Target-free Stereo PIV: a novel technique with inherent error estimation and improved accuracy

A novel, accurate and simple stereo particle image velocimetry (SPIV) technique utilising three cameras is presented. The key feature of the new technique is that there is no need of a separate calibration phase. The calibration data are measured concurrently with the PIV data by a third paraxial camera. This has the benefit of improving ease of use and reducing the time taken to obtain data. This third camera also provides useful velocity information, considerably improving the accuracy of the resolved 3D vectors. The additional redundancy provided by this third perspective in the stereo reconstruction equations suggests a least-squares approach to their solution. The least-squares process further improves the utility of the technique by means of the reconstruction residual. Detailed error analysis shows that this residual is an accurate predictor of resolved vector errors. The new technique is rigorously validated using both pure translation and rotation test cases. However, while this kind of validation is standard, it is shown that such validation is substantially flawed. The case of the well-known confined vortex breakdown flow is offered as an alternative validation. This flow is readily evaluated using CFD methods, allowing a detailed comparison of the data and evaluation of PIV errors in their entirety for this technique.     

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.     

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     

Experimental and numerical comparisons of the break-up of a large bubble

 PIV measurement and numerical simulation of a large scale collapsing gas bubble that results from the burst of a balloon in a deep water pool are presented. There is seen to be excellent qualitative agreement between computation and experiment, and good quantitative agreement to within 8–10% when using a normalised error. This validation allowed subsequent investigation of the bubble flow field in areas not measurable using the PIV technique, such the central jet which generates splash, and in flow areas relevant to an industrial smelting process which can be used to determine a suitable tuyere separation. Received: 14 January 1998/Accepted: 12 August 1998     

3D Flow reconstruction using ultrasound PIV

Ultrasound particle image velocimetry (PIV) can be used to obtain velocity fields in non-transparent geometries and/or fluids. In the current study, we use this technique to document the flow in a curved tube, using ultrasound contrast bubbles as flow tracer particles. The performance of the technique is first tested in a straight tube, with both steady laminar and pulsatile flows. Both experiments confirm that the technique is capable of reliable measurements. A number of adaptations are introduced that improve the accuracy and applicability of ultrasound PIV. Firstly, due to the method of ultrasound image acquisition, a correction is required for the estimation of velocities from tracer displacements. This correction accounts for the fact that columns in the image are recorded at slightly different instances. The second improvement uses a slice-by-slice scanning approach to obtain three-dimensional velocity data. This approach is here demonstrated in a strongly curved tube. The resulting flow profiles and wall shear stress distribution shows a distinct asymmetry. To meaningfully interpret these three-dimensional results, knowledge of the measurement thickness is required. Our third contribution is a method to determine this quantity, using the correlation peak heights. The latter method can also provide the third (out-of-plane) component if the measurement thickness is known, so that all three velocity components are available using a single probe.     

Dual-plane stereoscopic particle image velocimetry: system set-up and its application on a lobed jet mixing flow

 The technical basis and system set-up of a dual-plane stereoscopic particle image velocimetry (PIV) system, which can obtain the flow velocity (all three components) fields at two spatially separated planes simultaneously, is summarized. The simultaneous measurements were achieved by using two sets of double-pulsed Nd:Yag lasers with additional optics to illuminate the objective fluid flow with two orthogonally linearly polarized laser sheets at two spatially separated planes, as proposed by Kaehler and Kompenhans in 1999. The light scattered by the tracer particles illuminated by laser sheets with orthogonal linear polarization were separated by using polarizing beam-splitter cubes, then recorded by high-resolution CCD cameras. A three-dimensional in-situ calibration procedure was used to determine the relationships between the 2-D image planes and three-dimensional object fields for both position mapping and velocity three-component reconstruction. Unlike conventional two-component PIV systems or single-plane stereoscopic PIV systems, which can only get one-component of vorticity vectors, the present dual-plane stereoscopic PIV system can provide all the three components of the vorticity vectors and various auto-correlation and cross-correlation coefficients of flow variables instantaneously and simultaneously. The present dual-plane stereoscopic PIV system was applied to measure an air jet mixing flow exhausted from a lobed nozzle. Various vortex structures in the lobed jet mixing flow were revealed quantitatively and instantaneously. In order to evaluate the measurement accuracy of the present dual-plane stereoscopic PIV system, the measurement results were compared with the simultaneous measurement results of a laser Doppler velocimetry (LDV) system. It was found that both the instantaneous data and ensemble-averaged values of the stereoscopic PIV measurement results and the LDV measurement results agree well. For the ensemble-averaged values of the out-of-plane velocity component at comparison points, the differences between the stereoscopic PIV and LDV measurement results were found to be less than 2%. Received: 18 April 2000/Accepted: 2 February 2001     

