Reconstruction Of Velocity Field Research Articles

Enforcing temporal consistency in physically constrained flow field reconstruction with FlowFit by use of virtual tracer particles

Processing techniques for particle-based optical flow measurement data such as 3D particle tracking velocimetry (PTV) or the novel dense Lagrangian particle tracking method ‘Shake-the-Box’ (STB) can provide time-series of velocity and acceleration information scattered in space. The following post-processing is key to the quality of space-filling velocity and pressure field reconstruction from the scattered particle data. In this work we describe a straight-forward extension of the recently developed data assimilation scheme FlowFit, which applies physical constraints from the Navier–Stokes equations in order to simultaneously determine velocity and pressure fields as solutions to an inverse problem. We propose the use of additional artificial Lagrangian tracers (virtual particles), which are advected between the flow fields at single time instants to achieve meaningful temporal coupling. This is the most natural way of a temporal constraint in the Lagrangian data framework. FlowFit’s core method is not altered in the current work, but rather its input in the form of Lagrangian tracks. This work shows that the introduction of such particle memory to the reconstruction process significantly improves the resulting flow fields. The method is validated in virtual experiments with two independent DNS test cases. Several contributions are revised to explain the improvements, including correlations of velocity and acceleration errors in the reconstructions and the flow field regularization within the inverse problem.

Multiple joint wavefield inversions: Theory and field data implementations

Accurate velocity models for the near surface and overburden are needed for seismic processing and reliable depth imaging. Seismic with multiphysics data, well logs, and geology information need to be quantitatively integrated to obtain high-resolution velocity models. We detail our development and application of the joint wavefield inversion software platform, which enables flexible algorithmic schemes for the integration of multiparameter data and constraints. Inversion is performed in cascade or simultaneously using a variety of input data to constrain the velocity field reconstruction at multiple scales. Coupling mechanisms based on structure similarity together with rock-physics relations are optimally combined to boost resolution and enhance accuracy of the inverted velocity models. Ill-posed inversion problems are then solved using extensive geologic and rock-physics regularization instead of relying on smoothness constraints alone. We detail workflows and algorithms to guide the application of multiparameter joint inversion for velocity model building whether the input data are seismic traveltimes, electromagnetics (time/frequency domains), gravity, and/or surface waves. Extensive applications of multiparameter joint inversion are presented for a variety of complex geologic scenarios in which various multiparameter coupling strategies are illustrated. Robust velocity modeling and enhanced seismic imaging in time and depth domains are obtained as a result, proving the importance of multiphysics integration for reliable earth model parameter estimation.

Multi-parameter inversion with the aid of particle velocity field reconstruction

Multi-parameter inversion for medical ultrasound leads to an improved tissue classification. In general, simultaneous reconstruction of volume density of mass and compressibility would require knowledge of the particle velocity field along with the pressure field. However, in practice the particle velocity field is not measured. Here, the authors propose a method for multi-parameter inversion where the particle velocity field is reconstructed from the measured pressure field. To this end, the measured pressure field is described using outward propagating Hankel functions. For a synthetic setup, it is shown that the reconstructed particle velocity field matches the forward modelled particle velocity field. Next, the reconstructed particle velocity field is used together with the synthetically measured pressure field to reconstruct density and compressibility profiles with the aid of contrast source inversion. Finally, comparing the reconstructed speed of sound profiles obtained via single-parameter versus multi-parameter inversion shows that multi-parameter outperforms single-parameter inversion with respect to accuracy and stability.

A note on the reconstruction of a 3D-3C velocity field for box turbulence

We examine the reconstruction of a three-dimensional three-component (3D-3C) snapshot velocity field in a torus using a denoising method of compressed sensing. Using 30% of the total grid points, we could reconstruct the velocity with a relative error of approximately 10%.

Low-order estimation of the velocity, hydrodynamic pressure, and acoustic radiation for a three-dimensional turbulent wall jet

A method for the experimental characterization of the velocity, hydrodynamic pressure, and acoustic generation in a subsonic (ReH=25,500), three-dimensional, turbulent wall jet is presented. An acoustic analogy formulated for the turbulent wall jet shows that the far-field acoustics relate to the Reynolds stress fluctuations of the velocity field or the product of the hydrodynamic pressure fluctuations and the rate-of-strain field. As these quantities cannot be measured directly with sufficient resolution, low-order reconstructions of the velocity field based on the use of the Proper Orthogonal Decomposition and Stochastic Estimation are developed. Reconstruction of the three-dimensional field is accomplished using spanwise-aligned, stereoscopic particle image velocimetry measurements, obtained at 16 streamwise locations synchronously with an array of 32 surface pressure transducers. The velocity field reconstruction is then used to calculate the fluctuating pressure field (via Poisson’s equation) allowing for the evaluation of coupled pressure-velocity terms in addition to an acoustic analogy for the acoustic far-field. Application of these methods show that the large-scale motion throughout the shear layer is captured by the velocity and hydrodynamic pressure field estimates and features of the acoustic far-field are recovered.

