Measurement of two-dimensional velocity fields in porous media by particle image displacement velocimetry

Local measurements of the phase function and of two components of the velocity can be performed in transparent porous media by means of particle image displacement velocimetry (P.I.D.V.). Some preliminary results are presented and discussed.     

A method for automatic estimation of instantaneous local uncertainty in particle image velocimetry measurements

The uncertainty of any measurement is the interval in which one believes the actual error lies. Particle image velocimetry (PIV) measurement error depends on the PIV algorithm used, a wide range of user inputs, flow characteristics, and the experimental setup. Since these factors vary in time and space, they lead to nonuniform error throughout the flow field. As such, a universal PIV uncertainty estimate is not adequate and can be misleading. This is of particular interest when PIV data are used for comparison with computational or experimental data. A method to estimate the uncertainty from sources detectable in the raw images and due to the PIV calculation of each individual velocity measurement is presented. The relationship between four error sources and their contribution to PIV error is first determined. The sources, or parameters, considered are particle image diameter, particle density, particle displacement, and velocity gradient, although this choice in parameters is arbitrary and may not be complete. This information provides a four-dimensional “uncertainty surface” specific to the PIV algorithm used. After PIV processing, our code “measures" the value of each of these parameters and estimates the velocity uncertainty due to the PIV algorithm for each vector in the flow field. The reliability of our methodology is validated using known flow fields so the actual error can be determined. Our analysis shows that, for most flows, the uncertainty distribution obtained using this method fits the confidence interval. An experiment is used to show that systematic uncertainties are accurately computed for a jet flow. The method is general and can be adapted to any PIV analysis, provided that the relevant error sources can be identified for a given experiment and the appropriate parameters can be quantified from the images obtained.     

3-Component acceleration field measurement by dual-time stereoscopic particle image velocimetry

In this article, a multiplane stereo-particle image velocimetry (PIV) system was implemented and validated to measure the three-component acceleration field in a plane of turbulent flows. The employed technique relies on the use of two stereoscopic particle image velocimetry (SPIV) systems to measure pairs of velocity fields superimposed in space but shifted in time. The time delay between the two velocity fields enables the implementation of a finite difference scheme to compute temporal derivatives. The use of two synchronized SPIV systems allows us to overcome the limited acquisition rate of PIV systems when dealing with highly turbulent flows. Moreover, a methodology based on the analysis of the spectral error distribution is described here to determine the optimal time delay to compute time derivatives. The present dual-time SPIV arrangement and the proposed analysis method are applied to measure three-component acceleration fields in a cross section of a subsonic plane turbulent mixing layer.     

Measurement of spectrum with particle image velocimetry

The purpose of this paper is to show that the measurement of turbulent spectrum using wholefield velocity techniques such as particle image velocimetry (PIV) is possible. Toward this end, data from the axial plane of a self-similar turbulent axisymmetric jet, at a Reynolds number, based on Taylor microscale of 30 has been analyzed. The two-dimensional velocity data are first high-pass filtered, which educes the vortices. An automated method is then used to identify the vortices and measure their properties. By directly measuring the energy of the vortices, it is possible to plot the turbulence spectrum. The spectrum presented here shows the presence of energy containing and inertial regimes. However, the smallest scales have not been resolved in the measurements. The slope of the spectrum in the inertial subrange is about −1.6. The number of vortices in the two regimes have also been measured. The number of vortices in the energy containing regime is substantially smaller than those in the inertial subrange. The technique has been verified by analyzing another dataset. These results show that the direct measurement of vortex properties with reasonable confidence is possible using PIV and an appropriate vortex eduction technique.     

Digital particle image thermometry: The method and implementation

A computerized flow visualization technique capable of automatically quantifying the temperature field in a two-dimensional cross section of a flow field is described. The temperature sensors used are fast-response temperature-sensitive micro-encapsulated liquid crystal particles. Illuminating the flow by a thin sheet of white light, the reflected colors from the liquid-crystal particles were captured through a 3-chip video color camera and stored onto a videotape for subsequent data processing. The temperature field was obtained through an automatic color-temperature calibration scheme in HSI rather than RGB space, thus allowing for data processing of approximately one-third the time of RGB processing. The technique is finally applied to the study of a heated vortex-ring and some preliminary results are discussed.     

