Simultaneous LII/PIV measurements are performed within a set of sooting turbulent non-premixed jet flames to study the relationship between soot, velocity and strain rate downstream of the soot inception region. A dual-sensor PIV system was developed which effectively mitigates the broadband luminosity interference from highly sooting flames. The most probable values of velocity where soot is located varies as a function of Reynolds number and downstream location, but likely correspond to common values of mixture fraction (due to the inherent structure of a jet) and indicates a preference towards specific mixing states. Furthermore, the correlation between the local soot volume fraction and velocity fluctuations shows transport behavior indicative of passive scalar mixing. PDFs of total strain rate conditioned on fv show no discernible relationship between strain rate magnitude and fv and no observable difference between sooting and non-sooting conditions. This indicates that the strain rate magnitude plays a negligible role in the occurrence of soot at these locations; that is, finite-rate chemistry effects are minimal compared to transport. Soot layers tend to be aligned with the extensive principal strain rate axis and perpendicular to the compressive principal strain rate axis. The alignment of the soot layers in this region are characteristic of “sheet-like” dissipation layers and further demonstrates that downstream of the soot inception region soot is controlled by passive scalar mixing.Novelty and significance statement: The novelty of this research is the application of joint velocity/soot measurements downstream of the inception region in turbulent non-premixed flames. Particle image velocimetry (PIV) measurements within sooting flames are challenging due to high luminosity interference from the flames when the soot loadings increase beyond a certain threshold. The current paper applies a novel dual-sensor PIV technique which effectively mitigates luminous soot interference and allows simultaneous velocity/soot volume fraction measurements under moderate soot loadings (> 100 ppb). This work extends previous experimental work in the inception region of turbulent jet flames to examine turbulence–soot interaction downstream where turbulent mixing and transport is increasingly important. This work demonstrates the strong alignment between soot structures and principal strain rate components and shows that soot acts as a passive scalar at these conditions. This analysis extends the understanding of the role of flow turbulence and mixing on soot transport.

Filtered Rayleigh scattering (FRS) is a proven laser-based measurement technique that can be used to determine gas-phase properties in the presence of interference from unwanted surface or particulate scattering. In combustion environments, an important issue for conversion of measured FRS signals into temperature is the strong dependence on the local gas mixture composition. Previously, the importance of accurately characterizing the local chemical state has not been systematically evaluated in terms of FRS-based thermometry. Simultaneous quantitative measurements of all pertinent species are quite challenging and involve complex and expensive experimental setups. Thus, there have been previous FRS-specific approaches developed to approximate species composition that circumvent additional multi-scalar measurements. This paper is one of a two-part series that first seeks to evaluate the sensitivity of derived temperature estimates to the local composition and assess existing simplifying assumptions for approximating the unknown composition in laminar premixed flames. This paper uses a combination of simulations and experiments in laminar premixed flames of various fuels and equivalence ratios to understand the importance of composition knowledge/approximation for accurate FRS thermometry results. In general, results show that there is a need to reliably represent the most abundant species and their associated Rayleigh-Brillouin scattering spectral contributions. Approximations of the local composition by a single species lead to significant error (up to 50%) and non-physical results over abroad range of flame conditions. Finally, a simple but robust framework based on state relations from laminar flame calculations is recommended for accounting for composition effects. This approach leads to accurate (<2% error) and reliable FRS-based temperature results in laminar premixed flames without the need for simultaneous species concentration measurements.

The influence of several potential error sources and non-ideal experimental effects on the accuracy of a wavelet-based optical flow velocimetry (wOFV) method when applied to tracer particle images is evaluated using data from a series of synthetic flows. Out-of-plane particle displacements, severe image noise, laser sheet thickness reduction, and image intensity non-uniformity are shown to decrease the accuracy of wOFV in a similar manner to correlation-based particle image velocimetry (PIV). For the error sources tested, wOFV displays a similar or slightly increased sensitivity compared to PIV, but the wOFV results are still more accurate than PIV when the magnitude of the non-ideal effects remain within expected experimental bounds. For the majority of test cases, the results are significantly improved by using image pre-processing filters and the magnitude of improvement is consistent between wOFV and PIV. Flow divergence does not appear to have an appreciable effect on the accuracy of wOFV velocity estimation, even though the underlying fluid transport equation on which wOFV is based implicitly assumes that the motion is divergence-free. This is a significant finding for the broader applicability of planar velocimetry measurements using wOFV. Finally, it is noted that the accuracy of wOFV is not reduced notably in regions of the image between tracer particles, as long as the overall seeding density is not too sparse i.e. below 0.02 particles per pixel. This explicitly demonstrates that wOFV (when applied to particle images) yields an accurate whole field measurement, and not only at or adjacent to the discrete particle locations.

