Main results of the Second International PIV Challenge

This paper presents the main results of the Second International PIV Challenge which took place in Busan (Korea) on the 19th and 20th of September 2003. This workshop was linked to the PIV03 International Symposium, which was held at the same place the following week. The present contribution gives the objectives of the Challenge, describes the test cases and the algorithms used by the participants, and presents the main results together with some discussion and conclusions on the accuracy and robustness of various PIV and PTV algorithms. As all the results obtained cannot be detailed, this contribution should serve as a guide for the use of the full database of images and results which is available at .     

The challenge of stereo PIV measurements in the tip gap of a transonic compressor rotor with casing treatment

This contribution is aimed at summarizing the effort taken to apply stereoscopic PIV (SPIV) measurements in the tip clearance of a transonic compressor rotor equipped with a casing treatment. A light sheet probe was placed downstream of the stator and aligned to pass the light sheet through a stator passage into the blade tip clearance of the rotor. A setup with three cameras has been used in order to record the entire 2C velocity field and the smaller area of 3C field of view at the same time instance for comparison with earlier 2C PIV results. A homogeneous seeding distribution was achieved by means of a smoke generator. The main emphasis of the SPIV measurement was to establish a data set with high spatial resolution close to the compressor casing, where the aerodynamic effects of a CT are known to be strong. The paper will discuss some major aspects of the utilized PIV data processing and point out a variety of frequently underestimated error sources that influence the overall quality of the recovered data in spite of the fact that the individual PIV recordings seemed to be of very good quality. Thus, the authors will not focus on the PIV results and related interpretation of the flow field, but on the optimization and procedures applied during setup of the experiment and data processing, respectively.     

Single-pixel resolution ensemble correlation for micro-PIV applications

A new correlation method for particle image velocimetry (PIV) is proposed that yields velocity data at single-pixel spatial resolution. This method is an extension of the ensemble correlation method for PIV. This single-pixel ensemble correlation method is particularly suited for (quasi-) stationary and periodic flows, which are typically encountered in many micro-PIV applications, such as microfluidics and micro-scale biological flows. The method can yield data at the same level of precision and reliability as conventional PIV data. The main advantage of the new method is that it can resolve steep velocity gradients and obtain unbiased measurements of the velocity in the vicinity of flow boundaries (viz. walls). The performance as a function of the ensemble size is investigated by means of synthetic PIV images. Both ensemble correlation and single-pixel correlation are applied to micro-channel flow. With single-pixel ensemble correlation we obtained a spatial resolution of 300 nm. The results demonstrate that ensemble correlation over-estimates the measured channel width, whereas single-pixel correlation yields a result that is in agreement with the actual channel dimensions.Parts of this paper were previously presented at the 11th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, 8–11 July 2002, and the 5th International Symposium on Particle Image Velocimetry, Busan, 22–24 September 2003.

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Quantitative evaluation of PIV peak locking through a multiple Δ<Emphasis Type="Italic">t</Emphasis> strategy: relevance of the rms component

The possibility of using different times between laser pulses (Δt) in a PIV (Particle Image Velocimetry) measurement of the same real flow field for error assessment has already been proposed by the authors in a recent paper Nogueira et al. (Meas Sci Technol 20, 2009). It is a simple procedure that is available with the usual PIV setup. In that work, peak locking was considered basically as a bias error. Later measurements indicated that, using appropriate processing algorithms, this error is not the main peak-locking effect. Scenarios with the rms (root mean square) error due to peak locking as the most relevant contribution are more common than initially expected and require a differentiated approach. This issue is relevant due to the impact of the rms error in the evaluation of flow quantities like turbulent kinetic energy. The first part of this work is centred on showing that peak-locking error in PIV is not always a measurement bias towards the closest pixel integer displacement. Insight in the subject indicates that this is the case only for algorithm-induced peak locking. The peak locking coming out of image acquisition limitations (i.e. resolution) is not ‘a priory’ biased. It is a random error with a peculiar probability density function. Discussion on the subject is offered, and a particular approach to use a simple multiple Δt strategy to asses this error is proposed. The results reveal that in real images where amplitude of the peak-locking bias error is assessed to be as small as 0.02 pixels, rms errors can be in the order of 0.1 pixels. As PIV approaches maturity, providing a quantitative confidence interval by estimating measurement error seems essential. The method developed is robust enough to quantify these values in the presence of turbulence with rms up to ~0.6 pixels. This proposal constitutes a relevant step forward from the traditional histogram-based considerations that only reveal whether strong peak-locking error is present or not, without any information on its magnitude or whether its origin is bias or rms.     