Probing the velocity fields of gas and liquid phase simultaneously in a two-phase flow

The feasibility of simultaneous measurements of the instantaneous velocity fields of gaseous and liquid phase is demonstrated in a laminar, unsteady two-phase flow. Thus, the instantaneous relative velocity field can be measured in such media. This is achieved by combining Particle Image Velocimetry (PIV) and a gas-phase velocimetry technique, which is based on laser-induced fluorescence (LIF) from a gaseous tracer. The wavelength shift of LIF is exploited to separate it from Mie scattering from the liquid phase. The new technique and the PIV measurement system work independently in this approach. Thus, the measurement accuracy and precision of the new technique can be validated by comparing it to the PIV results in regions of the flow field where the relative velocity vanishes. Received: 18 October 1998/Accepted: 16 October 1999     

On the effect of particle image intensity and image preprocessing on the depth of correlation in micro-PIV

The depth of correlation (DOC) is an experimental parameter, introduced to quantify the thickness of the measurement volume and thus the depth resolution in microscopic particle image velocimetry (μPIV). The theory developed to estimate the value of the DOC relies on some approximations that are not always verified in actual experiments, such as a single thin-lens optical system. In many practical μPIV experiments, a deviation of the actual DOC from its nominal value can be expected, due for instance to additional components present in the optical path of the microscope or to the use of image preprocessing before the PIV evaluation. In the presented paper, the effect of real particle image intensity distribution and image preprocessing on the thickness of the measurement volume is investigated. This is performed studying the defocusing of tracer particles and the DOC-related bias error present in μPIV measurements in a Poiseuille flow. The analysis shows that the DOC predicted using the conventional formulas can be significantly smaller than its actual value. To overcome this problem, the use of an effective NA determined experimentally from the curvature of the image autocorrelations is proposed. The accuracy of this approach to properly predict the actual size of DOC is discussed and validated on the experimental data. The effectiveness of image preprocessing to reduce the DOC-related bias error is tested and discussed as well.     

Volume self-calibration for 3D particle image velocimetry

Planar self-calibration methods have become standard for stereo PIV to correct misalignments between laser light sheet and calibration plane. Computing cross-correlation between images from camera 1 and 2 taken at the same time, non-zero disparity vectors indicate rotational and translational misalignments relative to the coordinate system defined by a calibration plate. This approach works well for thin light sheets but fails for extended volumes recorded in 3D-PTV or tomographic PIV experiments. Here it is primarily necessary to correct calibration errors leading to triangulation errors in 3D-PTV or in degraded tomographic volume reconstruction. Tomographic PIV requires calibration accuracies of a fraction of a pixel throughout the complete volume, which is difficult to achieve experimentally. A new volumetric self-calibration technique has been developed based on the computation of the 3D position of matching particles by triangulation as in 3D-PTV. The residual triangulation error (‘disparity’) is then used to correct the mapping functions for all cameras. A statistical clustering method suitable for dense particle images has been implemented to find correct disparity map peaks from true particle matches. Disparity maps from multiple recordings are summed for better statistics. This self-calibration scheme has been validated using several tomographic PIV experiments improving the vector quality significantly. The relevance for other 3D velocimetry methods is discussed.     

