Time-resolved Particle Image Velocimetry Data Research Articles

Vortex-induced sound prediction of slat noise from time-resolved particle image velocimetry data

A data-driven method for predicting the vortex-induced sound from time-resolved velocimetry data is presented and applied to the sound generated by flow passing through the slat in a multi-element high-lift airfoil. The time-dependent velocity fields in the slat-cove region of the 30P30N multi-element airfoil are obtained from time-resolved particle image velocimetry measurements, and a low-order reconstruction is achieved by using the rank-one vbnm modes from spectral proper orthogonal decomposition. The pressure force and associated dipole sound are then computed via the application of the force and acoustic partitioning methods (Seo et al. in Phys Fluids 34(5):053607, 2002) which involve volume integrals of the product of the second invariant of the velocity gradient tensor and geometry-dependent influence fields. The method enables estimation of the dipole sound generated by local flow structures, and the results are shown to be consistent with theory of vortex sound. Comparison with the measured sound data suggests that while the shear layer modes are responsible for the tonal noise, the interactions between the shear layer modes and other parts of the wing also generate a substantial level of flow noise.

Characteristics of geometry-and pressure-induced laminar separation bubbles at an enhanced level of free-stream turbulence

Responses of a geometry-induced separation bubble (GISB) and a pressure-induced separation bubble (PISB) at enhanced levels of free-stream turbulence (FST) have experimentally been investigated for a comparative study using the particle image velocimetry (PIV) technique. The outlines of separation bubbles based on the dividing streamlines are self-similar for different levels of FST and Reynolds numbers. The spectral analyses of the time-resolved PIV data show that the vortex shedding frequency of a separated shear layer remains unchanged for the GISB cases even with an enhanced level of FST. In contrast, it is different for the PISB cases. We propose a criterion that determines whether the frequency will remain the same even for the cases with FST. Linear stability analyses reveal that the inviscid-inflectional instability dominates the transition process, and the linear stages of transition are not completely bypassed even at an enhanced level of FST. The most amplified frequencies, while scaling with the displacement thickness and the boundary layer edge velocity, collapse in a single curve for all the cases. Furthermore, measurements in the spanwise plane show that the streamwise velocity streak/Klebanof mode at an enhanced level of FST is not a general flow feature for all types of separation bubbles. However, at an enhanced level of FST for the PISB case, the boundary layer streaks are found to distort the two-dimensional vortex structure associated with the Kelvin–Helmholtz instability, eventually leading to a three-dimensional $\varLambda$ -like structure in the spanwise plane.

Gappy spectral proper orthogonal decomposition

Experimental spatio-temporal flow data often contain gaps or other types of undesired artifacts. To reconstruct flow data in the compromised or missing regions, a data completion method based on spectral proper orthogonal decomposition (SPOD) is developed. The algorithm leverages the temporal correlation of the SPOD modes with preceding and succeeding snapshots, and their spatial correlation with the surrounding data at the same time instant. For each gap, the algorithm first computes the SPOD of the remaining, unaffected data. In the next step, the compromised data are projected onto the basis of the SPOD modes. This corresponds to a local inversion of the SPOD problem and yields expansion coefficients that permit the reconstruction in the affected regions. This local reconstruction is successively applied to each gap. After all gaps are filled in, the procedure is repeated in an iterative manner until convergence. This method is demonstrated on two examples: direct numerical simulation of laminar flow around a cylinder, and time-resolved PIV data of turbulent cavity flow obtained by Zhang et al. (2019) [47]. Randomly added gaps correspond to 1%, 5%, and 20% of data loss. Even for 20% data corruption, and in the presence of measurement noise in the experimental data, the algorithm recovers 97% and 80% of the original data in the corrupted regions of the simulation and PIV data, respectively. These values are higher than those achieved by established methods like gappy POD and Kriging.