The performance of wavelet-based optical flow velocimetry (wOFV) applied to tracer particle images from hypersonic boundary layer flows is assessed. Two modifications of wOFV to account for the no-slip boundary condition are implemented and assessed to extend the applicability and performance of wOFV to wall-bounded high-speed flows. The first modification (wOFV+) enforces the no-slip boundary condition via constrained optimization, whereas the second modification (wOFV-Ext) performs an antisymmetric extension of the particle images before wOFV processing. The original wOFV and two modified versions are assessed on both (i) synthetic particle images generated from a direct numerical simulation (DNS) of a Mach 4.9 turbulent boundary layer and (ii) actual particle images acquired from a Mach 5 turbulent boundary layer experiment. The velocity estimates using wOFV methods are directly compared to velocity estimates produced by state-of-the-art particle image velocimetry (PIV) software. All three wOFV methodologies were shown to have an increase in accuracy and spatial resolution when compared to PIV. The increase in spatial resolution was shown to be important in the near-wall region (within the viscous sublayer and buffer layer) and for computing shear velocities, u(tau). Overall, both of the no-slip boundary condition modifications were shown to improve accuracy in the near-wall region when compared to both wOFV and PIV.

This paper examines the relationship between soot, thermal gradients, and dissipation rate in a set of sooting, turbulent non-premixed jet flames. Simultaneous two-dimensional filtered Rayleigh scattering (FRS) is used to measure the gas-phase temperature field, while laser-induced incandescence is used to measure soot volume fraction (f(v)). The FRS-based temperature measurements are of sufficiently high signal-to-noise ratio (SNR) and spatial resolution such that accurate temperature gradients and thermal dissipation rate (chi(T)) are determined. chi(T) is used as a surrogate for scalar dissipation rate (chi) within the current sooting flames owing to the high measurement fidelity. Statistical analysis is used to characterize the correlation between soot and dissipation at locations downstream of soot inception, where turbulent transport becomes important. Joint and conditional probability density functions (PDFs) show that for increasing values of f(v), the most probable value of chi(T) shifts to larger magnitudes and that for increases in chi(T), the probability of larger values of f(v) increases. In addition, the conditional mean value of fv increases with increasing values of chi(T). Differences in dissipation statistics were also noted between sooting and non-sooting samples, where the presence of soot is correlated with higher values of chi(T). The alignment between soot and dissipation structures was examined statistically using an alignment angle (theta). PDFs of theta showed high probability of alignment between soot and dissipation layers, indicating their spatial coincidence. Overall, the current results differ from previous direct numerical simulation (DNS) and experimental results that studied the f(v-chi) relationship during early soot inception and concluded soot is associated with low values of dissipation. Potential reasons for the discrepancies are discussed. It is likely that the current measurements are acquired sufficiently downstream such that turbulent mixing and transport govern the observed topology and soot-dissipation relationship.

The current study focuses on characterizing the auto-ignition process from turbulent fuel injection into a high-temperature, vitiated environment using the jet-in-hot-coflow (JHC) burner configuration. High-speed (10-kHz acquisition rate) optical and laser-based diagnostics are used to identify ignition kernel formation and to determine the most probable mixture fraction and temperature conditions that directly facilitate ignition. Four operating cases are studied that present variations in coflow temperature, jet velocity, and fuel type. High-speed OH* chemiluminescence (CL) imaging is used to obtain data on the spatial position and delay time (following fuel injection) of the formation of the first auto-ignition kernels. Over the limited conditions tested, the ignition delay times and heights show a strong sensitivity to temperature and fuel type, but only a mild sensitivity to jet velocity. High-resolution, kHz-rate laser Rayleigh scattering (LRS) is used to provide simultaneous mixture fraction and temperature measurements prior to and at the onset of ignition. High signal-to-noise ratios (SNR >200) enable reliable measurements of mixture fraction at ultra-lean conditions that seemingly promote auto-ignition. A statistical characterization of the most probable mixture fraction values leading to ignition (ξig) is presented and compared with calculated values of the most reactive mixture fraction, ξMR, which has been identified previously from theory and simulations as the parameter governing auto-ignition. Results show that very lean conditions near ξMR are preferentially encountered, but the probability density function (PDF) of ξig is described by a near-exponential distribution, spanning values across the flammability limits. Some limitations to the current methodologies for determining ξig are discussed, which are due primarily to the fact that the discretely sampled mixture fraction data is inherently asynchronous with the ignition event itself.

