Local field correction PIV: on the increase of accuracy of digital PIV systems

Cross-correlation Particle Image Velocimetry (PIV) has become a well known and widely used experimental technique. It has been already documented that difficulties arise resolving velocity structures smaller than the interrogation window. This is caused by signal averaging over this window. A new cross-correlation PIV method that eliminates this restriction is presented. The new method brings some other enhancements, such as the ability to deal with large velocity gradients, seeding density inhomogeneities, and high dispersion in the brightness of the particles. The final result is a method with a remarkable capability for accurately resolving small scale structures in the flow, down to a few times the mean distance between particles. When compared to particle tracking velocimetry, the new method is capable of obtaining measurements at high seeding density concentrations. Therefore, better overall performance is obtained, especially with the limited resolutions of video CCDs. In this paper, the new method is described and its performance is evaluated and compared to traditional PIV systems using synthetic images. Application to real PIV data are included and the results discussed. Received: 9 March 1998 / Accepted: 25 August 1998     

Improved MPS method with variable‐size particles

Using variable‐size particles in the moving particle semi‐implicit method (MPS) could lead to inaccurate predictions and/or numerical instability. In this paper, a variable‐size particle moving particle semi‐implicit method (VSP‐MPS) scheme is proposed for the MPS method to achieve more reliable simulations with variable‐size particles. To improve stability and accuracy, a new gradient model is developed based on a previously developed MPS scheme that requires no surface detection MPS. The dynamic particle coalescing and splitting algorithm is revised to achieve dynamic multi‐resolution. A cubic spline function with additional function is employed as the kernel function. The effectiveness of the VSP‐MPS method is demonstrated by three verification examples, that is, a hydrostatic pressure problem, a complicated free surface flow problem with large deformation, and a dynamic impact problem. The new VSP‐MPS scheme with variable‐size particles is found to have balanced efficiency and accuracy that is suitable for simulating large systems with complex flow patterns. Copyright © 2015 John Wiley & Sons, Ltd.     

Review and evaluation of the double-torsion technique for fracture toughness and fatigue testing of brittle materials

This paper reviews the double-torsion (DT) test as an experimental technique for the measurement of fracture toughness and slow-crack-growth behavior in brittle materials based on the authors' experiences and an evaluation of current literature. The DT technique has numerous advantages due primarily to the fact that the stress intensity is independent of crack length, at least for the central half of the specimen. Although the technique was first proposed about 20 years ago, and has been used extensively since then, there are a number of important unresolved questions concerning the methodology. To date there has been no standardization of test procedure or specimen geometry. A review of specimen geometries in use indicates that the proportions that are most commonly employed (based on the literature and experience) are width:W, length: 3W, thickness:W/6–W/15. Grooves on both the top and the bottom surfaces have been used to guide the crack, however it has been found that ungrooved, but very accurately aligned, specimens give the best results. Theoretical thickness-correction factors which account for both relatively thick specimens (with respect to width) and the effect of the size of the loading points, have been considered. The effect of crack-front profile on measured values of crack velocity and stress intensity is contentious. Althogh the stress intensity,K, varies along the crack front, the front merely translates axially. For the presentation of crackvelocity stress-intensity (V-K) data, the consensus seems to be that the only rational velocity to use is that based on the crack's intersection with the tensile surface. Despite some of the shortcomings mentioned above, the DT technique is widely accepted and gaining in popularity. It is particularly useful under cyclic fatigue conditions for investigating the effect of a change in a single parameter on crack-growth rate, using the very effective and elegant ‘changeover’ method.     