Effect of a front inclined hole on multiscale vortical structures around a wall-mounted cube

To reveal the multiscale wake structures of a wall-mounted cube and the effects of a front inclined hole (FIH), a combination of wavelet multiresolution analysis and vortex identification techniques is applied to analyze time-resolved particle image velocimetry data. The cube model has a side length D = 50 mm and the Reynolds number ReD = 7800. The inlet of the FIH is located at a height 0.71D on the front surface of the cube, and the outlet is located at the center of the free end. Statistical analysis indicates that an FIH can reduce the recirculation zone around the cube, suppress downwash flow, and alter the development of free-end shear flow. The turbulence intensity and turbulent kinetic energy in the wake also decrease significantly in the presence of an FIH. The wavelet multiresolution analysis shows that the main structures of the flow field experience a transformation from small to intermediate and then large scales from the shear layer around the standard cube to its wake. However, in the presence of an FIH, the scale of the flow structure near the free end becomes smaller, the large-scale structure in the wake is weakened, and the transition from small to intermediate scales is no longer obvious. The wavelet vortex dynamics analysis reveals the evolutions of vortex structures with different scales. In the presence of an FIH, the trend of large- and intermediate-scale coherent structures moving to the bottom wall is weakened, while the streamwise extent of small-scale structures is greater. In the large-scale component of the wake, a transverse secondary vortex is observed, which is formed by the combined action of a shedding transverse vortex and downwash flow.

Transitional flow structures in heated hypersonic boundary layers

Transition in a Mach 6 flared cone boundary layer over a heated wall has been investigated in the Mach 6 wind tunnel at Peking University using visualization, focused laser differential interferometry, infrared imaging, particle image velocimetry (PIV), and direct numerical simulation (DNS). The model's wall-temperature ratio η=Tw/T0 (where Tw and T0 are, respectively, the wall temperature and oncoming stream stagnation temperature) can be controlled to vary from 0.66 to 1.77. An ultrafast illumination image system has been used for Rayleigh-scattering visualization and PIV to experimentally capture the dynamics of the transition. Lagrangian flow structures are revealed by both the DNS results and the time-resolved PIV data. The effect of wall temperature on the transition is investigated, and it is found that increasing η initially delays but then promotes the transition to turbulence, with the reversal point being near η≈1. The turbulence onset mechanism over the heated wall for η=1.50, where first-mode-induced oblique breakdown dominates, is then investigated, and it is shown that lifting-up three-dimensional (3D) waves appear around the critical layer owing to the nonlinear development of the oblique first mode. Consequently, a downward sweep motion occurs to compensate for the lifting low-speed fluid, with the formation of a warped wave front. High-shear layers are created around the 3D Lagrangian waves and strengthened to cause the formation of a Λ-vortex. In general, this lifting-up 3D wavepacket has been confirmed to play a determining role in hypersonic turbulence production over a heated wall, which is similar to the findings in incompressible boundary layers.

Role of flow reversals in transition to turbulence and relaminarization of pulsatile flows

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Temporal characteristics of the probability density function of velocity in wall-bounded turbulent flows

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A few techniques to improve data-driven reduced-order simulations for unsteady flows

A key step to improve data-driven reduced-order simulations is to compute a transfer function that predicts the time evolution of the reduced-order modes accurately. We demonstrate a couple of useful techniques to achieve this objective: One is to pre-process time-series of reduced-order modes with a low-pass filter, e.g. a polynomial filter and B-spline, and the other is to compute a data-driven transfer function from multiple past time-steps, corresponding to a high-order temporal scheme. These techniques are exercised with POD modes generated from time-resolved planar PIV data. A fully separated flow past the NACA0012 airfoil at the angle of attack of 30∘ and Re=1000 is measured in a water tunnel, and non-periodic unsteady flow is analyzed in two dimensions. From the first 1000 frames, transfer functions are calculated based on minimization of different cost functions, which define least-squares errors in the predicted POD modes at the next time step; subsequently, their prediction capabilities are evaluated during the following 1000 frames based on the accuracy of the predicted POD modes at the next time steps. The multistep schemes can reduce the root-mean-square errors of the predicted mode coefficients by up to 10% without a low-pass filter. Combining a low-pass filter with the second-order temporal scheme can further reduce the errors by 7%, and introduction of an L1-norm constraint for the mode coefficients decreases it by extra 2%. In contrast, nonlinear transfer functions with more degrees of freedom deteriorate the prediction during time duration outside of the sampling period even relative to the linear prediction.