Investigations of the measurement accuracy of stereo particle image velocimetry

With a stereo PIV system, in order to perform reliable measurements of the three velocity components in liquid flow, it is mandatory to minimise the errors made in determining the 2D displacement vectors and the viewing direction of each of the two cameras. We present a method for determining the viewing direction in the angular displacement stereo system by means of a digital imaging procedure such that the direct measurement of geometrical parameters of the set-up is avoided. This makes the method particularly useful for measurements through the transparent walls confining the liquid flow. A third order polynomial used for calibrating the stereo system is shown to provide more accurate results than imaging functions of lower order. Further improvement of the evaluation accuracy is obtained with the application of an artificial neuronal network, but at the expense of considerably increasing the computation time. A comparison of the evaluation results obtained with the operational procedures presented in this paper with those generated with another method that is applicable to liquid flow (Soloff et al. 1997) shows, that the present procedures can be considered as a viable alternative to existing methods.     

Explosively driven particle fields imaged using a high speed framing camera and particle image velocimetry

A high speed framing camera and a particle image velocimetry instrument were used to determine the properties of explosively driven particle fields in early microsecond and later millisecond times. Test items were configured in a two inch long cylindrical shape with a half inch diameter core of organic explosive. The core was surrounded by a particle bed of aluminum or tungsten powder of a specific particle size distribution. Position data from the leading edge of the particle fronts for each charge was recorded with a high speed framing camera at early time and with a particle image velocimetry (PIV) instrument at later time to determine particle velocity. Using a PIV image, a velocity gradient along the length of the particle field was established by using the mean particle velocity value determined from three separate horizontal bands that transverse the particle field. The results showed slower particles at the beginning of the particle field closest to the source and faster ones at the end. Differences in particle dispersal, luminescence, and agglomeration were seen when changes in the initial particle size and material type were made. The aluminum powders showed extensive luminescence with agglomeration forming large particle structures while the tungsten powder showed little luminescence, agglomeration and no particle structures. Combining velocity data from the high speed framing camera and PIV, the average drag coefficient for each powder type was determined. The particle field velocities and drag coefficients at one meter showed good agreement with the numerical data produced from a computational fluid dynamics code that takes advantage of both Eulerian and Lagrangian solvers to track individual particles after a set post detonation time interval.     

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     

Analysis and interpretation of instantaneous turbulent velocity fields

Methods of analyzing and interpreting velocity-field data (both two- and three-dimensional) to understand the kinematics, dynamics, and scales of turbulence are discussed. Reynolds decomposition and vorticity are traditionally used; however, several other methods, including Galilean (constant convection velocity) and LES decompositions (low-pass filtering), in conjunction with critical-point analysis of the local velocity gradient tensor, reveal more about the structure of turbulence. Once the small-scale structures have been identified, it is necessary to assess their importance to the overall dynamics of the turbulence by visualizing the motions they induce and the stresses they impose both on other small-scale vortices and on the larger-scale field.     

Evaluation of transient turbulent flow fields using digital cinematographic particle image velocimetry

This paper describes an experimental development for temporal and spatial reconstruction of continuously varying flow fields by means of digital cinematographic particle image velocimetry (PIV). The system uses a copper-vapor laser illumination synchronized with a high-speed camera, and continuously samples at 250 fps to measure transient and non-periodic turbulent flows with relatively low frequencies, i.e., the surf zone turbulence produced by depth-limited wave break in a long laboratory flume. The use of the developed PIV system comprehensively records the temporal development of both phase-averaged and instantaneous turbulent vortex flows descended from the breaking waves to the bottom. Also, the measured power spectra show harmonic frequencies, ranging from the orbital frequency of 0.5 Hz up to the order of 5 Hz, and the well-known −5/3 dependence upon the turbulence fluctuation frequencies thereafter. Received: 2 December 1999/Accepted: 6 September 2000     

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

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

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Three-dimensional particle tracking method using FPGA-based real-time image processing and four-view image splitter