A new artificial neural network tracking technique for particle image velocimetry

 The analysis of Particle Image Velocimetry (PIV) data requires effective algorithms to track efficiently the particles suspended in the fluid flow. The artificial neural network algorithm method described here presents a new approach to solve this problem. Contrary to the classic cross correlation method, this new method does not require a large number of particles per frame, it can handle flows with large velocity gradients, and is suited for tracking images with multiple exposures as well as tracking through consecutive images. The algorithm was tested on synthetic and available experimental data to provide a thorough performance analysis. Received: 28 May 1996/Accepted: 25 December 1996     

A Peierls criterion for the onset of deformation twinning at a crack tip

A criterion for the onset of deformation twinning (DT) is derived within the Peierls framework for dislocation emission from a crack tip due to Rice (J. Mech. Phys. Solids 40(2) (1992) 239). The critical stress intensity factor (SIF) is obtained for nucleation of a two-layer microtwin, which is taken to be a precursor to DT. The nucleation of the microtwin is controlled by the unstable twinning energyγ_ut, a new material parameter identified in the analysis. γ_ut plays the same role for DT as γ_us, the unstable stacking energy introduced by Rice, plays for dislocation emission. The competition between dislocation emission and DT at the crack tip is quantified by the twinning tendencyT defined as the ratio of the critical SIFs for dislocation nucleation and microtwin formation. DT is predicted when T>1 and dislocation emission when T<1. For the case where the external loading is proportional to a single load parameter, T is proportional to . The predictions of the criterion are compared with atomistic simulations for aluminum of Hai and Tadmor (Acta Mater. 51 (2003) 117) for a number of different crack configurations and loading modes. The criterion is found to be qualitatively exact for all cases, predicting the correct deformation mode and activated slip system. Quantitatively, the accuracy of the predicted nucleation loads varies from 5% to 56%. The sources of error are known and may be reduced by appropriate extensions to the model.     

Three-dimensional micro-PTV using deconvolution microscopy

A three-dimensional micro-particle tracking velocimetry (micro-PTV) scheme is presented using a single camera with deconvolution microscopy. This method devises tracking of the line-of-sight (z) flow vectors by correlating the diffraction pattern ring size variations with the defocusing distances of small particle locations. The working principle is based on optical serial sectioning microscopy, or equivalently deconvolution microscopy, that records images of an infinitesimally small particle, and generates a point-spread function of the three-dimensional diffraction patterns. A new image-processing algorithm has also been developed to digitally identify the center locations and measure the radii of the diffraction rings, which allows simultaneous tracking of all three-vector components. The developed PTV technique uses a 40×, 0.75 NA dry objective lens with 500-nm fluorescent seeding particles of SG=1.05, and successfully measures the fully three-dimensional fields flowing over a spherical obstacle snuggly fitted inside a 100 μm × 100 μm micro-channel. The volumetric measurement resolution of the present system is equivalent to a 5.16 μm × 5.16 μm × 5.16 μm cube, and the overall measurement uncertainty for single-point velocity vector detection is estimated to ±7.58%.

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Effect of particle number density in in-line digital holographic particle velocimetry

A digital in-line holographic particle tracking velocimetry (HPTV) system was developed to measure 3D (three-dimensional) velocity fields of turbulent flows. The digital HPTV (DHPTV) procedure consists of four steps: recording, numerical reconstruction, particle extraction and velocity extraction. In the recording step, a digital CCD camera was used as a recording device. Holograms contained many unwanted images or noise. To get clean holograms, digital image processing techniques were adopted. In the velocity extraction routine, we improved the HPTV algorithm to extract 3D displacement information of tracer particles. In general, the results obtained using HPTV were not fully acceptable due to technical limitations such as low spatial resolution, small volume size, and low numerical aperture (NA). The problems of spatial resolution and NA are closely related with a recording device. As one experimental parameter that can be optimized, we focused on the particle number density. Variation of the reconstruction efficiency and recovery ratio were compared quantitatively with varying particle number density to check performance of the developed in-line DHPTV system. The reconstruction efficiency represented the particle number distribution acquired through the numerical reconstruction procedure. In addition the recovery ratio showed the performance of 3D PTV algorithm employed for DHPTV measurements. The particle number density in the range of C _o = 13–17 particles/mm³ was found to be optimum for the DHPTV system tested in this study.     