High-resolution and high signal-to-noise (SNR) planar Rayleigh scattering thermometry measurements are performed to investigate preheat and reaction zone broadening, turbulent transport of hightemperature gases, and the internal flame structure in a series of highly turbulent, lean ( phi = 0.75), premixed methane-air turbulent jet flames. These flames are characterized by turbulence intensities ranging from u ' /S L of 35 to 150 and turbulent Reynolds numbers approaching 10 4 , as determined from separate particle image velocimetry (PIV) measurements. Average flame profiles obtained using a gradient-based flame reconstruction method and probability density functions (PDFs) of the preheat, reaction, and thermal layer thicknesses show substantial broadening of the preheat and thermal layers. Instantaneous preheat zones are broadened by as much as a factor of 30 compared to laminar flames, with an average broadening approaching a factor of 14 for the most turbulent case. Moderate broadening of the reaction layer is observed with up to a factor of eight times that of a laminar premixed flame for instantaneous realizations and an average broadening of four times that of a laminar flame for the most turbulent case. Conditional statistics of temperature obtained at isodistance contours within and upstream of the preheat zone show large shifts towards significantly higher temperatures compared to laminar flame values. In addition, broad temperature distributions and reduced thermal gradients at each position provide strong evidence of persistent turbulent transport of high-temperature gases ahead of the preheat zone. Finally, a detailed analysis of scalar dissipation rate statistics and dissipation layer topology was conducted. The conditional mean scalar dissipation rates for the turbulent flames show significant reductions compared to calculated laminar flame values and a shift towards higher values of the reaction progress variable ( C T ) for increasing turbulence levels. PDFs show a transition from near-Gaussian to highly negatively skewed with increasing turbulence levels, where the most probable values of the scalar dissipation rate shift towards higher values of C T , indicating that the primary reaction zone and flame front are subjected to increased strain. In terms of structure, no significant broadening of the small-scale dissipation layers was observed with increasing turbulence intensity. However, as turbulence intensity increases, there is a transition from a sparse number of continuous layers to a large number of shorter, "broken", nearly straight segments. The reduction of individual layer lengths (i.e., "breaking") is favored over increases in dissipation layer wrinkling, where the sharp decreases in the local dissipation rate values are highly correlated with regions of high curvature. A final notable outcome of this work is that there were negligible differences in all statistical and topological results when moving between the two highest turbulent cases, even though the turbulence intensity, turbulent Reynolds number, and the turbulence Karlovitz number increased substantially (70 - 120%). This implies that there may be an asymptotic limit in which turbulence affects flame behavior for the current configuration. (c) 2023 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

The framework and implementation of a tomographic wavelet-based optical flow velocimetry (TwOFV) technique is demonstrated and assessed. Three-dimensional extensions for both optical flow and the wavelet transform are derived and implemented to extend wavelet-based optical flow velocimetry (wOFV) beyond planar measurements. A quantitative comparison is made for both TwOFV and tomographic particle image velocimetry (tomo-PIV) by applying the algorithms to synthetically generated volumetric particle fields dervied from a direct numerical simulation (DNS) of homogenous isotropic turbulence (HIT). In particular, the techniques were evaluated at four different seed densities that are representative of values used in experiments. TwOFV was shown to have a significant increase in spatial resolution and accuracy at higher seed densities as the TwOFV results show a great deal of similarity between the DNS velocity field ("truth”) and the TwOFV velocity estimate. This work represents a preliminary step towards the realization of high-resolution, volumetric velocimetry using TwOFV and will be utilized to start to guide the selection of a tomographic reconstruction technique along with setting experimental requirements.

