Reconstruction Of Velocity Field Research Articles

Enhancement of flow measurements using fluid-dynamic constraints

Novel experimental modalities acquire spatially resolved velocity measurements for steady state and transient flows which are of interest for engineering and biological applications. One of the drawbacks of such high resolution velocity data is their susceptibility to measurement errors. In this paper, we propose a novel filtering strategy that allows enhancement of the noisy measurements to obtain reconstruction of smooth divergence free velocity and corresponding pressure fields which together approximately comply to a prescribed flow model. The main step in our approach consists of the appropriate use of the velocity measurements in the design of a linearized flow model which can be shown to be well-posed and consistent with the true velocity and pressure fields up to measurement and modeling errors. The reconstruction procedure is then formulated as an optimal control problem for this linearized flow model. The resulting filter has analyzable smoothing and approximation properties. We briefly discuss the discretization of the approach by finite element methods and comment on the efficient solution by iterative methods. The capability of the proposed filter to significantly reduce data noise is demonstrated by numerical tests including the application to experimental data. In addition, we compare with other methods like smoothing and solenoidal filtering.

X-ray Doppler Velocimetry: An imaging diagnostic of 3D fluid flow in turbulent plasma

We describe a novel technique for measuring bulk fluid motion in materials that is particularly applicable to very hot, x-ray emitting plasmas in the high energy density physics (HEDP) regime. This X-ray Doppler Velocimetry technique relies on monochromatic imaging in multiple closely-spaced wavelength bands near the center of an x-ray emission line in a plasma, and utilizes bent crystals to provide the monochromatic images. Shorter wavelength bands are preferentially sensitive to plasma moving toward the viewer, while longer wavelength bands are preferentially sensitive to plasma moving away from the viewer. Combining multiple images in different wavelength bands allows for reconstruction of the fluid velocity field integrated along the line of sight. Extensions are also possible for absorption geometries, and for three dimensions. We describe the technique, and we present the results of simulations performed to benchmark the viability of the technique for implosion plasma diagnosis.

Proper orthogonal decomposition truncation method for data denoising and order reduction

Proper orthogonal decomposition (POD) is used widely in experimental fluid dynamics for reducing noise in a measured flow field. The efficacy of POD is governed by the selection of modes used for the velocity field reconstruction. Currently, the determination of which or how many modes to keep is a user-defined subjective choice, where an arbitrary amount of energy to retain in the reconstruction, such as 99% cumulative energy, is chosen. Here, we present a novel, fully autonomous, and objective mode-selection method, which we term the entropy-line fit (ELF) method. The ELF method computes the Shannon entropy of the spatial discrete cosine transform of the eigenmodes, and using a two-line fit of the entropy mode spectrum, distinguishes between the modes carrying meaningful signal and those containing noise. We compare the ELF and existing methods using the analytical Hama flow field, synthetic PIV velocity fields derived from DNS turbulent channel flow data, and experimental particle image velocimetry vortex ring data. Overall, the ELF method improves the effectiveness of POD at removing noise from experimentally measured flow fields and subsequently the accuracy of post-processing calculations.

Correlated noise and prior models in electromagnetic flow tomography

Electromagnetic flow meters are a gold standard in measuring the mean flow velocity of conductive liquids and slurries in process industry. A drawback of this approach is that the velocity field cannot be determined. Information about velocity fields is important for characterizing multiphase flows in the process industry. Recently, electromagnetic flow tomography (EMFT) has been proposed for measuring velocity fields using several coils and a set of electrodes attached to the inner surface of the pipe. The velocity field reconstruction method utilizes a finite element based computational forward model and a Bayesian framework for inverse problem. In the approach, a priori probability and noise models are written describing the flow and measurement error characteristics, respectively. In this work, the effect of additive, possibly correlated, measurement noise and different prior models on the velocity field reconstructions in EMFT are tested using numerical simulations. The results show that the velocity field reconstruction method produces feasible estimates even with relatively high level of correlated measurement noise if the covariance structure of the noise is taken into account. In practice, the noise covariance can be estimated from measurements using sample based methods. Moreover, it is shown that a smoothness prior using a squared exponential covariance function is in general a good choice for the prior model and more advanced prior models for specific flow types such as stratified or turbulent flows can be used.

