 0.1–2?K/m. The PIV results revealed that significant flow exists already at low vertical temperature gradients. The velocity of the stable large-scale circulations increased linearly with temperature gradient (<1?K/m) from 8?×?10^?5 to 1?×?10^?3?m/s. At higher temperature gradients (1–2?K/m), a transition from quasi-stationary into time-dependent flow was observed, where convection cells changed position, number, and form temporarily. The motivation of this research was to gain more insight into density-driven convection in boreholes and groundwater monitoring wells.     

Investigation of a turbulent spot using multi-plane stereo particle image velocimetry

The multi-plane stereo particle image velocimetry (MSPIV) technique has been applied to an investigation of the spatial and temporal development of turbulent spots in a laminar flat-plate boundary-layer flow with a slight adverse pressure gradient. On the basis of a large number of evaluated instantaneous 3- and 2-component velocity-vector fields, measured synchronously and separated in space, or with different time separations in one or two planes, the technique enabled the determination of several statistical quantities of fluid mechanical significance. The shape and role of coherent substructures for the growth and turbulent mixing of the spot were the focus of this investigation.List of symbols x, y, z stream-, normal-, and spanwise coordinate - U freestream velocity (U=7 m/s) - Re Reynolds number, =Re_x^1/2 - u, v, w instantaneous velocity components - u, v, w fluctuation velocity components - Q-1,...,4 quadrants of Reynolds stress uv' - PDF probability density function - R_ii space–(time)-correlation function - wavelength of laser light - TE trailing edge of turbulent spot - LE leading edge of turbulent spot     

Twenty years of particle image velocimetry

The development of the method of particle image velocimetry (PIV) is traced by describing some of the milestones that have enabled new and/or better measurements to be made. The current status of PIV is summarized, and some goals for future advances are addressed.     

Spatially correlated precision error in digital particle image velocimetry measurements of turbulent flows

The purpose of the current paper is to describe an experimental study of the spatially correlated precision errors associated with particle image velocimetry (PIV) measurements made in turbulent flows. A free jet was used as the base flow for the study. The precision error of time-averaged statistics of the mean and turbulent flowfield is governed by the probability distribution function of the various quantities and the finite sample size of the data sets. Spatial measurements that are separated by a distance that is shorter than the size of the large turbulent scales will not be independent, resulting in a correlated precision error. The characteristics of the precision error for various statistics will be described. It is found that mean vorticity has a correlated precision error that is limited to a much smaller length scale. The results demonstrate the importance of understanding the role of error correlation in the interpretation of PIV data.     

Treatment of interfaces in particle image velocimetry

A first-order accurate method of extending the capability of image velocimetry to interfaces is presented. In this method, the image fields are locally extended across interfaces using fields from the other image of an image pair. During this image parity exchange, the extension of the image fields amounts to locally reversing and reflecting the relative velocity field across the interface. Numerous experimental examples are given to demonstrate and validate the accuracy of the method. These are the plane Couette flow and the laminar pipe flow demonstrating straight rigid boundaries; uniform flow past a sphere and a sphere moving in a stagnant fluid demonstrating curved rigid surfaces; and a free-surface flow and a liquid–liquid interface flow demonstrating compliant interfaces. Received: 3 November 1998/Accepted: 18 August 1999