This work presents results from simultaneous high-resolution temperature and velocity measurements in a series of turbulent non-premixed jet flames. The filtered Rayleigh scattering (FRS)-based temperature measurements demonstrate sufficient signal-to-noise (SNR) and spatial resolution to estimate the smallest scalar length scales and accurately determine dissipation rate fields. A comprehensive set of conditional statistics are used to characterize the small-scale structure, including the dependence of dissipation layer widths on Reynolds number, temperature, and dissipation magnitude. In general, the dissipation layer thickness decrease with increasing Reynolds number and increase with increasing temperature. However, dissipation layer widths show two distinct behaviors with respect to dissipation magnitude. For small dissipation values, increases in magnitude results in broadening of the dissipation layer, while for larger magnitude values of dissipation, the layer widths are thinned, highlighting the complexity of small-scale turbulent mixing. Additionally, measured ratios of the dissipation layer width to the Batchelor length scale are consistent across all Reynolds numbers and agree with previous studies in non-reacting flows. The unique aspect about the current set of measurements is the ability to examine the interaction of dissipation structure with turbulent flow parameters for the first time in turbulent non-premixed flames. Particularly, the strain rate/dissipation relationship is examined and compared to previous studies in non-reacting flows. It is found that the dissipation layers tend to align normal to the principal compressive strain axis and this tendency increases with increasing Reynolds number. For the lowest Reynolds number case, no dependence of the dissipation layer width nor dissipation rate magnitude on strain rate is found. However, for higher Reynolds numbers, a strong dependence of the dissipation layer width and dissipation rate magnitude on the principal compressive strain rate is observed. These results indicate the direct role of the compressive strain rate field on small-scale mixing structure in reacting flows.

Multi-parameter measurements in sooting turbulent non-premixed flames are presented in this paper. Simultaneous laser-induced incandescence (LII), filtered Rayleigh scattering (FRS), and dual-sensor particle imaging velocimetry (PIV) are applied to yield soot volume fraction, temperature and velocity, respectively. Measurements are acquired within a C2H2/H2/Ar non-premixed flame operating at Reynolds number of 10000. Previous and current results show good accuracy of the FRS-derived temperature in the regions with low soot concentrations. As soot increases, the FRS measurements are subjected to increasing soot interference due to anomalous luminescence which leads to the artificial low temperature structures at the location of the soot. Simultaneous FRS/LII at x/d = 25 and x/d = 50 show different soot interference levels on the FRS measurements with comparable soot volume fractions. This likely implies that the soot interference is a strong function of soot particle diameter versus soot number density. Future analysis is needed to determine the interference-free limits for the FRS measurements under turbulent flame conditions. Dual-sensor PIV is applied to reject high levels of luminous and scattering background interference associated with sooting flames. With proper image registration and calibration, results are consistent with those using a traditional dual-frame, single camera. Instantaneous simultaneous 2D soot volume fraction/temperature/velocity fields are presented to demonstrate the feasibility of yielding a quantitative experimental multi-parameter dataset in soot inception and growth regions within turbulent non-premixed flames. Future work on statistical analyses are discussed in the end of this paper.

This program targeted an improved understanding of how turbulence affects soot formation chemistry (directly and indirectly) with a particular focus on detailing the multiscale coupling between flow turbulence, mixing, thermal transport, and soot formation kinetics in gas-phase reacting systems. In this project, simultaneous, quantitative multi-dimensional velocity, soot volume fraction, and gas-phase temperature measurements in turbulent non-premixed sooting flames were developed. These new diagnostics tools can be used to elucidate the relative effects of fluid kinematics, mixing, thermal processes, and turbulence/scalar time/length scales on soot formation chemistry and topology. Simultaneous multi-parameter measurements were acquired within a series of flames with different Reynolds numbers and spatial locations to investigate the inter-dependence of soot, temperature, and turbulence within the soot inception, growth, and oxidation region. Preliminary assessment of the results has been completed at the project end and detailed analysis is planned following the completed program.

The application of the inverse Abel transformation to statistically axisymmetric data is described in this work. The general theory of Abel inversion tomography is discussed, and it is shown that in order to properly apply the Abel inversion, an ensemble operator must be axisymmetric and commute with path integration. For statistically axisymmetric data where the individual realizations are asymmetric (such as turbulent flows issuing from circular nozzles), only the planar mean can be properly recovered. Higher-order moments, such as the standard deviation (root mean square) cannot be recovered because path integration is not commutative with the statistical moment operators. It is further shown that the Abel transformation cannot be used to recover the one-sided Fourier spectrum for the same reason. For the mean, the Abel inversion can be applied to the ensemble quantity, or the ensemble operator can be applied to the Abel inversion of individual asymmetric realizations. These findings are rigorously verified with numerical simulations and demonstrated on experimental data by comparing planar particle image velocimetry data to path-averaged schlieren image velocimetry results from a turbulent jet of CO2 issuing into ambient air.