Towards an optimal sampling of peculiar velocity surveys for Wiener Filter reconstructions

The Wiener Filter (WF) technique enables the reconstruction of density and velocity fields from observed radial peculiar velocities. This paper aims at identifying the optimal design of peculiar velocity surveys within the WF framework. The prime goal is to test the dependence of the quality of the reconstruction on the distribution and nature of data points. Mock datasets, extending to 250 Mpc/h, are drawn from a constrained simulation that mimics the local Universe to produce realistic mock catalogs. Reconstructed fields obtained with these mocks are compared to the reference simulation. Comparisons, including residual distributions, cell-to-cell and bulk velocities, imply that the presence of field data points is essential to properly measure the flows. The fields reconstructed from mocks that consist only of galaxy cluster data points exhibit poor quality bulk velocities. In addition, the quality of the reconstruction depends strongly on the grouping of individual data points into single points to suppress virial motions in high density regions. Conversely, the presence of a Zone of Avoidance hardly affects the reconstruction. For a given number of data points, a uniform sample does not score any better than a sample with decreasing number of data points with the distance. The best reconstructions are obtained with a grouped survey containing field galaxies: Assuming no error, they differ from the simulated field by less than 100 km/s up to the extreme edge of the catalogs or up to a distance of three times the mean distance of data points for non-uniform catalogs. The overall conclusions hold when errors are added.

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Effect of smoothing of density field on reconstruction and anisotropic BAO analysis.

The reconstruction algorithm introduced by Eisenstein et al., which is widely used in clustering analysis, is based on the inference of the first-order Lagrangian displacement field from the Gaussian smoothed galaxy density field in redshift space. The smoothing scale applied to the density field affects the inferred displacement field that is used to move the galaxies, and partially erases the non-linear evolution of the density field. In this article, we explore this crucial step in the reconstruction algorithm. We study the performance of the reconstruction technique using two metrics: first, we study the performance using the anisotropic clustering, extending previous studies focused on isotropic clustering; secondly, we study its effect on the displacement field. We find that smoothing has a strong effect in the quadrupole of the correlation function and affects the accuracy and precision with which we can measure DA(z) and H(z). We find that the optimal smoothing scale to use in the reconstruction algorithm applied to Baryonic Oscillations Spectroscopic Survey-Constant (stellar) MASS (CMASS) is between 5 and 10 h−1 Mpc. Varying from the ‘usual’ 15–5 h−1 Mpc shows ∼0.3 per cent variations in DA(z) and ∼0.4 per cent H(z) and uncertainties are also reduced by 40 per cent and 30 per cent, respectively. We also find that the accuracy of velocity field reconstruction depends strongly on the smoothing scale used for the density field. We measure the bias and uncertainties associated with different choices of smoothing length.

The role of 3D-hydraulics in habitat modelling of hydropeaking events

One way to study ecological implications induced by hydropeaking represents the coupling of hydrodynamic models with habitat suitability models, in which hydrodynamic parameters are typically used to describe the physical habitat of indicator species. This article discusses the differences in habitat suitability assessment between 2D and 3D CFD modelling as input for the habitat simulation tool CASiMiR. In the first part of the article, the accuracy of the hydraulic model is evaluated by comparing the model results with laboratory (model of a laboratory channel with erodible bed) and field measurements (Valsura River, Bolzano, Italy). In the second part, the habitat suitability for the Valsura River case study (affected by hydropeaking), is analyzed comparing different approaches for the reconstruction of the velocity field (depth-averaged velocities from 2D modelling, bottom velocity field reconstruction with log-law approach from 2D modelling and bottom velocity field from 3D modelling). The results show that the habitat suitability index (HSI) using 2D or 3D hydrodynamic models can be significantly different. These differences can be ascribed to a higher capability to depict the features of the flow field with highly variable and heterogeneous boundary conditions and to the possibility to simulate the near bed hydrodynamic parameters, which are relevant for certain target species. In particular, the HSI-values using 3D hydraulics lead to larger areas of highly suitable habitats compared to 2D simulations. Moreover, considering the entire flow range of hydropeaking events, the habitat simulations with bottom flow velocities from 3D modelling provide suitable habitats over the entire flow range representing the availability of stable suitable habitats, while the habitat availability of 2D modelled flow velocity is continuously decreasing with increasing flow rates.

Goodness-of-fit analysis of the Cosmicflows-2 data base of velocities

The goodness-of-fit (GoF) of the Cosmicflows-2 (CF2) database of peculiar velocities with the LCDM standard model of cosmology is presented. Standard application of the Chi^2 statistics of the full database, of its 4,838 data points, is hampered by the small scale nonlinear dynamics which is not accounted for by the (linear regime) velocity power spectrum. The bulk velocity constitutes a highly compressed representation of the data which filters out the small scales non-linear modes. Hence the statistics of the bulk flow provides an efficient tool for assessing the GoF of the data given a model. The particular approach introduced here is to use the (spherical top-hat window) bulk velocity extracted from the Wiener filter reconstruction of the 3D velocity field as a linear low pass filtered highly compressed representation of the CF2 data. An ensemble 2250 random linear realizations of the WMAP/LCDM model has been used to calculate the bulk velocity auto-covariance matrix. We find that the CF2 data is consistent with the WMAP/LCDM model to better than the 2 sigma confidence limits. This provides a further validation that the CF2 database is consistent with the standard model of cosmology.