Interfacial PIV to resolve flows in the vicinity of curved surfaces

PIV measurements near a wall are generally difficult due to low seeding density, low velocity, high velocity gradient, and strong reflections. Such problems are often compounded by curved boundaries, which are commonly found in many industrial and medical applications. To systematically solve these problems, this paper presents two novel techniques for near-wall measurement, together named Interfacial PIV, which extracts both wall-shear gradient and near-wall tangential velocity profiles at one-pixel resolution. To deal with curved walls, image strips at a curved wall are stretched into rectangles by means of conformal transformation. To extract the maximal spatial information on the near-wall tangential velocity field, a novel 1D correlation function is performed on each horizontal pixel line of the transformed image template to form a “correlation stack”. This 1D correlation function requires that the wall-normal displacement component of the particles be smaller than the particle image diameter in order to produce a correlation signal. Within the image regions satisfying this condition, the correlation function yields peaks that form a tangential velocity profile. To determine this profile robustly, we propose to integrate gradients of tangential velocity outward from the wall, wherein the gradient at each wall-normal position is measured by fitting a straight line to the correlation peaks. The capability of Interfacial PIV was validated against Particle Image Distortion using synthetic image pairs generated from a DNS velocity field over a sinusoidal bed. Different velocity measurement schemes performed on the same correlation stacks were also demonstrated. The results suggest that Interfacial PIV using line fitting and gradient integration provides the best accuracy of all cases in the measurements of velocity gradient and velocity profile near wall surfaces.     

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     

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:

Time-resolved particle imaging velocimetry for the investigation of rotating stall in a radial pump

The operating range of turbomachines is limited in terms of the low flow rate by instabilities appearing in flow-leading parts of the machinery resulting in the creation of vortices. If the flow is further throttled, stall cells can start to propagate in the impeller at a fraction of the rotor speed. This article presents an investigation of rotating stall at different flow rates in a radial pump using time-resolved particle imaging velocimetry (PIV). This technique was used to investigate the flow field at the same position in every channel of the impeller during several revolutions. Frequency analysis was applied to the measured velocities to calculate the angular speed of the rotating stall in the impeller. The interest of time-resolved PIV to understand rotating stall is demonstrated, as it allows measurement of transient, irregularly appearing flow fields.     

Identification of a new source of peak locking, analysis and its removal in conventional and super-resolution PIV techniques

One of the key factors that limit accuracy of particle image velocimetry (PIV) is the peak-locking effect. In this paper, a previously uncharacterised source of peak locking is presented. This source is neither related to the sensor geometry nor the subpixel resolution peak-fitting algorithms. It is present even when the particles are well described in terms of sensor spatial resolution (i.e. for particle diameters larger than 2 pixels). If no specific actions to avoid it are taken, its effect is especially important in those super-resolution systems that are based on iteratively reducing the size of the interrogation window. In this work, the mentioned source and its effects are studied and modelled. Based on this study, the actions required to avoid this type of peak locking are described. This includes the most usual correlation-based PIV systems, as well as super-resolution ones. Once this source of inaccuracy is avoided, it is possible to discriminate the performance of different types of correlation algorithms. As a consequence, specific proposals for the algorithms in the last steps of multigrid super-resolution PIV systems are given. The performances of the proposed solutions are verified using both synthetic and real PIV images. Received: 31 January 2000/Accepted: 2 May 2000     

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.     

An experimental study of a turbulent vortex ring: a three-dimensional representation

This paper presents a reconstruction of the three-dimensional velocity field of a turbulent vortex ring by means of Taylor’s hypothesis. Stereoscopic PIV is used to acquire three velocity component information on a plane. The accuracy of the Taylor’s hypothesis for this particular flow pattern is first discussed, and the three-dimensional velocity and vorticity information are then presented. This study also introduces an azimuthally averaging method in order to give a mean structure in cylindrical coordinates from a single realization and from which turbulent stresses and production can be estimated. The azimuthally averaged quantities are then compared with the ensemble-averaged results from the previous planar (two-dimensional and stereoscopic) PIV experiments.     