An overview of a series of experimental studies focusing on autoignition dynamics at atmospheric conditions is presented. The transient physics, including fluid mechanics and turbulent mixing, governing the formation of the ignition kernels is of primary interest, dictating the necessity for quantitative, high-speed optical and laser diagnostic techniques. Atmospheric pressure studies consist of a cold turbulent fuel-jet issuing in a hot vitiated coflow. High-speed OH* chemiluminescence (CL) imaging is performed to obtain data on the spatial position and the ignition delay time of the formation of the first autoignition kernels under turbulent fuel injection. Simultaneous velocity measurements and OH* CL are performed to directly investigate the effects of the turbulent flow field (through vorticity and strain rate measurements) on autoignition. Rayleigh scattering measurements provide quantitative, simultaneous high-speed mixture fraction and temperature measurements prior to and at the onset of ignition. These measurements provide valuable information on the local mixing and thermal conditions that support ignition under turbulent flow conditions.

Planar velocity measurements were performed in a non-premixed turbulent jet flame using double-shot OH planar laser-induced fluorescence (PLIF) imaging and a wavelet-based optical flow velocimetry (wOFV) method. This study represents an initial experimental evaluation at the feasibility of ``seedless'' velocimetry in reacting flows using wOFV. Results were compared against simultaneous PIV measurements to assess the accuracy of the OH PLIF-wOFV measurements. The accuracy of OH PLIF-wOFV is found to be highly sensitive to the inter-frame displacement of the flow features in the OH PLIF images, as well as the magnitude of the local OH PLIF image intensity gradients. When these two factors are controlled for OH PLIF-wOFV (i.e., rejection of vectors where the image intensity gradient is too small), the velocity results from the two techniques agree in the mean for the streamwise component of the velocity field, although more images are required for OH PLIF-wOFV to converge statistics. However, the transverse velocities estimated with OH PLIF-wOFV have considerably larger error than the PIV results, likely due to a combination of smaller magnitude inter-frame displacements than the streamwise component, and the effect of out-of-plane scalar transport.

A wavelet-based optical flow velocimetry (wOFV) method is evaluated in the context of determining flow velocity from scalar images. A hierarchy of data sets are used to provide an assessment of the scalar-based methodology, including synthetic image pairs of passive scalar fields from 2D and 3D DNS sets and experimental data from a series of turbulent jets. For evaluation on the synthetic data, results are compared to other optical flow methods (using scalar images) found within the literature and correlation-based PIV using synthetic tracer particle images generated from the same DNS. For scalar-based velocimetry, there are two primary sources of error that do not occur for correlation-based PIV or when wOFV is applied to tracer particle-based images: (i) low occurrences (spatially isolated) of high-magnitude errors due to motion ambiguity resulting from poor local contrast in the scalar images and (ii) out-of-plane scalar flux. Overall, the application of the wOFV method to scalar images is less accurate than tracer particle-based approaches (correlation-based PIV or wOFV), but still yields reasonably accurate velocity estimations. The current scalar-based wOFV method compares very favorably to previous scalar image-based optical flow methods and may find utility in cases where it is undesirable or impossible to seed the flow with tracer particles. A parametric study is performed to determine experimental design parameters, including optimal conditions for spatial resolution (i.e., image contrast) and maximum inter-frame displacement. Data from a three-dimensional DNS is used to directly assess errors caused by scalar transport in the direction perpendicular to the imaging plane, which could be present in laser-based planar measurements. Finally, the scalar-based wOFV method is applied to experimental image sequences of passive scalar fields from a series of turbulent jets to serve as proof-of-concept. Initial results show that wOFV may be suitable for velocimetry on experimental scalar images if there is a primary flow direction (i.e., sufficiently two-dimensional flows).

This paper demonstrates the application of a thermometry method in turbulent sooting non-premixed flames using filtered Rayleigh scattering (FRS). Fuel tailoring is used to establish a specific C2H2-based fuel mixture such that temperature can be determined accurately by a single FRS measurement over the entirety of mixture fraction space, or equivalently, for all relevant thermo-chemical states. Evaluation is performed in a hierarchy of flows to establish measurement precision and accuracy. Initial assessments in a series of heated fuel mixtures; non-sooting, near-adiabatic flat flames; and laminar non-premixed sooting flames show accuracy of the approach over a full range of expected temperatures and high single-shot measurement precision (e.g., 65<SNR<80) for temperatures between 1900 and 2200 K. Subsequently, 2D temperature measurements are evaluated in a turbulent non-premixed sooting flame. For the current fuel mixture, the local mixture-averaged Rayleigh scattering cross section is nearly constant over all composition space, and thus traditional laser Rayleigh scattering (LRS) is used as a measurement standard in the absence of soot. The results show excellent agreement between the proposed FRS thermometry approach and LRS in non-sooting regions. In the presence of soot, the proposed FRS-based approach shows no signs of interference. In addition, 2D temperature imaging shows high SNR (60-74) over all temperature conditions. Thus, we believe the proposed methodology successfully provides a high-resolution 2D temperature method under turbulent sooting flame conditions.