Reconstruction of velocity fields in electromagnetic flow tomography.

Electromagnetic flow meters (EMFMs) are the gold standard in measuring flow velocity in process industry. The flow meters can measure the mean flow velocity of conductive liquids and slurries. A drawback of this approach is that the velocity field cannot be determined. Asymmetric axial flows, often encountered in multiphase flows, pipe elbows and T-junctions, are problematic and can lead to serious systematic errors. Recently, electromagnetic flow tomography (EMFT) has been proposed for measuring velocity fields using several coils and a set of electrodes attached to the surface of the pipe. In this work, a velocity field reconstruction method for EMFT is proposed. The method uses a previously developed finite-element-based computational forward model for computing boundary voltages and a Bayesian framework for inverse problems. In the approach, the vz-component of the velocity field along the longitudinal axis of the pipe is estimated on the pipe cross section. Different asymmetric velocity fields encountered near pipe elbows, solids-in-water flows in inclined pipes and in stratified or multiphase flows are tested. The results suggest that the proposed reconstruction method could be used to estimate velocity fields in complicated pipe flows in which the conventional EMFMs have limited accuracy. This article is part of the themed issue 'Supersensing through industrial process tomography'.

Mass-conservative reconstruction of Galerkin velocity fields for transport simulations

Accurate calculation of mass-conservative velocity fields from numerical solutions of Richards’ equation is central to reliable surface–subsurface flow and transport modeling, for example in long-term tracer simulations to determine catchment residence time distributions. In this study we assess the performance of a local Larson-Niklasson (LN) post-processing procedure for reconstructing mass-conservative velocities from a linear (P1) Galerkin finite element solution of Richards’ equation. This approach, originally proposed for a-posteriori error estimation, modifies the standard finite element velocities by imposing local conservation on element patches. The resulting reconstructed flow field is characterized by continuous fluxes on element edges that can be efficiently used to drive a second order finite volume advective transport model. Through a series of tests of increasing complexity that compare results from the LN scheme to those using velocity fields derived directly from the P1 Galerkin solution, we show that a locally mass-conservative velocity field is necessary to obtain accurate transport results. We also show that the accuracy of the LN reconstruction procedure is comparable to that of the inherently conservative mixed finite element approach, taken as a reference solution, but that the LN scheme has much lower computational costs. The numerical tests examine steady and unsteady, saturated and variably saturated, and homogeneous and heterogeneous cases along with initial and boundary conditions that include dry soil infiltration, alternating solute and water injection, and seepage face outflow. Typical problems that arise with velocities derived from P1 Galerkin solutions include outgoing solute flux from no-flow boundaries, solute entrapment in zones of low hydraulic conductivity, and occurrences of anomalous sources and sinks. In addition to inducing significant mass balance errors, such manifestations often lead to oscillations in concentration values that can moreover cause the numerical solution to explode. These problems do not occur when using LN post-processed velocities.

The alignment of galaxy spin with the shear field in observations

Tidal torque theory suggests that galaxies gain angular momentum in the linear stage of structure formation. Such a theory predicts alignments between the spin of haloes and tidal shear field. However, non-linear evolution and angular momentum acquisition may alter this prediction significantly. In this paper, we use a reconstruction of the cosmic shear field from observed peculiar velocities combined with spin axes extracted from galaxies within $115\, \mathrm{Mpc} $ ($\sim8000 \, {\mathrm {km}}{\mathrm s}^{-1}$) from 2MRS catalog, to test whether or not galaxies appear aligned with principal axes of shear field. Although linear reconstructions of the tidal field have looked at similar issues, this is the first such study to examine galaxy alignments with velocity-shear field. Ellipticals in the 2MRS sample, show a statistically significant alignment with two of the principal axes of the shear field. In general, elliptical galaxies have their short axis aligned with the axis of greatest compression and perpendicular to the axis of slowest compression. Spiral galaxies show no signal. Such an alignment is significantly strengthened when considering only those galaxies that are used in velocity field reconstruction. When examining such a subsample, a weak alignment with the axis of greatest compression emerges for spiral galaxies as well. This result indicates that although velocity field reconstructions still rely on fairly noisy and sparse data, the underlying alignment with shear field is strong enough to be visible even when small numbers of galaxies are considered - especially if those galaxies are used as constraints in the reconstruction.