两相流显微PIV/PTV系统的开发

开发了一个能同时测量两相流中两相速度和细颗粒尺寸分布的显微PIV/PTV系统,其硬件系统包括大功率连续激光器、显微镜、高速摄像机;软件系统由改进的球形颗粒图像识别算法、各种图像处理算法和各种先进的PIV/PTV算法组成。其中改进的圆弧识别算法能够进行更准确地进行曲线分割而能对充满噪音并相互重叠的颗粒图像给出较好的识别结果。应用该PIV系统,可以在微秒和微米数量级上捕获细颗粒/气泡图像,并能较准确地同时得到两相速度、颗粒尺寸和浓度分布。对焚香可吸入颗粒物进行了速度和尺寸的同时测量,得到了较满意的结果。     

Segregated finite element algorithms for the numerical solution of large-scale incompressible flow problems

This paper presents results of an ongoing research program directed towards developing fast and efficient finite element solution algorithms for the simulation of large-scale flow problems. Two main steps were taken towards achieving this goal. The first step was to employ segregated solution schemes as opposed to the fully coupled solution approach traditionally used in many finite element solution algorithms. The second step was to replace the direct Gaussian elimination linear equation solvers used in the first step with iterative solvers of the conjugate gradient and conjugate residual type. The three segregated solution algorithms developed in step one are first presented and their integrity and relative performance demonstrated by way of a few examples. Next, the four types of iterative solvers (i.e. two options for solving the symmetric pressure type equations and two options for solving the non-symmetric advection–diffusion type equations resulting from the segregated algorithms) together with the two preconditioning strategies employed in our study are presented. Finally, using examples of practical relevance the paper documents the large gains which result in computational efficiency, over fully coupled solution algorithms, as each of the above two main steps are introduced. It is shown that these gains become increasingly more dramatic as the complexity and size of the problem is increased.     

Investigation of the vortex induced unsteadiness of a separation bubble via time-resolved and scanning PIV measurements

A transitional separation bubble on the suction side of an SD7003 airfoil is considered. The transition process that forces the separated shear layer to reattach seems to be governed by Kelvin–Helmholtz instabilities. Large scale vortices are formed due to this mechanism at the downstream end of the bubble. These vortices possess a three-dimensional structure and detach from the recirculation region, while other vortices are formed within the bubble. This separation of the vortex is a highly unsteady process, which leads to a bubble flapping. The structure of these vortices and the flapping of the separation bubble due to these vortices are temporally and spatially analyzed at angles of attack from 4° to 8° and chord-length based Reynolds numbers Re _c = 20,000–60,000 using time-resolved PIV measurements in a 2D and a 3D set-up, i.e., stereo-scanning PIV measurements are done in the latter case. These measurements complete former studies at a Reynolds number of Re _c = 20,000. The results of the time-resolved PIV measurements in a single light-sheet show the influence of the angle of attack and the Reynolds number. The characteristic parameters of the separation bubble are analyzed focusing on the unsteadiness of the separation bubble, e.g., the varying size of the main recirculation region, which characterizes the bubble flapping, and the corresponding Strouhal number are investigated. Furthermore, the impact of the freestream turbulence is investigated by juxtaposing the current and former results. The stereo-scanning PIV measurements at Reynolds numbers up to 60,000 elucidate the three-dimensional character of the vortical structures, which evolve at the downstream end of the separation bubble. It is shown that the same typical structures are formed, e.g., the c-shape vortex and the screwdriver vortex at each Reynolds number and angle of attack investigated and the occurrence of these patterns in relation to Λ-structures is discussed. To evidence the impact of the freestream turbulence, these results are compared with findings of former measurements.     

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.     

Pulsed, high-power LED illumination for tomographic particle image velocimetry

This paper investigates the use of high-power light-emitting diode (LED) illumination for tomographic particle image velocimetry (PIV) as an alternative to traditional laser-based illumination. Modern solid-state LED devices can provide averaged radiant power in excess of 10 W and by operating the LED with short high current pulses theoretical pulse energies up to several tens of mJ can be achieved. In the present work, a custom-built drive circuit is used to drive a Luminus PT-120 high-power LED at pulsed currents of up to 150 A and 1 μs duration. Volumetric illumination is achieved by directly projecting the LED into the flow to produce a measurement volume of ≈3–4 times the size of the LED die. The feasibility of the volumetric LED illumination is assessed by performing tomographic PIV of homogenous, grid-generated turbulence. Two types of LEDs are investigated, and the results are compared with measurements of the same flow using pulsed Nd:YAG laser illumination and DNS data of homogeneous isotropic turbulence. The quality of the results is similar for both investigated LEDs with no significant difference between the LED and Nd:YAG illumination. Compared with the DNS, some differences are observed in the power spectra and the probability distributions of the fluctuating velocity and velocity gradients. These differences are attributed to the limited spatial resolution of the experiments and noise introduced during the tomographic reconstruction (i.e. ghost particles). The uncertainty in the velocity measurements associated with the LED illumination is estimated to approximately 0.2–0.3 pixel for both LEDs, which compares favourably with similar tomographic PIV measurements of turbulent flows. In conclusion, the proposed high-power, pulsed LED volume illumination provides accurate and reliable tomographic PIV measurements in water and presents a promising technique for flow diagnostics and velocimetry.     