Experimental analysis of the stability of the jet wiping process, part II: Multiscale modal analysis of the gas jet-liquid film interaction

This second part of a two-part article on the stability of the jet wiping process focuses on the interaction between the impinging gas jet and the coating liquid film. Using a simplified laboratory model, the first part of the study (Gosset et al., 2019) has shown that this coating process is unstable and leads to wavy coating films. The scaling laws of the problem suggest that this coating nonuniformity does not originate from the liquid coating stability itself, but from a hydrodynamic feedback between the liquid and the impinging jet. This hydrodynamic feedback is herein investigated by combining several optical techniques and data processing methods. Time-Resolved Light Absorption (LAbs) technique is used for the 3D characterization of the coating layer thickness downstream the wiping region, while Time-Resolved Particle Image Velocimetry (TR-PIV) is used to analyze the dynamics of the impinging gas jet, in combination with liquid interface tracking via image processing and Laser Induced Fluorescence (LIF). A link between the frequency content in the liquid film and the jet flow is established. Specifically, the dynamics of the gas jet is analyzed via Multiscale Proper Orthogonal Decomposition (mPOD) of the TR-PIV data and reveals large-scale oscillations which are coupled with waves in the liquid film upstream the wiping, referred to as runback flow. The interaction between the flow structures responsible for the oscillation and the runback liquid film is discussed, showing how this self-sustained mechanism is potentially responsible for the nonuniformity of the final coating.

Dynamic mode decomposition for the inspection of three-regime separated transitional boundary layers using a least squares method

Transitional boundary layers undergoing separated flow transition for different free stream turbulence intensity levels and Reynolds numbers have been inspected by applying dynamic mode decomposition (DMD) to time-resolved particle image velocimetry data. The identification of the unstable modes responsible for transition suffers from nonlinear effects if the whole dataset is considered for the construction of the snapshot matrix underlying the flow evolution. To overcome this limit, piecewise linear models aimed at the identification of the different regimes in the entire transition process are proposed. In particular, the flow is initially laminar (i.e., stable), it becomes unstable due to transition, and once transition is completed, the fully turbulent condition leads the boundary layer to a stable regime. The norm of the residuals resulting from the application of DMD on a variable streamwise extension of the dataset shows a trend that is associated with the variation of regime. This trend is analyzed by means of the least squares method, which allows identifying the change in the regime with stable, unstable, and turbulent behaviors. The validity of this procedure is proved by comparing it with previously published results. Moreover, since the DMD is applied to limited temporal snapshots, it provides a temporal resolution of growth rate and positions of switch between the boundary layer states. Such information is used to extract from the big dataset under analysis the time sequences characterized by the largest growth rate, hence quickly highlighting the flow physics driving transition.

Unsteady pressure estimation and compensation capabilities of the hybrid simulation combining PIV and DNS

The hybrid unsteady-flow simulation, which has been developed to assimilate the Navier–Stokes simulation into a time-resolved particle image velocimetry (PIV) field by synchronizing the frame rate with the direct-numerical-simulation time step, can simultaneously produce an unsteady pressure field. The hybrid process typically introduces a ‘patch function’, which transplants the PIV fields inside the camera window into a larger computational domain. This study evaluates the pressure fields produced by the hybrid simulation inside the patch function (i.e. estimation) and outside of it (i.e. compensation). We take time-resolved planar PIV data of a separated flow past the NACA 0012 airfoil at an angle of attack of 30° in a water tunnel as an example. First, an unsteady pressure field produced from the hybrid simulation is compared with other existing pressure-estimation methods in two dimensions over the entire domain of the camera window. The results of the two-dimensional (2D) hybrid simulation are found to agree best with those of the sequential-integration method with much lower noise levels in time and space. Next, the domain of the forcing is reduced by truncating the patch function in the hybrid simulation, and the pressure fields in the missing parts of the patch function are compared with those solved using the full patch function. When at least the regions in which 2D vortical structures collapse are included in the patch function downstream, the rest of the pressure fields can be compensated for relatively well. In contrast, the forces acting on the airfoil can be estimated accurately only if it is enclosed by the camera window.

Error reduction for time-resolved PIV data based on Navier–Stokes equations

The post-processing of the measured velocity in particle image velocimetry (PIV) is a critical step in reducing error and predicting missing information of the flow field. In this work, time-resolved PIV data are incorporated with the incompressible Navier–Stokes (N–S) equations to reduce the measurement error and improve the accuracy. A pressure correction scheme (PCS) based on the projection method is adopted to solve the N–S equations, and an optimization algorithm is introduced to balance the fidelity between the PIV data and the numerical solutions. The PCS for PIV data, called PIV–PCS, cannot only reduce the errors in the velocity divergence and the curl of the pressure gradient but also ensure that the flow field satisfies the dynamic constraints imposed by the momentum equation. An important weight coefficient s that balances the level of the velocity modification with the residual of the governing equation is defined and numerically assessed. A method for optimizing the value of s is provided. The new approach is evaluated by two time-resolved PIV experiments: one on the 2D wake flow of a circular cylinder at low Reynolds number and one on tomographic PIV for the 3D wake flow of a hemisphere at high Reynolds number. All the numerical assessments and experimental applications are compared with the divergence-free smoothing (DFS) method. The results indicate that the presented PIV–PCS method is superior to the DFS method in terms of reducing the measurement error and recovering the real physical flow structures.