Bayesian 3D velocity field reconstruction with virbius

I describe a new Bayesian based algorithm to infer the full three dimensional velocity field from observed distances and spectroscopic galaxy catalogues. In addition to the velocity field itself, the algorithm reconstructs true distances, some cosmological parameters and specific non-linearities in the velocity field. The algorithm takes care of selection effects, miscalibration issues and can be easily extended to handle direct fitting of, e.g., the inverse Tully-Fisher relation. I first describe the algorithm in details alongside its performances. This algorithm is implemented in the VIRBIuS (VelocIty Reconstruction using Bayesian Inference Software) software package. I then test it on different mock distance catalogues with a varying complexity of observational issues. The model proved to give robust measurement of velocities for mock catalogues of 3,000 galaxies. I expect the core of the algorithm to scale to tens of thousands galaxies. It holds the promises of giving a better handle on future large and deep distance surveys for which individual errors on distance would impede velocity field inference.

Analysis of Particle Image Velocimetry Measurements of Natural Convection in an Enclosure Using Proper Orthogonal Decomposition

This work investigates natural convection in an enclosure with localized heating on the bottom wall with a flushed or protruded heat source and cooled on the top and the side walls. Velocity field measurements are done by using 2D particle image velocimetry (PIV) technique. Proper orthogonal decomposition (POD) has been used to create low dimensional approximations of the system for predicting the flow structures. The POD-based analysis reveals the modal structure of the flow field and also allows reconstruction of velocity field at conditions other than those used in PIV study.

Modified gravity and large scale flows

Reconstruction of the local velocity field from the overdensity field and a gravitational acceleration that falls off from a point mass as r −2 yields velocities in broad agreement with peculiar velocities measured with galaxy distance indicators. MONDian gravity does not. To quantify this, we introduce the velocity angular correlation function as a diagnostic of peculiar velocity field alignment and coherence as a function of scale. It is independent of the bias parameter of structure formation in the standard model of cosmology and the acceleration parameter of MOND. A modified gravity acceleration consistent with observed large scale structure would need to asymptote to zero at large distances more like r −2, than r −1.

Experimental investigation of the vortex breakdown in a lean premixing prevaporizing burner

The spiral vortex breakdown has been experimentally studied in the flow field generated by a lean premixing prevaporizing (LPP) combustor model. The vortex breakdown structures are characterized by a solid-body rotation. Hence, phase-locked laser Doppler velocimeter measurements, performed in a meridional plane, have allowed reconstruction of the periodic velocity and Reynolds stress fields within a time period and in a relative cylindrical frame of reference. Then, the turbulent kinetic energy (TKE) production term has been computed. The velocity distribution analysis indicates that a spiral vortex core wraps around an inner reverse flow zone. Both are characterized by a precessing motion. Then, the main contributions to the TKE production have been identified together with their spatial locations. Their distribution indicates that the maxima are placed in two regions: one located between the inner reverse flow and the spiral vortex and the second between the spiral vortex core and the external nearly quiescent fluid. In the latter, the TKE production term distributions have the features of a Kelvin–Helmholtz-like instability. In the former, the TKE production seems to be related to a Kelvin–Helmholtz-like instability only at the interface between the bubble and the spiral vortex core.

Signal Processing in Synthestic-Aperture Radars During the Formation of the Earth-Surface Velocity Fields

We consider the signal-processing principles during the Earth-surface sounding by syntheticaperture radars (SARs) including the along-track interference radars. The aperture-synthesis features for solving two problems, namely the measurements of the local-reflector velocity and reconstruction of the velocity pattern of the rough surface, are discussed. The features of these problems and restrictions related to the aperture-synthesis process and other factors including the limited radiated power of a space radar are considered. Conclusions on the possibilities of the radar reconstruction of the surface velocity fields for both the local reflectors and the extended surface (sea currents) are drawn. Approximate calculations of the available parameters of the recorded fields in the SARs mounted onboard low-orbit spacecraft are performed.