We present a cost-effective solution of the three-dimensional particle tracking velocimetry (3D-PTV) system based on the real-time image processing method (Kreizer et al. Exp Fluids 48:105–110, 2010) and a four-view image splitter. The image processing algorithm, based on the intensity threshold and intensity gradients estimated using the fixed-size Sobel kernel, is implemented on the field-programmable gate array integrated into the camera electronics. It enables extracting positions of tracked objects, such as tracers or large particles, in real time. The second major component of this system is a four-view split-screen device that provides four views of the observation volume from different angles. An open-source ray-tracing software package allows for a customized optical setup for the given experimental settings of working distances and camera parameters. The specific design enables tracking in larger observation volumes when compared to the designs published up to date. The present cost-effective solution is complemented with open-source particle tracking software that receives raw data acquired by the real-time image processing system and returns trajectories of the identified particles. The combination of these components simplifies the 3D-PTV technique by reducing the size and increasing recording speed and storage capabilities. The system is capable to track a multitude of particles at high speed and stream the data over the computer network. The system can provide a solution for the remotely controlled tracking experiments, such as in microgravity, underwater or in applications with harsh experimental conditions.     

A method to provide statistical measures of large-scale instantaneous particle clusters from planar images

Particle clusters are preferential accumulations of a solid, secondary phase that can be caused by turbulence. It is well known that particle clusters can influence the performance of systems employing suspension flows, such as pulverised fuel combustion systems. However, statistical analysis of clusters is limited by available methods to quantify them. In the current study, a method to identify planar slices of large-scale particle clusters from planar images of instantaneous particle distributions is presented. The method employs smoothing of instantaneous particle scatter images by a length scale, L _S , to produce pseudo-scalar fields of particle distributions. The scalar fields are compared with mean (not smoothed) images to produce cluster masks that are then multiplied by the original instantaneous image to produce a map of the locations of cluster slices. The sensitivity to the smoothing length scale is assessed parametrically for its influence on the statistical measures of the following parameters characterising slices of large-scale clusters in four representative flows: the physical locations of the cluster slice centroids; the area of the cluster slice; and the number of cluster slices per image. While the results are influenced by the selected value of smoothing length scale, L _S , the sensitivity is low in a physically reasonable range and the method performs well in this range for the four different flow cases. The method could be extended to provide volumetric measurements with suitable volumetric imaging systems.     

Influence of molecular diffusion on alignment of vector fields: Eulerian analysis

The effect of diffusive processes on the structure of passive vector and scalar gradient fields is investigated by analyzing the corresponding terms in the orientation and norm equations. Numerical simulation is used to solve the transport equations for both vectors in a two-dimensional, parameterized model flow. The study highlights the role of molecular diffusion in the vector orientation process and shows its subsequent action on the geometric features of vector fields.     

Measurement of fully-developed turbulent pipe flow with digital particle image velocimetry

A new and unique high-resolution image acquisition system for digital particle image velocimetry (DPIV) in turbulent flows is used for the measurement of fully-developed turbulent pipe flow at a Reynolds number of 5300. The flow conditions of the pipe flow match those of a direct numerical simulation (DNS) and of measurements with conventional (viz., photographic) PIV and with laser-Doppler velocimetry (LDV). This experiment allows a direct and detailed comparison of the conventional and digital implementations of the PIV method for a non-trivial unsteady flow. The results for the turbulence statistics and power spectra show that the level of accuracy for DPIV is comparable to that of conventional PIV, despite a considerable difference in the interrogation pixel resolution, i.e. 32 × 32 (DPIV) versus 256 × 256 (PIV). This result is in agreement with an earlier analytical prediction for the measurement accuracy. One of the advantages of DPIV over conventional PIV is that the interrogation of the DPIV images takes only a fraction of the time needed for the interrogation of the PIV photographs.     

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.     

Theory of plasma acceleration in electric and magnetic fields

The problem of the acceleration of a plasma in crossed electric and magnetic fields under the simplest physical conditions suitable for comparison with experiment is considered. Analytical expressions are obtained for the velocity of the electrons, the value of the resonance acceleration zone, and the increment of the potential of the accelerated plasma.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 14–17, November–December, 1972.     

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.