Particle tracking velocimetry in three-dimensional flows

Particle Tracking Velocimetry (PTV) is a well-known technique for the determination of velocity vectors within an observation volume. However, for a long time it has rarely been applied because of the intensive effort necessary to measure coordinates of a large number of flow marker particles in many images. With today's imaging hardware in combination with the methods of digital image processing and digital photogrammetry, however, new possibilities have arisen for the design of completely automatic PTV systems. A powerful 3D PTV has been developed in a cooperation of the Institute of Geodesy and Photogrammetry with the Institute of Hydromechanics and Water Resources Management at the Swiss Federal Institute of Technology. In this paper hardware components for 3D PTV systems wil be discussed, and a strict mathematical model of photogrammetric 3D coordinate determination, taking into account the different refractive indices in the optical path, will be presented. The system described is capable of determining coordinate sets of some 1000 particles in a flow field at a time resolution of 25 datasets per second and almost arbitrary sequence length completely automatically after an initialization by an operator. The strict mathematical modelling of the measurement geometry, together with a thorough calibration of the system provide for a coordinate accuracy of typically 0.06 mm in X, Y and 0.18 mm in Z (depth coordinate) in a volume of 200 × 160 × 50 mm³.     

The solution of two‐dimensional free‐surface problems using automatic mesh generation

A new method is described for the iterative solution of two‐dimensional free‐surface problems, with arbitrary initial geometries, in which the interior of the domain is represented by an unstructured, triangular Eulerian mesh and the free surface is represented directly by the piecewise‐quadratic edges of the isoparametric quadratic‐velocity, linear‐pressure Taylor–Hood elements. At each time step, the motion of the free surface is computed explicitly using the current velocity field and, once the new free‐surface location has been found, the interior nodes of the mesh are repositioned using a continuous deformation model that preserves the original connectivity. In the event that the interior of the domain must be completely remeshed, a standard Delaunay triangulation algorithm is used, which leaves the initial boundary discretisation unchanged. The algorithm is validated via the benchmark viscous flow problem of the coalescence of two infinite cylinders of equal radius, in which the motion is due entirely to the action of capillary forces on the free surface. This problem has been selected for a variety of reasons: the initial and final (steady state) geometries differ considerably; in the passage from the former to the latter, large free‐surface curvatures—requiring accurate modelling—are encountered; an analytical solution is known for the location of the free surface; there exists a large body of literature on alternative numerical simulations. A novel feature of the present work is its geometric generality and robustness; it does not require a priori knowledge of either the evolving domain geometry or the solution contained therein. Copyright © 1999 John Wiley & Sons, Ltd.     

Wettability and impact dynamics of water droplets on rice (Oryza sativa L.) leaves

A displacement-shifted approach is introduced to the vision-based particle tracking velocimetry (VB-PTV) technique described in Lei et al. (Exp Fluids 53(5):1251–1268, 2012), using translational and angular displacements. The particle matching algorithm in VB-PTV is based on a proximity matrix, G _ij , which favors short distance particle matches over long distance matches. By modifying the formula used in constructing G _ij , particles that lie at the expected location of the match are favored. Two displacement-shifted methods are introduced: the first of which relies on particle image velocimetry estimates of particle displacements and the second of which relies on both the expected displacement and direction of the correct match to construct the proximity matrix. These displacement-shifted algorithms improve performance in high gradient (0.3 px/px and above), high displacement flows (upwards of 20 pixels), broadening the range of flows for which VB-PTV can be used. RMS errors in PTV results are reduced by 33 % or more when these displacement-shifted algorithms are made to the VB-PTV algorithm which is used to process Oseen vortex images. Experimental images of shear layer and the wake region of vortex shedding were used to verify the performances of the proposed methods, and the results are in agreement with the synthetic tests.     

