A generalized processing technique in digital particle image velocimetry with direct estimation of velocity gradients

A technique is proposed for the processing of digital particle image velocimetry (PIV) images, in one single step providing direct estimates of fluid velocity, out-of-plane vorticity and in-plane shear rate tensor. The method is based on a generalization of the standard PIV cross-correlation technique and substitutes the usual discrete cross-correlation of image pairs with a correlation of interpolated two-dimensional image intensity functions, being subject to affine transformations. The correlation is implemented by using collocation points, on which image intensity values are interpolated. The resulting six-dimensional correlation function is maximized using a general purpose optimization algorithm. The use of the method is demonstrated by application to different types of synthetically generated image pairs constructed with known particle displacement functions. The resulting errors are assessed and compared with those of a representative standard PIV method as well as with those of the present technique using no differential quantities in the search of the peak location. The examples demonstrate that significant improvements in accuracy can be obtained for flow fields with regions containing strong velocity gradients.     

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.     

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.     

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.     

Reynolds stress estimation up to single-pixel resolution using PIV-measurements

This article derives a theory for estimating Reynolds normal and shear stresses from PIV images with single-pixel resolution. The main idea is the analysis of the correlation function to identify the probability density function from which the Reynolds stresses can be derived in a 2-D regime. The work establishes a theoretical framework including the influence of the particle image diameter and the velocity gradients on the shape of the correlation function. Synthetic data sets are used for the validation of the proposed method. The application of the evaluation method on two experimental data sets shows that high resolution and accuracy are also obtained with experimental data. The approach is very general and can also be applied to correlation peaks that are obtained from sum-of-correlation PIV evaluations.     

Volumetric correlation PIV: a new technique for 3D velocity vector field measurement

A method is proposed that allows three-dimensional (3D) two-component measurements to be made by means of particle image velocimetry (PIV) in any volume illuminated over a finite thickness. The method is based on decomposing the cross-correlation function into various contributions at different depths. Because the technique is based on 3D decomposition of the correlation function and not reconstruction of particle images, there is no limit to particle seeding density as experienced by 3D particle tracking algorithms such as defocusing PIV and tomographic PIV. Correlations from different depths are differentiated by the variation in point spread function of the lens used to image the measurement volume over that range of depths. A number of examples are demonstrated by use of synthetic images which simulate micro-PIV (μPIV) experiments. These examples vary from the trivial case of Couette flow (linear variation of one velocity component over depth) to a general case where both velocity components vary by different complex functions over the depth. A final validation—the measurement of a parabolic velocity profile over the depth of a microchannel flow—is presented. The same method could also be applied using a thick light sheet in macro-scale PIV and in a stereo configuration for 3D three-component PIV.     

Fast 3D PIV with direct sparse cross-correlations

The extension of the well-assessed high-accuracy algorithms for two-dimensional-two components particle image velocimetry (PIV) to the case of three-dimensional (3D) data involves a considerable increase of the computational cost. Tomographic PIV is strongly affected by this issue, relying on 3D cross-correlation to estimate the velocity field. In this study, a number of solutions are presented, enabling a more efficient calculation of the velocity field without any significant loss of accuracy. A quick estimation of the predictor displacement field is proposed, based on voxels binning in the first steps of the process. The corrector displacement field is efficiently computed by restricting the search area of the correlation peak. In the initial part of the process, the calculation of a reduced cross-correlation map by using Fast Fourier Transform on blocks is suggested, in order to accelerate the processing by avoiding redundant calculations in case of overlapping interrogations windows. Eventually, direct cross-correlations with a search radius of only 1?pixel in the neighborhood of the estimated peak are employed; the final iterations are consistently faster, since direct correlations can better enjoy the sparsity of the distributions, reducing the number of operations to be performed. Furthermore, three different approaches to reduce the number of redundant calculations for overlapping windows are presented, based on pre-calculations of the contributions to the cross-correlations coefficients along segments, planes or blocks. The algorithms are tested both on synthetic and real images, showing that a potential speed-up of up to 800 times can be obtained, depending on the complexity of the flow field to be analyzed. The challenging application on a real swirling jet results in a speed-up of an order of magnitude.     

The influence of peak-locking errors on turbulence statistics computed from PIV ensembles

The influence of peak-locking errors on turbulence statistics computed from ensembles of PIV data is considered. PIV measurements are made in the streamwise–wall-normal plane of turbulent channel flow. The PIV images are interrogated in three distinct ways, generating ensembles of velocity fields with absolute, moderate, and minimal peak locking. Turbulence statistics computed for all three ensembles of data indicate a general sensitivity to peak locking in the single-point statistics, except for the mean velocity profile. Peak-locking errors propagate into the fluctuations of velocity, rendering single-point statistics inaccurate when severe peak locking is present. Multi-point correlations of both streamwise and wall-normal velocity are also found to be influenced by severe levels of peak locking. The displacement range of the measurement, defined by the PIV time delay, appears to affect the influence of peak-locking errors on turbulence statistics. Smaller displacement ranges, particularly those that produce displacement fluctuations that are less than one pixel in magnitude, yield inaccurate turbulence statistics in the presence of peak locking.     

3-D PIV via spatial correlation in a color-coded light-sheet

Coding of the light-sheet in depth with different colors and recording with color-sensitive films or CCD cameras enables three-dimensional correlation analysis to obtain the out-of-plane velocity component in 3-D PIV. In the system used, two overlapping light-sheets of different color are recorded simultaneously and the particles' images of the separate sheets are discernible by color splitting. For only two successive exposures as usual in cross-correlation PIV, the resulting images allow for cross-wise plane-to-plane correlations between the separated sheets. This yields altogether three independent correlations. In addition to the usual procedure to obtain the in-plane component, one can determine the out-of-plane velocity component from the three correlation peak values by an appropriate fit of the correlation profile in depth to determine the maximum location with higher accuracy compared to previous methods. In addition, there is no need of a third exposure at a third moment which increases the accuracy for time-varying flows.     

Simultaneous digital image correlation/particle image velocimetry to unfold fluid–structure interaction during air-backed impact

Predicting the response of air-backed panels to impulsive hydrodynamic loading is essential to the design of marine structures operating in extreme conditions. Despite significant effort in this area of research, the lack of full-field measurement techniques of structural dynamics and flow physics hinders our understanding of the fluid–structure interaction. To fill this gap in knowledge, we designed a laboratory-scale experiment to elucidate fluid–structure interaction associated with impulsive hydrodynamic loading on a flexible plate. A combined experimental approach based on digital image correlation (DIC) and particle image velocimetry (PIV) was developed to afford spatially- and temporally-resolved measurements of the plate deflection and fluid velocity. From the velocity field measured through PIV, the hydrodynamic loading on the structure was estimated via a pressure-reconstruction algorithm. Experimental results point at a strong bidirectional coupling between structural dynamics and flow physics, which influence temporal and spatial patterns in counter-intuitive ways. While the plate deflection follows the fundamental in-vacuum mode shape of a clamped plate, the pressure exhibits a complex evolution. Not only does the location of the peak loading on the plate alternates between the clamp and the center as time progresses, but also the time evolution of the peak loading anticipated the peak displacement of the plate. This study contributes a new methodological approach to study fluid–structure interaction in three dimensions, offering insight in the physics of air-backed impact that could inform engineering design and scientific inquiry.     

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:

Spatially adaptive PIV interrogation based on data ensemble

This paper proposes a specific application of the approach recently proposed by the authors to achieve an autonomous and robust adaptive interrogation method for PIV data sets with the focus on the determination of mean velocity fields. Under circumstances such as suboptimal flow seeding distribution and large variations in the velocity field properties, neither multigrid techniques nor adaptive interrogation with criteria based on instantaneous conditions offer enough robustness for the flow field analysis. A method based on the data ensemble to select the adaptive interrogation parameters, namely, the window size, aspect ratio, orientation, and overlap factor is followed in this study. Interrogation windows are sized, shaped and spatially distributed on the basis of the average seeding density and the gradient of the velocity vector field. Compared to the instantaneous approach, the ensemble-based criterion adapts the windows in a more robust way especially for the implementation of non-isotropic windows (stretching and orientation), which yields a higher spatial resolution. If the procedure is applied recursively, the number of correlation samples can be optimized to satisfy a prescribed level of window overlap ratio. The relevance and applicability of the method are illustrated by an application to a shock-wave-boundary layer interaction problem. Furthermore, the application to a transonic airfoil wake verifies by means of a dual-resolution experiment that the spatial resolution in the wake can be increased by using non-isotropic interrogation windows.     

Instantaneous planar pressure determination from PIV in turbulent flow

This paper deals with the determination of instantaneous planar pressure fields from velocity data obtained by particle image velocimetry (PIV) in turbulent flow. The operating principles of pressure determination using a Eulerian or a Lagrangian approach are described together with theoretical considerations on its expected performance. These considerations are verified by a performance assessment on a synthetic flow field. Based on these results, guidelines regarding the temporal and spatial resolution required are proposed. The interrogation window size needs to be 5 times smaller than the flow structures and the acquisition frequency needs to be 10 times higher than the corresponding flow frequency (e.g. Eulerian time scales for the Eulerian approach). To further assess the experimental viability of the pressure evaluation methods, stereoscopic PIV and tomographic PIV experiments on a square cylinder flow (Re _D  = 9,500) were performed, employing surface pressure data for validation. The experimental results were found to support the proposed guidelines.     