An implementation of stereoscopic wavelet-based optical flow velocimetry (swOFV) using a general mapping approach for stereoscopic reconstruction is presented that is suitable for experiments. The methodology is evaluated quantitatively using synthetic tracer particle images generated from a direct numerical simulation (DNS) of homogeneous isotropic turbulence (HIT) and experimental data from a laminar axisymmetric vortex ring. Statistical comparisons between velocity components and gradient quantities are made between swOFV and stereoscopic PIV (sPIV) results. Overall, swOFV shows higher accuracy (approximately 35\% less error near the optimal off-axis angle) and increased spatial resolution as evident through field quantity visualization. The increases in spatial resolution also are observed in the energy and dissipation spectra, as swOFV is capable of resolving the finest dissipative scales. Experimental particle images from a laminar axisymmetric vortex ring were were evaluated and showed a strong topological agreement between swOFV and sPIV as expected for laminar flows. However, the swOFV results exhibited much less noise in the velocity field estimates, which was especially evident in the reconstruction of the out-of-plane velocity ($w$ )component and the out-of-plane vorticity, $\omega_z$. Overall, the updated and generalized implementation of swOFV, which can be implemented experimentally, has been shown to provide higher accuracy and spatial resolution capabilities when compared to sPIV.

The influence of several non-ideal experimental effects on the accuracy of a wavelet-based optical flow (wOFV) method is evaluated using data from a series of simulated flows. Out-of-plane particle displacements and image intensity non-uniformity are shown to decrease the accuracy of wOFV in a similar manner to correlation-based PIV, but with an increased sensitivity compared to correlation-based PIV. However, wOFV is still found to be more accurate than PIV when the magnitude of these effects remain within expected experimental bounds. It is noted that for some cases, the results are significantly improved by using image pre-processing filters. It is observed that flow divergence does not have an appreciable effect on the accuracy of wOFV velocity estimation, even though the fluid transport equation on which wOFV is based implicitly assumes that the motion is divergence-free. This is a significant finding for the broader applicability of planar velocimetry measurements using wOFV. Finally, it is noted that the accuracy of wOFV is not significantly reduced in regions of the image that do not contain particles, as long as the seeding density is sufficiently high. This explicitly demonstrates that wOFV (when applied to particle images) yields an accurate whole field measurement, and not just at the particle locations.

This Letter establishes a physical interpretation of the regularization process that occurs as part of the solution to an optical flow problem within fluids. In doing so, a new regularization scheme for optical flow velocimetry (OFV) methods is developed through direct inspection of the Navier–Stokes equations. To the authors’ knowledge, this is the first time that a regularization scheme has been derived using the governing fluid transport equations for viscous fluids. The current regularization scheme is based on the insight that regularization in OFV should play the same role as viscosity in fluid dynamics. Evaluation on synthetic particle image data from 2D and 3D direct numerical simulations of nonreacting and reacting flows show that the proposed regularization scheme reduces the absolute error and leads to enhanced robustness with respect to the choice of the strength of regularization.

Experimental assessment of a wavelet-based optical flow velocimetry (wOFV) approach for the estimation of two-dimensional velocity fields from tracer particle images is performed. Assessment is performed within a series of free-shear flows and compared to correlation-based particle image velocimetry (PIV). Particle field images were acquired in a series of turbulent jets and in laminar and turbulent wakes behind a circular cylinder. Broad variations in operating conditions were considered, including Reynolds numbers, measurement locations, and image resolution (i.e., magnification or sampling frequency). wOFV is a novel technique that produces a high-resolution velocity estimation with the potential for significant increases in spatial resolution and accuracy when compared to traditional correlation-based PIV. Velocity fields, vorticity fields, and turbulent energy spectra are derived from the wOFV and PIV results for direct comparison. While qualitative agreement is observed between wOFV and PIV results, wOFV is shown to significantly outperform PIV in terms of noise for experiments in which the flow is overly resolved spatially (vector resolution << smallest flow scales), and in terms of effective spatial resolution where the flow is not overly resolved.