Suspended Particles Transport and Deposition in Saturated Granular Porous Medium: Particle Size Effects

An experimental study on the transport and deposition of suspended particles (SP) in a saturated porous medium (calibrated sand) was undertaken. The influence of the size distribution of the SP under different flow rates is explored. To achieve this objective, three populations with different particles size distributions were selected. The median diameter $d_{50}$ of these populations was 3.5, 9.5, and $18.3~\upmu \hbox {m}$ . To study the effect of polydispersivity, a fourth population noted “Mixture” ( $d_{50} = 17.4\; \upmu \hbox {m}$ ) obtained by mixing in equal proportion (volume) the populations 3.5 and $18.3\;\upmu \hbox {m}$ was also used. The SP transfer was compared to the dissolved tracer (DT) one. Short pulse was the technique used to perform the SP and the DT injection in a column filled with the porous medium. The breakthrough curves were competently described with the analytical solution of a convection–dispersion equation with first-order deposition kinetics. The results showed that the transport of the SP was less rapid than the transport of the DT whatever the flow velocity and the size distribution of the injected SP. The mean diameter of the recovered particles increases with flow rate. The longitudinal dispersion increases, respectively, with the increasing of the flow rates and the SP size distribution. The SP were more dispersive in the porous medium than the DT. The results further showed that the deposition kinetics depends strongly on the size of the particle transported and their distribution.     

A further assessment of interpolation schemes for window deformation in PIV

We have evaluated the performances of the following seven interpolation schemes used for window deformation in particle image velocimetry (PIV): the linear, quadratic, B-spline, cubic, sinc, Lagrange, and Gaussian interpolations. Artificially generated images comprised particles of diameter in a range 1.1 ≤ d _p ≤ 10.0 pixel were investigated. Three particle diameters were selected for detailed evaluation: d _p = 2.2, 3.3, and 4.4 pixel with a constant particle concentration 0.02 particle/pixel². Two flow patterns were considered: uniform and shear flow. The mean and random errors, and the computation times of the interpolation schemes were determined and compared.     

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     

Intensity Capping: a simple method to improve cross-correlation PIV results

A common source of error in particle image velocimetry (PIV) is the presence of bright spots within the images. These bright spots are characterized by grayscale intensities much greater than the mean intensity of the image and are typically generated by intense scattering from seed particles. The displacement of bright spots can dominate the cross-correlation calculation within an interrogation window, and may thereby bias the resulting velocity vector. An efficient and easy-to-implement image-enhancement procedure is described to improve PIV results when bright spots are present. The procedure, called Intensity Capping, imposes a user-specified upper limit to the grayscale intensity of the images. The displacement calculation then better represents the displacement of all particles in an interrogation window and the bias due to bright spots is reduced. Four PIV codes and a large set of experimental and simulated images were used to evaluate the performance of Intensity Capping. The results indicate that Intensity Capping can significantly increase the number of valid vectors from experimental image pairs and reduce displacement error in the analysis of simulated images. A comparison with other PIV image-enhancement techniques shows that Intensity Capping offers competitive performance, low computational cost, ease of implementation, and minimal modification to the images.     

A contact searching algorithm for contact-impact problems

A new contact searching algorithm for contact-impact systems is proposed in this paper. In terms of the cell structure and the linked-list, this algorithm solves the problem of sorting and searching contacts in three dimensions by transforming it to a retrieving process from two one-dimensional arrays, and binary searching is no longer required. Using this algorithm, the cost of contact searching is reduced to the order ofO(N) instead ofO(Nlog₂ N) for traditional ones, whereN is the node number in the system. Moreover, this algorithm can handle contact systems with arbitrary mesh layouts. Due to the simplicity of this algorithm it can be easily implemented in a dynamic explicit finite element program. Our numerical experimental result shows that this algorithm is reliable and efficient for contact searching of three dimensional systems. The project supported by the National Natural Science Foundation of China (59875045), and the State Key Laboratory of Automobile Safety and Energy Saving (K9705)     