Non-intrusive temperature measurement using microscale visualization techniques

μPIV is a widely accepted tool for making accurate measurements in microscale flows. The particles that are used to seed the flow, due to their small size, undergo Brownian motion which adds a random noise component to the measurements. Brownian motion introduces an undesirable error in the velocity measurements, but also contains valuable temperature information. A PIV algorithm which detects both the location and broadening of the correlation peak can measure velocity as well as temperature simultaneously using the same set of images. The approach presented in this work eliminates the use of the calibration constant used in the literature (Hohreiter et al. in Meas Sci Technol 13(7):1072–1078, 2002), making the method system-independent, and reducing the uncertainty involved in the technique. The temperature in a stationary fluid was experimentally measured using this technique and compared to that obtained using the particle tracking thermometry method and a novel method, low image density PIV. The method of cross-correlation PIV was modified to measure the temperature of a moving fluid. A standard epi-fluorescence μPIV system was used for all the measurements. The experiments were conducted using spherical fluorescent polystyrene-latex particles suspended in water. Temperatures ranging from 20 to 80°C were measured. This method allows simultaneous non-intrusive temperature and velocity measurements in integrated cooling systems and lab-on-a-chip devices.     

Comparison of PIV data using multiple configurations and processing techniques

Particle image velocimetry (PIV) data have been acquired using three different experimental configurations in the far-field of the interaction created by a transverse supersonic jet exhausting from a flat plate into a transonic crossflow. The configurations included two-component PIV in the centerline streamwise plane at two overlapping stations, as well as stereoscopic PIV in both the same streamwise plane and in the crossplane. All measurement planes intersected at a common line. Data from both two-component measurement stations and the stereoscopic streamwise configuration agreed to within the estimated uncertainty, but data from the crossplane exhibited reduced velocity and turbulent stress magnitudes by a small but significant degree. Subsequent reprocessing of the data in nominally the same manner using a newer software package brought all values into close agreement with each other, but produced substantially higher turbulent stresses. The error source associated with the choice of software was traced to the use of image deformation in the newer software to treat velocity gradients, which is shown by synthetic PIV tests to yield a more accurate result for turbulence measurements even for gradients within the recommended limits for classical PIV. These detailed comparisons of replicate data suggest that routine methods of uncertainty quantification used for a turbulent PIV experiment may not fully capture the actual error sources.     

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.     

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.     

Determination of complete velocity gradient tensor by using cinematographic stereoscopic PIV in a turbulent jet

Cinematographic stereoscopic PIV measurements were performed in the far field of an axisymmetric co-flowing turbulent round jet (Re _T ≈ 150, where Re _T is the Reynolds number based on Taylor micro scale) to resolve small and intermediate scales of turbulence. The time-resolved three-component PIV measurements were performed in a plane normal to the axis of the jet and the data were converted to quasi-instantaneous three-dimensional (volumetric) data by using Taylor’s hypothesis. The availability of the quasi-three-dimensional data enabled the computation of all nine components of the velocity gradient tensor over a volume. The use of Taylor’s hypothesis was validated by performing a separate set of time-resolved two component “side-view” PIV measurements in a plane along the jet axis. Probability density distributions of the velocity gradients computed using Taylor’s hypothesis show good agreement with those computed directly with the spatially resolved data. The overall spatial structure of the gradients computed directly exhibits excellent similarity with that computed using Taylor’s hypothesis. The accuracy of the velocity gradients computed from the pseudo-volume was assessed by computing the divergence error in the flow field. The root mean square (rms) of the divergence error relative to the magnitude of the velocity gradient tensor was found to be 0.25, which is consistent with results based on other gradient measurement techniques. The velocity gradients, vorticity components and mean dissipation in the self-similar far field of the jet were found to satisfy the axisymmetric isotropy conditions. The divergence error present in the data is attributed to the intrinsic uncertainty associated with performing stereoscopic PIV measurements and not to the use of Taylor’s hypothesis. The divergence error in the data is found to affect areas of low gradient values and manifests as nonphysical values for quantities like the normalized eigenvalues of the strain-rate tensor. However, the high gradients are less affected by the divergence error and so it can be inferred that structural features of regions of intense vorticity and dissipation will be faithfully rendered.     