Automated topology classification method for instantaneous velocity fields

Topological concepts provide highly comprehensible representations of the main features of a flow with a limited number of elements. This paper presents an automated classification method of instantaneous velocity fields based on the analysis of their critical points distribution and feature flow fields. It uses the fact that topological changes of a velocity field are continuous in time to extract large scale periodic phenomena from insufficiently time-resolved datasets. This method is applied to two test-cases : an analytical flow field and PIV planes acquired downstream a wall-mounted cube.     

On The Validation of LES Applied to Internal Combustion Engine Flows: Part 1: Comprehensive Experimental Database

Improved understanding of in-cylinder flows requires knowledge from well-resolved experimental velocimetry measurements and flow simulation modeling. Engine simulations using large eddy simulations (LES) are making large progress and the need for well documented velocimetry measurements for model validation is high. This work presents velocimetry measurements from PIV, high-speed PIV, stereoscopic PIV, and tomographic PIV to extensively describe the in-cylinder flow field in a motored optical engine operating at 800 RPM. These measurements also establish a comprehensive database designed for LES model development and validation. Details of the engine, engine accessory components, and well-controlled boundary conditions and engine operation are presented. The first two statistical moments of the flow field are computed and show excellent agreement among the PIV database. Analysis of statistical moments based on limited sample size is presented and is important for modeling validation purposes. High-speed PIV resolved the instantaneous flow field throughout entire engine cycles (i.e. 719 consecutive crank-angles), while tomographic PIV images are further used to investigate the 3D flow field and identify regions of strong vortical structures identified by the Q-criterion. Principle velocity gradient components are computed and emphasize the need to resolve similar spatial scales between experimental and modeling efforts for suitable model validation.     

变形能分解的新概念与圣维南原理

在小变形情况下分析了三维各向异性弹塑性体当表面小区域受载时的变形能，所得表达式的每一项都具有明确的物理意义，能清晰地显示出载荷的各特征因素对变形能的贡献，文中提出的有关变形能分解的新概念对于揭示圣维南原理所描述现象的力学机理具有重要意义。     

PIV with volume lighting in a narrow cell: An efficient method to measure large velocity fields of rapidly varying flows

In this work we test a methodology for PIV measurements when a large field of view is required in planar confined geometries. Using a depth of field larger than the channel width, we intend to measure the in-plane variations of the velocity of the fluid averaged through the width of the channel, and we examine in which operating conditions this becomes possible. Measurements of the flow through a narrow channel by PIV are challenging because of the strong velocity gradients that develop between the walls. In particular, all techniques that use small particles as tracers have to deal with the possible migration of the tracers in the direction perpendicular to the walls. Among the complex mechanisms for migration, we focus on the so called Segré-Silberberg effect which can lead to transverse migration of neutrally buoyant tracers of finite size. We report experimental PIV measurements in a Hele-Shaw cell of 1 mm gap, which have been carried out by using neutrally buoyant tracers of size around 10 μm. By considering steady flows, we have observed, in particular flow regimes, the effect of an accumulation of the tracers at a certain distance to the wall due to the so called Segré-Silberberg effect. The particle migration is expected to occur at any Reynolds numbers but the migration velocity depends on the Reynolds number. A significant migration therefore takes place each time the observation duration is large enough compared to the migration time. For a given observation duration, the tracers remain uniformly distributed at low Reynolds numbers whereas they all accumulate at the equilibrium position at large ones. When using volume lighting, the PIV algorithm provides the average velocity of the flow through the gap at low Reynolds number, while it leads to the velocity of the flow at the equilibrium position of the tracers at large Reynolds numbers. By considering unsteady flows, we have observed that the migration does not occur if the timescale of flow variation is short compared to the time required for the parabolic flow to develop across the gap. In this case, there is no transverse velocity gradient and the PIV algorithm provides the fluid velocity. Altogether, these results allow us to propose guidelines for the interpretation of PIV measurements in confined flow, which are based on the theoretical predictions of the tracer migration derived by Asmolov [1].