Insights into the dynamics of conical breakdown modes in coaxial swirling flow field

The main idea of this paper is to understand the fundamental vortex breakdown mechanisms in the coaxial swirling flow field. In particular, the interaction dynamics of the flow field is meticulously addressed with the help of high fidelity laser diagnostic tools. Time-resolved particle image velocimetry (PIV) (${\sim}1500~\text{frames}~\text{s}^{-1}$) is employed in $y{-}r$ and multiple $r{-}\unicode[STIX]{x1D703}$ planes to precisely delineate the flow dynamics. Experiments are carried out for three sets of co-annular flow Reynolds number $Re_{a}=4896$, 10 545, 17 546. Furthermore, for each $Re_{a}$ condition, the swirl number ‘$S_{G}$’ is varied independently from $0\leqslant S_{G}\leqslant 3$. The global evolution of flow field across various swirl numbers is presented using the time-averaged PIV data. Three distinct forms of vortex breakdown namely, pre-vortex breakdown (PVB), central toroidal recirculation zone (CTRZ; axisymmetric toroidal bubble type breakdown) and sudden conical breakdown are witnessed. Among these, the conical form of vortex breakdown is less explored in the literature. In this paper, much attention is therefore focused on exploring the governing mechanism of conical breakdown. It is should be interesting to note that, unlike other vortex breakdown modes, conical breakdown persists only for a very short band of $S_{G}$. For any small increase/decrease in $S_{G}$ beyond a certain threshold, the flow spontaneously reverts back to the CTRZ state. Energy ranked and frequency-resolved/ranked robust structure identification methods – proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) respectively – are implemented over instantaneous time-resolved PIV data sets to extract the dynamics of the coherent structures associated with each vortex breakdown mode. The dominant structures obtained from POD analysis suggest the dominance of the Kelvin–Helmholtz (KH) instability (axial $+$ azimuthal; accounts for ${\sim}80\,\%$ of total turbulent kinetic energy, TKE) for both PVB and CTRZ while the remaining energy is contributed by shedding modes. On the other hand, shedding modes contribute the majority of the TKE in conical breakdown. The frequency signatures quantified from POD temporal modes and DMD analysis reveal the occurrence of multiple dominant frequencies in the range of ${\sim}10{-}400~\text{Hz}$ with conical breakdown. This phenomenon may be a manifestation of high energy contribution by shedding eddies in the shear layer. Contrarily, with PVB and CTRZ, the dominant frequencies are observed in the range of ${\sim}20{-}40~\text{Hz}$ only. We have provided a detailed exposition of the mechanism through which conical breakdown occurs. In addition, the current work explores the hysteresis (path dependence) phenomena of conical breakdown as functions of the Reynolds and Rossby numbers. It has been observed that the conical mode is not reversible and highly dependent on the initial conditions.

Poststall Hysteresis and Flowfield Unsteadiness on a NACA 0012 Airfoil

The current study was conducted to understand flowfield unsteadiness associated with static stall hysteresis on a NACA 0012 airfoil at . Unsteady pressure measurements were acquired to evaluate the performance of the airfoil, and the presence of a hysteresis loop was identified in the vicinity of the airfoil . At poststall angles of attack, two fundamentally different flow regimes were observed between the upstroke and downstroke branches of the hysteresis loop. A Fourier analysis of the surface pressure distributions was used to attribute the flowfield unsteadiness to a low-frequency, high-amplitude oscillation in the flow near the leading edge, along with a regular bluff-body shedding frequency across the separated region of the airfoil. The low-frequency oscillations were observed to be more dominant for the upstroke branch, whereas the bluff-body shedding process was more dominant in the downstroke branch. Time-resolved particle image velocimetry data were acquired across the airfoil to qualitatively and quantitatively describe the low-frequency unsteadiness in the flow. These data were used to link the oscillations across the leading edge during the upstroke to a quasi-periodic surging of the flow, along with an advancement and retreating of the separation location across the surface.