Evaluation of aero-optical distortion effects in PIV

Aero-optical distortion effects on the accuracy of particle image velocimetry (PIV) are investigated. When the illuminated particles are observed through a medium that is optically inhomogeneous due to flow compressibility, the resulting particle image pattern is subjected to deformation and blur. In relation to PIV two forms of error can be identified: position error and velocity error. In this paper a model is presented that describes these errors and particle image blur in relation to the refractive index field of the flow. In the case of 2D flows the model equations can be simplified and, furthermore, the background oriented schlieren technique (BOS) can be applied as a means to assess and correct for the optical error in PIV. The model describing the optical distortion is validated by both computer simulation and real experiments of 2D flows. Two flow features are considered: one with optical distortion normal to the velocity (shear layer) and one with optical distortion in the direction of the flow (expansion fan). Both simulation and experiments demonstrate that the major source for the velocity error is the second derivative of the refractive index in the direction of the velocity vector. The aero-optical distortion effect is less critical for shearing interfaces in comparison with compression/expansion fronts, the most critical case being represented by shock waves. Based on the results from the simulated experiments, it is concluded that for the 2D flow case the BOS method allows a measurement of the mean velocity error in PIV and can reduce it to a large extent.     

Theory of non-isotropic spatial resolution in PIV

The spatial resolution of the PIV interrogation technique is discussed from an analytical standpoint and assessed with Monte Carlo numerical simulation of particle image motion. The PIV measurement error associated with lack of spatial resolution is modelled associating the cross-correlation operator to a moving average filter. The error associated with the "low-pass filtering" effect is investigated by adopting a second-order polynomial expression for the velocity spatial distribution. According to the present error analysis, the measurement error is proportional to the second-order spatial derivative of the velocity field and increases with the square of the window linear size. The strategy for the selection of the window size and properties (aspect ratio and orientation) so as to minimize the error is discussed. The principle is based on nonisotropic interrogation windows of elliptical shape, with a constant area and elongated in the direction of the largest curvature radius. The nonisotropic parameters are defined as eccentricity and orientation, which are based on the local eigenvalues/vectors of the Hessian tensor of the displacement spatial distribution. The technique is implemented in a recursive PIV interrogation method. The performance of nonisotropic interrogation technique is assessed by means of synthetic PIV images, which simulate three situations: first, a one-dimensional sinusoidal shear displacement, which allows comparison of the cross-correlation spatial response with the transfer function of linear filters. Second, the stream-wise exponential velocity decay is simulated, which simulates the particle tracers decelerating downstream of a shock wave and gives an example of a flow with main velocity differences aligned with the velocity direction. The results show that keeping the image density fixed, the error caused by insufficient spatial resolution can be reduced by a factor two when a preferential direction is found in the flow field. Finally, a Lamb–Oseen vortex flow is presented, which shows the complex pattern formed by the interrogation windows in a two-dimensional case. In this case, the improvement in interrogation performance is limited due to the isotropic nature of the velocity spatial fluctuation.     

PIV速度场坏矢量的本征正交分解处理技术

介绍了一种针对粒子图像测速(PIV)基于本征正交分解(POD)的速度场后处理技术.该技术改变了现在后处理技术将速度场坏矢量识别和修正分开实现的局面,通过迭代方法有效地实现了速度场坏点统一的识别和修复算法.算法利用POD分解的低阶模态信息重构出可以用于坏矢量识别的参考速度场,利用该参考速度场对全流场进行坏点识别并完成修正.通过对一套光滑的PIV速度场数据引入高斯分布的随机误差,测试验证了该POD方法的优越性.在坏矢量识别方面新方法较归一化中值检验有更高的正确性,能识别大面积出现的坏矢量区域.在坏矢量修补的插值算法中,新方法的计算效率又高于传统Gappy POD方法,且计算精度优于常见的矢量场内插数学方法.特别是在数据缺失的大连通区域,该方法对物理流场有很好的预测效果.     

Visualisation of air–water bubbly column flow using array Ultrasonic Velocity Profiler

In the present work, an experimental study of bubbly two-phase flow in a rectangular bubble column was performed using two ultrasonic array sensors, which can measure the instantaneous velocity of gas bubbles on multiple measurement lines. After the sound pressure distribution of sensors had been evaluated with a needle hydrophone technique, the array sensors were applied to two-phase bubble column. To assess the accuracy of the measurement system with array sensors for one and two-dimensional velocity, a simultaneous measurement was performed with an optical measurement technique called particle image velocimetry(PIV). Experimental results showed that accuracy of the measurement system with array sensors is under 10% for one-dimensional velocity profile measurement compared with PIV technique. The accuracy of the system was estimated to be under 20% along the mean flow direction in the case of two-dimensional vector mapping.