Three-dimensional reconstruction of cardiac flows based on multi-planar velocity fields

Measurement of the three-dimensional flow field inside the cardiac chambers has proven to be a challenging task. This is mainly due to the fact that generalized full-volume velocimetry techniques cannot be easily implemented to the heart chambers. In addition, the rapid pace of the events in the heart does not allow for accurate real-time flow measurements in 3D using imaging modalities such as magnetic resonance imaging, which neglects the transient variations of the flow due to averaging of the flow over multiple heartbeats. In order to overcome these current limitations, we introduce a multi-planar velocity reconstruction approach that can characterize 3D incompressible flows based on the reconstruction of 2D velocity fields. Here, two-dimensional, two-component velocity fields acquired on multiple perpendicular planes are reconstructed into a 3D velocity field through Kriging interpolation and by imposing the incompressibility constraint. Subsequently, the scattered experimental data are projected into a divergence-free vector field space using a fractional step approach. We validate the method in exemplary 3D flows, including the Hill’s spherical vortex and a numerically simulated flow downstream of a 3D orifice. During the process of validation, different signal-to-noise ratios are introduced to the flow field, and the method’s performance is assessed accordingly. The results show that as the signal-to-noise ratio decreases, the corrected velocity field significantly improves. The method is also applied to the experimental flow inside a mock model of the heart’s right ventricle. Taking advantage of the periodicity of the flow, multiple 2D velocity fields in multiple perpendicular planes at different locations of the mock model are measured while being phase-locked for the 3D reconstruction. The results suggest the metamorphosis of the original transvalvular vortex, which forms downstream of the inlet valve during the early filling phase of the right ventricular model, into a streamline single-leg vortex extending toward the outlet.

Acoustic propagation in two-dimensional waveguide for membrane bounded ducts

This work aims to investigate the mode-matching (MM) and low frequency approximation (LFA) solutions of a two dimensional waveguide problem with flanged junction. The relative merits of each approach are compared for the scattering of fluid-coupled wave. The boundary value problem involving higher order derivatives at boundaries becomes a non-Sturm–Liouville problem where the use of standard orthogonality relation (OR) enables the MM solution. The derivation of LFA is made which proves to be surprisingly accurate for structure-borne mode incident. In order to validate the truncated model expansion the distribution of power in duct regions is discussed and Gibbs oscillations are incorporated by reconstruction of the normal velocity field using Lanczos filter.

Ultrasonic Tomographic Velocity Field Imaging Based on Interlaced Chord Network

Ultrasonic velocity tomography is a novel technique for velocity field measurement with the advantages of being non-invasive and insensitive to fluid properties. But its application is limited by poor spatial resolution. Thus, a novel ultrasonic velocity tomography method based on an interlaced chord network is proposed in this paper. To form the interlaced chord network, transducers are installed at two mounting planes of the pipe with N transducers on each plane, and 2×N transducers are equally spaced along the pipe circumference. In particular, N is selected to be an odd number to avoid blind zone. The average velocity on each chord is scanned in a fan-beam mode and used as projection data for velocity field reconstruction. The projection data are rearranged into a parallel beam mode and interpolated at a uniform interval. A filtered back projection algorithm is employed for 2-dimensional reconstruction of the velocity field. Numerical simulation experiments show that, the spatial resolution is improved obviously by the interlaced chord network without introducing extra transducers and 13 transducers on each mounting plane are enough for actual velocity field imaging downstream a single-bend pipe.

Study of in situ calibration performance of co-located multi-sensor hot-film and sonic anemometers using a ‘virtual probe’ algorithm

The performance of an in situ calibration technique, implementing neural network (NN) algorithms for co-located multi-wire hot-film and sonic anemometers, is studied. The NN-based calibration technique, proposed by Kit et al (2010 J. Atmos. Ocean. Technol. 27 23–41), allows performing direct measurement of fine scales in turbulent air flow, and offers a robust tool for measurements of micro-scale properties in atmospheric flows. Accuracy of the suggested calibration technique is examined in view of isotropic and anisotropic flow fields of various turbulence intensity (TI). Anisotropic velocity datasets of various TIs were generated using a ‘virtual probe’ simulating hot-film anemometer response to the sensed flow, while a kinematic model of homogeneous isotropic turbulent flow was implemented to generate isotropic flow datasets. NN calibration performance is examined by quantitative comparison between the original and reconstructed velocity components, using a specially constructed norm and by visual comparison of original and reconstructed time series. The examined NN calibration technique performance is shown to be of reasonable accuracy for all TI velocity fields examined, while a notable drop in accuracy is detected with the increase in TI. The reconstruction of isotropic velocity fields, using the NN algorithm for calibration, is apparently of slightly lower accuracy than in the case of anisotropic flows. The results are discussed in view of possible implementation of the suggested technique in direct field measurements of atmospheric turbulence fine scales.