Rod-like particles matching algorithm based on SOM neural network in dispersed two-phase flow measurements

A matching algorithm based on self-organizing map (SOM) neural network is proposed for tracking rod-like particles in 2D optical measurements of dispersed two-phase flows. It is verified by both synthetic images of elongated particles mimicking 2D suspension flows and direct numerical simulations-based results of prolate particles dispersed in a turbulent channel flow. Furthermore, the potential benefit of this algorithm is evaluated by applying it to the experimental data of rod-like fibers tracking in wall turbulence. The study of the behavior of elongated particles suspended in turbulent flows has a practical importance and covers a wide range of applications in engineering and science. In experimental approach, particle tracking velocimetry of the dispersed phase has a key role together with particle image velocimetry of the carrier phase to obtain the velocities of both phases. The essential parts of particle tracking are to identify and match corresponding particles correctly in consecutive images. The present study is focused on the development of an algorithm for pairing non-spherical particles that have one major symmetry axis. The novel idea in the algorithm is to take the orientation of the particles into account for matching in addition to their positions. The method used is based on the SOM neural network that finds the most likely matching link in images on the basis of feature extraction and clustering. The fundamental concept is finding corresponding particles in the images with the nearest characteristics: position and orientation. The most effective aspect of this two-frame matching algorithm is that it does not require any preliminary knowledge of neither the flow field nor the particle behavior. Furthermore, using one additional characteristic of the non-spherical particles, namely their orientation, in addition to its coordinate vector, the pairing is improved both for more reliable matching at higher concentrations of dispersed particles and for higher robustness against loss of particle pairs between image frames.     

A pattern matching technique for measuring sediment displacement levels

This paper describes a novel technique for obtaining accurate, high (spatial) resolution measurements of sediment redeposition levels. A sequence of different random patterns are projected onto a sediment layer and captured using a high-resolution camera, producing a set of reference images. The same patterns are used to obtain a corresponding sequence of deformed images after a region of the sediment layer has been displaced and redeposited, allowing the use of a high-accuracy pattern matching algorithm to quantify the distribution of the redeposited sediment. A set of experiments using the impact of a vortex ring with a glass ballotini particle layer as the resuspension mechanism are described to test and illustrate the technique. The accuracy of the procedure is assessed using a known crater profile, manufactured to simulate the features of the craters observed in the experiments.

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An enhanced treatment of boundary conditions in implicit smoothed particle hydrodynamics简

In this work, an enhanced treatment of the solid boundaries is proposed for smoothed particle hydrodynamics with implicit time integration scheme （Implicit SPH）. Three types of virtual particles, i.e., boundary particles, image particles and mirror particles, are used to impose boundary conditions. Boundary particles are fixed on the solid boundary, and each boundary particle is associated with two fixed image particles inside the fluid domain and two fixed mirror particles outside the fluid domain. The image particles take the flow properties through fluid particles with moving least squares （MLS） interpolation and the properties of mirror particles can be obtained by the corresponding image particles. A repulsive force is also applied for boundary particles to prevent fluid particles from unphysical penetra- tion through solid boundaries. The new boundary treatment method has been validated with five numerical examples. All the numerical results show that Implicit SPH with this new boundary-treatment method can obtain accurate results for non-Newtonian fluids as well as Newtonian fluids, and this method is suitable for complex solid boundaries and can be easily extended to 3D problems.     

g-η-Monotone mapping and resolvent operator technique for solving generalized implicit variational-like inclusions

A new class of g-η-monotone mappings and a class of generalized implicit variational-like inclusions involving g-η-monotone mappings are introduced. The resolvent operator of g-η-monotone mappings is defined and its Lipschitz continuity is presented. An iterative algorithm for approximating the solutions of generalized implicit variational-like inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved.