Denoising methods for time-resolved PIV measurements

The increasing capabilities of currently available high-speed cameras present several new opportunities for particle image velocimetry (PIV). In particular, temporal postprocessing methods can be used to remove spurious vectors but can also be applied to remove inherent noise. This paper explores this second possibility by estimating the error introduced by several denoising methods on manufactured velocity fields. It is found that PIV noise, while autocorrelated in space, is uncorrelated in time, which leads to a significant improvement in the efficiency of temporal denoising methods compared to their spatial counterparts. Among them, the optimal Wiener filter presents better results than convolution- or wavelet-based filters and has the valuable advantage that no adjustments are required, unlike other methods which generally involve the tuning of some parameters that depend on flow and measurement conditions and are not known a priori. Further refinements show that denoised data can be successfully deconvolved to increase the accuracy of remaining small-scale velocity fluctuations, leading in particular to the recovery of the true shape of turbulent spectra. In practice, the computation of the filter function is not always accurate and different procedures can be used to improve the method depending on the flow considered. Some of them are derived from the properties of the time-frequency spectrum provided by the wavelet transform.     

Fluid trajectory evaluation based on an ensemble-averaged cross-correlation in time-resolved PIV

A novel multi-frame particle image velocimetry (PIV) method, able to evaluate a fluid trajectory by means of an ensemble-averaged cross-correlation, is introduced. The method integrates the advantages of the state-of-art time-resolved PIV (TR-PIV) methods to further enhance both robustness and dynamic range. The fluid trajectory follows a polynomial model with a prescribed order. A set of polynomial coefficients, which maximizes the ensemble-averaged cross-correlation value across the frames, is regarded as the most appropriate solution. To achieve a convergence of the trajectory in terms of polynomial coefficients, an ensemble-averaged cross-correlation map is constructed by sampling cross-correlation values near the predictor trajectory with respect to an imposed change of each polynomial coefficient. A relation between the given change and corresponding cross-correlation maps, which could be calculated from the ordinary cross-correlation, is derived. A disagreement between computational domain and corresponding physical domain is compensated by introducing the Jacobian matrix based on the image deformation scheme in accordance with the trajectory. An increased cost of the convergence calculation, associated with the nonlinearity of the fluid trajectory, is moderated by means of a V-cycle iteration. To validate enhancements of the present method, quantitative comparisons with the state-of-arts TR-PIV methods, e.g., the adaptive temporal interval, the multi-frame pyramid correlation and the fluid trajectory correlation, were carried out by using synthetically generated particle image sequences. The performances of the tested methods are discussed in algorithmic terms. A high-rate TR-PIV experiment of a flow over an airfoil demonstrates the effectiveness of the present method. It is shown that the present method is capable of reducing random errors in both velocity and material acceleration while suppressing spurious temporal fluctuations due to measurement noise.     

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.     

Nonlinear temporal filtering of time-resolved digital particle image velocimetry data

Nonlinear filtering methods have been developed to identify and replace outlying data points in velocity time series obtained with time-resolved digital particle image velocimetry (PIV) of the flow around a surface-mounted cube at a Reynolds number of 20,000. Nuances associated with the spectral computation of the cross-correlation are highlighted, including the requirement of zero-padding an image interrogation area to eliminate the circular components of the cross-correlation. Three nonlinear filtering methods for the replacement of outliers are applied to the velocity time series sampled at 1,000 Hz: a median filter, a decision-based Hampel filter, and a PIV-specific Hampel filter. The particular benefit of the PIV-specific Hampel filter is that it allows the retention of actual measured data, sometimes derived from alternate peaks in the cross-correlation function, while still providing for the removal of outliers when a consistent, nonoutlying measurement is not available.     

Characterization of vortical structures and loads based on time-resolved PIV for asymmetric hovering flapping flight

Flight agility, resistance to gusts, capability to hover coupled with a low noise generation might have been some of the reasons why insects are among the oldest species observed in nature. Biologists and aerodynamicists focused on analyzing such flight performances for diverse purposes: understanding the essence of flapping wings aerodynamics and applying this wing concept to the development of micro-air vehicles (MAVs). In order to put into evidence the fundamentally non-linear unsteady mechanisms responsible for the amount of lift generated by a flapping wing (Dickinson et al. in Science 284:1954–1960, 1999), experimental and numerical studies were carried out on typical insect model wings and kinematics. On the other hand, in the recent context of MAVs development, it is of particular interest to study simplified non-biological flapping configurations which could lead to lift and/or efficiency enhancement. In this paper, we propose a parametrical study of a NACA0012 profile undergoing asymmetric hovering flapping motions at Reynolds 1000. On the contrary to normal hovering, which has been widely studied as being the most common configuration observed in the world of insects, asymmetric hovering is characterized by an inclined stroke plane. Besides the fact that the vertical force is hence a combination of both lift and drag (Wang in J Exp Biol 207:1137–1150, 2004), the specificity of such motions resides in the vortex dynamics which present distinct behaviours, whether the upstroke angle of attack leads to a partially attached or a strong separated flow, giving more or less importance to the wake capture phenomenon. A direct consequence of the previous remarks relies on the enhancement of aerodynamic efficiency with asymmetry. If several studies reported results based on the asymmetric flapping motion of dragonfly, only few works concentrated on parametrizing asymmetric motions (e.g. Wang in Phys Rev Lett 85:2216–2219, 2000). The present study relies on TR-PIV measurements which allow determination of the vorticity fields and provide a basis to evaluate the resulting unsteady forces through the momemtum equation approach.     

应用PIV技术测试涡旋波流场

涡旋波流动作为一种特殊的流动现象,可以使流体在相对较宽的槽道中产生较强的波动和对流混合,从而在小Re数条件下起到强化传质的效果。本文利用PIV流场显示技术,对振荡流在非对称槽道中所形成的涡旋波的产生机理和发展规律进行了实验研究和定量分析,测得了涡旋波流场的速度矢量图,阐明了涡旋波流场周期性变化的特点。分析了Re数和St数对涡旋波流动的影响,并得出了旋涡涡心位置以及涡心处涡量的动态变化规律。     

Automated critical point identification for PIV data using multimodal particle swarm optimization

A hybrid sequential niche algorithm is used for the automated identification of critical points of velocity fields. This method combines an adaptive sequential niche technique with deterministic local optimization to detect critical points: focus, node and saddle points. A particle swarm algorithm performs a global search whereas vortex core identification functions compute the precise location as the extremum of the corresponding function. Once a critical point is found, a rectangular niche is constructed around the point. The particle swarm then proceeds to explore different regions of the velocity field. The process advances sequentially, avoiding areas near previously found critical points by blocking niches obtained from previous steps. The niche size is automatically adjusted each time a search enters inside an existing niche. Vortex core functions are used for critical point identification and calculating its precise location inside each niche. The procedure is validated on particle image velocimetry data obtained with two types of flows, an impinging jet flow and a flow downstream of a model building. The hybrid algorithm proved to be very efficient and robust for automated detection and identification of critical points. It can be used as a first step for studying the time‐dependent dynamic behavior of instantaneous velocity fields by tracking topological critical points. This is the first study that uses a multi‐modal particle swarm algorithm for critical point identification. Copyright © 2011 John Wiley & Sons, Ltd.     

A tomographic PIV resolution study based on homogeneous isotropic turbulence DNS data

In order to accurately assess measurement resolution and measurement uncertainty in DPIV and TPIV measurements, a series of simulations were conducted based on the flow field from a homogeneous isotropic turbulence data set (Re _λ = 141). The effect of noise and spatial resolution was quantified by examining the local and global errors in the velocity, vorticity and dissipation fields in addition to other properties of interest such as the flow divergence, topological invariants and energy spectra. In order to accurately capture the instantaneous gradient fields and calculate sensitive quantities such as the dissipation rate, a minimum resolution of x/η = 3 is required, with smoothing recommended for the TPIV results to control the inherently higher noise levels. Comparing these results with experimental data showed that while the attenuation of velocity and gradient quantities was predicted well, higher noise levels in the experimental data led increased divergence.     

Optimisation of temporal averaging processes in PIV

A hybrid of correlation and vector averaging is introduced to capitalise on the advantages of each process. An extensive series of Monte Carlo simulations have been conducted to investigate hybrid averaging and evaluate it against both vector and correlation averaging. The simulations show that hybrid averaging improves the measurement accuracy over both correlation and vector averaging over a wide range of imaging conditions. The simulations are validated by applying hybrid averaging to experimental micro- and macro-flows. In pulsatile conditions, correlation averaging yields an averaged correlation function that is multi-modal, which can result in unpredictable measurements. A Monte Carlo simulation shows the benefits of hybrid averaging over correlation averaging in such conditions. This has been experimentally validated on the unsteady wake behind a shedding circular cylinder at Re = 98.     

Experimental investigation of global structures in an incompressible cavity flow using time-resolved PIV

Open-cavity flows are known to exhibit a few well-defined peaks in the power spectral distribution of velocity or pressure signals recorded close to the impinging corner. The measured frequencies are in fact common to the entire flow, indicating some global organisation of the flow. The modal structures, i.e. the spatial distribution of the most characteristic frequencies in the flow, are experimentally investigated using time-resolved particle image velocimetry. Each spatial point, of the resulting two-dimension-two-component (2D–2C) velocity fields, provides time-resolved series of the velocity components V _x and V _y , in a (x, y) streamwise plane orthogonal to cavity bottom. Each local time-series is Fourier-transformed, such as to provide the spectral distribution at any point of the PIV-plane. One finally obtains the spatial structure associated with any frequency of the Fourier spectrum. Some of the modal spatial structures are expected to represent the nonlinear saturation of the global modes, against which the stationary solution of the Navier–Stokes equations may have become linearly unstable. Following Rowley et al. (J Fluid Mech 641:115–127, 2009), our experimental modal structures may even correspond to the Koopman modes of this incompressible cavity flow.     

Lagrangian and Eulerian pressure field evaluation of rod-airfoil flow from time-resolved tomographic PIV

This work investigates the rod-airfoil air flow by time-resolved Tomographic Particle Image Velocimetry (TR-TOMO PIV) in thin-light volume configuration. Experiments are performed at the region close to the leading edge of a NACA0012 airfoil embedded in the von Kármán wake of a cylindrical rod. The 3D velocity field measured at 5 kHz is used to evaluate the instantaneous planar pressure field by integration of the pressure gradient field. The experimental data are treated with a discretized model based on multiple velocity measurements. The time separation used to evaluate the Lagrangian derivative along a fluid parcel trajectory has to be taken into account to reduce precision error. By comparing Lagrangian and Eulerian approaches, the latter is restricted to shorter time separations and is found not applicable to evaluate pressure gradient field if a relative precision error lower than 10% is required. Finally, the pressure evaluated from tomographic velocity measurements is compared to that obtained from simulated planar ones to discuss the effect of 3D flow phenomena on the accuracy of the proposed technique.     

Evaluation of unsteady pressure fields and forces in rotating airfoils from time-resolved PIV

The final stages of transitional phenomena in laminar separation bubbles play a key role in their reattachment process, and they condition the boundary layer properties and flow structure after reattachment. In this experimental study, the evolution of the perturbation velocity spectra found in this zone is first presented, showing the nonlinear growth of instabilities in their path to develop fully turbulent spectra. The study of the average flow field allows the scaling of the reattachment region, both in its extension and in the characterization of the integral boundary layer magnitudes. Experimental laws are proposed for the evolution of the momentum thickness and of the shape factor. In addition, a universal, wake-like mean velocity profile is found shortly after the reattachment station. The phase-locked characterization technique allows measurements conditioned to the presence of a fluid event. This technique is used to track the evolution of large-scale structures, whose dynamics is seen to dominate the fluid behavior in the reattachment zone. The simultaneous existence of two vortex blobs is found to characterize this flow region, with the longest lived one being convected toward the wall and stretched. This process results in the fast breakdown of the large-scale vorticity structure and the sudden formation of 3-D, small scales that promote the rapid flow evolution toward a fully developed turbulent state.     

Eulerian and Lagrangian views of a turbulent boundary layer flow using time-resolved tomographic PIV

Coherent structures and their time evolution in the logarithmic region of a turbulent boundary layer investigated by means of 3D space–time correlations and time-dependent conditional averaging techniques are the focuses of the present paper. Experiments have been performed in the water tunnel at TU Delft measuring the particle motion within a volume of a turbulent boundary layer flow along a flat plate at a free-stream velocity of 0.53 m/s at Re _θ = 2,460 based on momentum thickness by using time-resolved tomographic particle image velocimetry (PIV) at 1 kHz sampling rate and particle tracking velocimetry (PTV). The obtained data enable an investigation into the flow structures in a 3D Eulerian reference frame within time durations corresponding to 28 δ/U. An analysis of the time evolution of conditional averages of vorticity components representing inclined hairpin-like legs and of Q2- and Q4-events has been performed, which gives evidence to rethink the early stages of the classical hairpin development model for high Reynolds number TBLs. Furthermore, a PTV algorithm has been applied on the time sequences of reconstructed 3D particle image distributions identifying thousands of particle trajectories that enable the calculation of probability distributions of the three components of Lagrangian accelerations.     

Rotor crack identification based on neural networks and modal data

A model-based procedure for rotor crack localization and assessment is presented in this paper. The procedure is applied to a small-size test rig provided with a notch. Both the position and depth of the notch are estimated through a neural network on the basis of the first four natural frequencies of the rotor. A 3-D finite element model is used to generate the data for training the net. One of the contributions of this paper consists of a meshing procedure that reduces the systematic errors of the model, which have a significant influence in identification accuracy. A sensitivity analysis has been carried out for any size and position of the notch, which constitutes another original contribution in this field. In the studied case, the proposed procedure is able to predict both the position and depth of the notch when the notch depth is greater than 20 % of the rotor diameter. The sensitivity analysis reveals that there are blind spots in the rotor as regards notch identification.     

Limits on the resolution of correlation PIV iterative methods. Fundamentals

The spatial resolution of correlation particle image velocimetry (PIV) is a frequently addressed issue that still raises scientific interest. In conventional non-iterative PIV, the spatial resolution limits are of common knowledge (Willert and Gharib (1991) Exp Fluids 10:181–193; Raffel et al. (1998) ISBN 3-540-63683-8, Springer, Berlin Heidelberg New York, among others). On the contrary, those advanced iterative multipass methods that use image distortion techniques or multigrid techniques present a more complex scenario. One of the concepts that raises more debate is the limiting effect of the interrogation window size. This paper focuses on the subject, trying to clarify key points. The results indicate that iterative algorithms using an appropriate weighting function eliminate the window size from the ensemble of spatial resolution limits.     

Analysis of time-resolved PIV measurements of a confined turbulent jet using POD and Koopman modes

We present a comparative analysis of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) computed from experimental data of a turbulent, quasi 2-D, confined jet with co-flow (Re?=?11,500, co-flow ratio inner-to-outer flow ≈2:1). The experimental data come from high-speed 2-D particle image velocimetry. The flow is fully turbulent, and it contains geometry-dependent large-scale coherent structures; thus, it provides an interesting benchmark case for the comparison between POD and DMD. In this work, we address issues related to snapshot selections (1), convergence (2) and the physical interpretation (3) of both POD and DMD modes. We found that the convergence of POD modes follows the criteria of statistical convergence of the autocovariance matrix. For the computation of DMD modes, we suggest a methodology based on two criteria: the analysis of the residuals to optimize the sampling parameters of the snapshots, and a time-shifting procedure that allows us to identify the spurious modes and retain the modes that consistently appear in the spectrum. These modes are found to be the ones with nearly null growth rate. We then present the selected modes, and we discuss the way POD and DMD rank them. POD analysis reveals that the most energetic spatial structures are related to the large-scale oscillation of the inner jet (flapping); from the temporal analysis emerges that these modes are associated with a low-frequency peak at St?=?0.02. At this frequency, DMD identifies a similar mode, where oblique structures from the walls appear together with the flapping mode. The second most energetic group of modes identified is associated with shear-layer oscillations, and to a recirculation zone near the inner jet. Temporal analysis of these modes shows that the flapping of the inner jet might be sustained by the recirculation. In the DMD, the shear-layer modes are separated from the recirculation modes. These have large amplitudes in the DMD. In conclusion, the DMD modes with eigenvalues on the unit circle are found to be similar to the most energetic POD modes, although differences appear due to the fact that DMD isolates structures associated with one frequency only.