Proper orthogonal decomposition-based spatial refinement of TR-PIV realizations using high-resolution non-TR-PIV measurements

A proper orthogonal decomposition (POD)-based spatial refinement approach is proposed to increase the resolution of time-resolved particle image velocimetry (TR-PIV) realizations. POD analysis of the high-resolution non-TR-PIV measurements is used to construct the high-resolution POD modes, and the TR-PIV instantaneous realization with relatively low spatial resolution is cross-projected onto the POD modes to obtain the time-varying mode coefficients. Subsequently, the high-resolution time-resolved flow fields, which inherit the information of the superimposed multi-scale structures from the non-TR-PIV measurements, are reconstructed using the linear combination of the cross-projected mode coefficients and the corresponding high-resolution POD modes. Two main sources of error in the novel strategy are discussed: the cross-projected reconstruction of the instantaneous fields, which are excluded in the determination of the high-resolution POD modes, and the interpolation that maps the high-resolution POD modes onto the coarse grid in the cross-projection process when estimating the mode coefficients. To evaluate the method, the flow fields of a free round jet at Reynolds number $$Re$$ = 3000 are separately measured in the same field-of-view region using non-TR-PIV and TR-PIV setups with a spatial resolution ratio of 42:1. The high- and low-resolution realizations of the instantaneous flow fields measured by the non-TR-PIV setup are determined by applying fine (32 × 32 pixels) and coarse (128 × 128 pixels) interrogation windows, respectively, to ensure accurate fine-to-coarse mapping of the POD modes and for use as a reference to assess the refinement accuracy. This evaluation shows that the combination of these two error sources can be minimized when the POD-sample size (the number of snapshots employed in the decomposition) and the number of POD modes for refinement are optimized. Finally, application of the present method to TR-PIV data shows that the high-resolution time-resolved fields are successfully achieved with the temporal pattern similar to the original TR-PIV realizations, while much smaller structures are captured by the spatially refined flow.

Analysis of the Reynolds stress component production in a laminar separation bubble

Proper Orthogonal Decomposition has been applied to Time-Resolved Particle Image Velocimetry data describing the dynamics of laminar separation bubbles. The mutual orthonormality of the POD modes of the velocity components has been accounted for to separate the contributions to the Reynolds stress tensor due to the different modes, thus to the stress production and the mean flow energy dissipation. The low frequency motion of the separated shear layer, the shedding phenomenon and the formation of finer scales in the rear part of the bubble have been clearly isolated, and their role in the turbulence production identified by means of reduced order models. The low frequency activity observed in the fore part of the separated flow region drives the turbulence production through the normal strain mechanism. Only in the rear part of the bubble the high shear between adjacent vortices establishes the more common shear strain production mechanism, that definitively dominates the transition process. A limited number of modes captures almost the whole process responsible for stress production, even though both Reynolds number and free-stream turbulence intensity levels affect the number of modes involved in the stress generation for different dynamics.

Investigation of intermittent oscillations in a premixed dump combustor using time-resolved particle image velocimetry

The present work deals with time-resolved investigation of the flow field during acoustic self-excitation by a lean premixed flame in a dump combustor. Simultaneous measurements of unsteady pressure, velocity fields using time-resolved particle image velocimetry (TR-PIV) and CH* chemiluminescence are performed. As the equivalence ratio is varied, conditions of maximum pressure amplitude correspond to the prevalence of intermittent bursts in all the measured quantities. The intermittency is quantified by means of the permutation entropy of the pressure signals. The most significant frequencies are identified with the fundamental natural duct acoustic mode and the large-scale vortex roll-up (“wake mode”) frequency. The simultaneous occurrence of these multiple frequencies and shifts in their relative dominance of frequencies over time, shown by wavelet transform, result in the observed intermittent burst oscillations. Regimes of these ordered oscillations alternate with those of relative silence as well. The dynamic mode decomposition (DMD) of the TR-PIV data during windows of decay and growth of intermittent oscillations in the pressure signal quantifies the contribution of the above dominant modes in terms of their temporal growth rates. Besides the above two modes, the flapping mode and the shear layer mode of the flow field are also indicated. Consecutive PIV realisations and chemiluminescence images in a time-resolved sequence during excitation of high pressure amplitude show the large-scale vortex roll-up to substantially convolute the flame, leading to high heat release fluctuations. A further sequence of consecutive flow/flame fields is also examined as to how oscillations emerge out of a relatively silent time interval. The Kelvin–Helmholtz structures of the shear layer mode prevalent during the silent regime are seen to undergo a collective interaction to form a large-scale structure that excites the vortex and acoustic modes in turn.