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     

Navier–Stokes simulations in gappy PIV data

Velocity measurements conducted with particle image velocimetry (PIV) often exhibit regions where the flow motion cannot be evaluated. The principal reasons for this are the absence of seeding particles or limited optical access for illumination or imaging. Additional causes can be laser light reflections and unwanted out-of-focus effects. As a consequence, the velocity field measured with PIV contains regions where no velocity information is available, that is gaps. This work investigates the suitability of using the unsteady incompressible Navier–Stokes equations to obtain accurate estimates of the local transient velocity field in small gaps; the present approach applies to time-resolved two-dimensional experiments of incompressible flows. The numerics are based on a finite volume discretization with partitioned time-stepping to solve the governing equations. The measured velocity distribution at the gap boundary is taken as time-varying boundary condition, and an approximate initial condition inside the gap is obtained via low-order spatial interpolation of the velocity at the boundaries. The influence of this I.C. is seen to diminish over time, as information is convected through the gap. Due to the form of the equations, no initial or boundary conditions on the pressure are required. The approach is evaluated by a time-resolved experiment where the true solution is known a priori. The results are compared with a boundary interpolation approach. Finally, an application of the technique to an experiment with a gap of complex shape is presented.     

Diffusive mixing through velocity profile variation in microchannels

Rapid mixing does not readily occur at low Reynolds number flows encountered in microdevices; however, it can be enhanced by passive diffusive mixing schemes. This study of micromixing of two miscible fluids is based on the principle that (1) increased velocity at the interface of co-flowing fluids results in increased diffusive mass flux across their interface, and (2) diffusion interfaces between two liquids progress transversely as the flow proceeds downstream. A passive micromixer is proposed that takes advantage of the peak velocity variation, inducing diffusive mixing. The effect of flow variation on the enhancement of diffusive mixing is investigated analytically and experimentally. Variation of the flow profile is confirmed using micro-Particle Image Velocimetry (μPIV) and mixing is evaluated by color variations resulting from the mixing of pH indicator and basic solutions. Velocity profile variations obtained from μPIV show a shift in peak velocities. The mixing efficiency of the Σ-micromixer is expected to be higher than that for a T-junction channel and can be as high as 80%. The mixing efficiency decreases with Reynolds number and increases with downstream length, exhibiting a power law.     

三曝光三相关PIV技术研究

对不等间隔三次曝光单幅记录的PIV粒子图像,本文提出一和中三相关位移诊断方法,三相关函数有两个次大峰,且不对称地人布在最大峰两侧,本方法可同时获得位移值及判别位移方向,可有效解决位移方向二义性问题,对线性涡流模拟粒子图像,应用本方法进行粒子位移诊断,结果证实了本方法对含涡复杂流动速度方向判别的有效性。     

PIV measurements in a weakly separating and reattaching turbulent boundary layer

A high Reynolds number flat plate turbulent boundary layer was studied in a wind-tunnel experiment using particle image velocimetry (PIV). The flow is subjected to an adverse pressure gradient (APG) which is designed such that the boundary layer separates and reattaches, forming a weak separation bubble. With PIV we are able to get a more complete picture of this complex flow phenomenon. The view of a separation bubble being composed of large scale coherent regions of instantaneous backflow occurring randomly in a three-dimensional manner in space and time is verified by the present PIV measurements. The PIV database was used to test the applicability of various velocity scalings around the separation bubble. We found that the mean velocity profiles in the outer part of the boundary layer, and to some extent also the Reynolds shear-stress, are self-similar when using a velocity scale based on the local pressure gradient. The same can be said for the so called Perry–Schofield scaling, which suggests that the two velocity scales are connected. This can also be interpreted as an experimental evidence of the claimed relation between the latter velocity scale and the maximum Reynolds shear-stress.     

Analysis and treatment of errors due to high velocity gradients in particle image velocimetry

This paper deals with errors occurring in two-dimensional cross-correlation particle image velocimetry (PIV) algorithms (with window shifting), when high velocity gradients are present. A first bias error is due to the difference between the Lagrangian displacement of a particle and the real velocity. This error is calculated theoretically as a function of the velocity gradients, and is shown to reach values up to 1 pixel if only one window is translated. However, it becomes negligible when both windows are shifted in a symmetric way. A second error source is linked to the image pattern deformation, which decreases the height of the correlation peaks. In order to reduce this effect, the windows are deformed according to the velocity gradients in an iterative process. The problem of finding a sufficiently reliable starting point for the iteration is solved by applying a Gaussian filter to the images for the first correlation. Tests of a PIV algorithm based on these techniques are performed, showing their efficiency, and allowing the determination of an optimum time separation between images for a given velocity field. An application of the new algorithm to experimental particle images containing concentrated vortices is shown.     

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.