Comparison of a separated flow response to localized and global-type disturbances

The flow structure and lift response of a separated flow over an airfoil that is subjected to an impulsive type of pitching motion are compared to the response produced by a localized pulse disturbance at the leading edge of an airfoil. Time-resolved PIV data are used to obtain the velocity field on the suction side of the airfoil. POD analysis shows that the majority of energy is contained within the first four modes. Strong similarities in the shapes of the POD basis functions are found, especially for the second mode, irrespective of the type of actuation (global or local). The time-varying coefficient of this second POD mode tracks the negative of the lift coefficient or circulation in each case. Basis functions from the localized actuation data were projected on the velocity field of the globally actuated flow to obtain a hybrid set of coefficients. The hybrid coefficients matched reasonably well with the coefficients obtained from the original POD analysis for the globally excited flow. Both types of actuation were found to generate very similar Lagrangian flow structures. The results suggest a certain degree of universality in the POD modes/flow structures for the separated flow over an airfoil, irrespective of the type of excitation.

Time-supersampling of 3D-PIV measurements with vortex-in-cell simulation

The present work investigates the use of a numerical approximation to the Navier–Stokes equations to increase the temporal resolution of time-resolved PIV data for general flows. The solution of the governing equations is applied to 3D data obtained from tomographic PIV and is based on the vortex-in-cell method (Christiansen in J Comput Phys 13:363–379, 1973) under the hypothesis of incompressible flow. The principle of time-supersampling is that the spatial information can be leveraged to increase the temporal resolution. The unsteady numerical simulation of the dynamic evolution of the flow is applied within the 3D measurement domain and time integration is performed between each pair of consecutive measurements. Initial conditions are taken from the first measurement field and time-resolved boundary conditions are approximated between the two fields. Temporal continuity of the velocity field is obtained by imposing a weighted average of forward and backward time integration. The accuracy of this time-supersampling method is studied for two experimental datasets obtained from time-resolved tomographic PIV measurements: a turbulent wake and a circular jet. The results are compared to linear interpolation, advection-based supersampling, and measurement data at high sampling rate. In both flows, we demonstrate the ability to reconstruct detailed temporal dynamics using data sub-sampled at a rate far below the Nyquist frequency.

Computation of finite-time Lyapunov exponents from time-resolved particle image velocimetry data

This work presents two new methods for computing finite-time Lyapunov exponents (FTLEs) from noisy spatiotemporally resolved experimentally measured image data of the type used for particle image velocimetry (PIV) or particle tracking velocimetry (PTV). These new approaches are based on the simple insight that the particle images recorded during PIV experiments represent Lagrangian flow tracers whose trajectories lend themselves to the direct computation of flow maps, and related quantities such as flow map gradients and FTLEs. We show that using this idea we can improve the reliability and accuracy of FTLE calculation through the use of either direct pathline flow map (PFM) calculation, where individual particle pathlines over a fixed period of time are used to determine the flow map, or particle tracking flow map compilation (FMC), where instantaneous tracking results are used to estimate small snapshots of the flow map which are then compiled to describe the complete flow map. Comparisons of the traditional velocity field integration (VFI) method for computing FTLE fields with these new methods show that FMC produces significantly more accurate estimates of the FTLE field for both synthetic data and experimental data especially in cases where the particle number density is low. This is because the VFI estimates particle motion while PTV directly measures particle motion and therefore generates a more accurate flow map. Overall, our results suggest that VFI is not always a reliable approach when applied to noisy experimental PIV data. For cases where particle loss between frames is minimal, the PFM can also produce better results, but the final field is susceptible to error due to the unstructured nature of the raw flow maps. When comparing the ability to match the true separatrix of a flow, FMC is shown to be a far superior method. The separatrix from FMC has an 80 % overlap with the true solution as compared to approximately 25 % for the PFM and only 1 % for the VFI method. FMC shows a significant advantage when the particle seeding is low, which is particularly relevant for applications to environmental or biological flows where adding seed particles is not always practical, and investigation of Lagrangian flow structures must rely on naturally occurring flow tracers.