A CFD-DEM-IBM method for Cartesian grid simulation of gas-solid flow in complex geometries

The use of CFD-DEM method to accurately simulate gas-solid flows in complex geometries is challenging, mainly due to the complexity related to the use of unstructured computational grids. In order to solve this problem, researchers have simulated gas-solid fluidized beds with complex geometries using CFD-DEM-IBM method with Cartesian grids. In present study the gas-solid flows in complex geometries were simulated using Cartesian grids following the basic idea of CFD-DEM-IBM method (De Jong et al., 2012), where the interactions between gas phase and complex geometries were firstly modelled using the immersed boundary method (IBM) implemented by Tuković and Jasak (2012) in OpenFOAM®. It was found that the computational efficiency is quite low. To improve the efficiency of the CFD-DEM-IBM solver, a new IBM method was then proposed by removing the neighboring immersed boundary cells from the interpolated extended stencil in the reconstruction of the velocity and pressure fields near the wall, and further proposing a new zero-gradient boundary condition to replace the original Neumann boundary condition for reconstructing the pressure field. Single-phase flow past a stationary cylinder, single-phase pipe flow, gas-solid flow in a cylindrical fluidized bed and fluidized bed with immersed tubes were simulated with four different IBM imposition methods to assess the accuracy and efficiency of sharp-interface CFD-DEM-IBM solver. It was shown that (i) the results of CFD-DEM-IBM simulations agree well with the reported experimental, analytical and/or numerical results available in literature; and (ii) the computational efficiency of newly proposed CFD-DEM-IBM solver is one or two order of magnitudes faster than that of the original IBM of Tuković and Jasak (2012) in OpenFOAM®, due to the fact that internal iterations are not needed anymore during the reconstruction of velocity and pressure fields.

Secondary currents and very-large-scale motions in open-channel flow over streamwise ridges

It is widely acknowledged that streamwise ridges on the bed of open-channel flows generate secondary currents (SCs). A recent discovery of meandering long streamwise counter-rotating vortices in open-channel flows, known as very-large-scale motions (VLSMs), raises a question regarding the interrelations between VLSMs and SCs in flows over ridge-covered fully rough beds. To address it, we conducted long-duration experiments using stereoscopic particle image velocimetry, covering a range of ridge spacings ( ) from to flow depths ( ). For a benchmark no-ridge case, the flow is quasi-two-dimensional in the central part of the channel, exhibiting a strong spectral signature of VLSMs, as expected. With ridges on the bed at , two SC cells are formed between neighbouring ridges and VLSMs are entirely suppressed, suggesting that ridge-induced SCs prevent the formation of VLSMs by absorbing their energy or overpowering their formation. At the same time, velocity auto- and cross-spectra reveal a new feature that can be explained by low-amplitude meandering of the alternating low- and high-momentum flow regions associated with instantaneous manifestations of SCs. Two-point velocity correlations and smooth velocity field reconstructions using proper orthogonal decomposition further support the validity of this effect. Its origin is probably due to the instability related to the presence of inflection points in the spanwise distribution of the streamwise velocity within the SC cells. These results have implications for bed friction in open channels, where the friction factor may increase if depth-scale SCs are present, or decrease under conditions of sub-depth-scale SCs and suppressed VLSMs.

Testing self-interacting dark matter with galaxy warps

Self-interacting dark matter (SIDM) is an able alternative to collisionless dark matter. If dark matter does have self-interactions, we would expect this to cause a separation between the collisionless stars and the dark matter halo of a galaxy as it falls through a dark matter medium. For stars arranged in a disk, this would generate a U-shaped warp. The magnitude of this warping depends on the SIDM cross section, type of self-interaction, relative velocity of galaxy and background, halo structure, and density of the dark matter medium. In this paper, we set constraints on long-range (light mediator) dark matter self-interaction by means of this signal. We begin by measuring U-shaped warps in $3,213$ edge-on disk galaxies within the Sloan Digital Sky Survey. We then forward-model the expected warp from SIDM on a galaxy-by-galaxy basis by combining models of halo structure, density and velocity field reconstructions, and models for the dark matter interactions. We find no evidence for a contribution to the warps from SIDM. Our constraints are highly dependent on the uncertain velocities of our galaxies: for a normalized Rutherford-like cross section we find $\tilde{\sigma}/m_{\rm{DM}} \lesssim 3\times 10^{-13}~\rm{cm}^2/\rm{g}$ at fixed velocity $v = 300~\rm{km/s}$ -- a bound that scales roughly linearly with increasing $v$. In the appendix we translate these bounds into limits on the momentum transfer cross section, finding $\sigma_T(300~\rm{km/s})/m_{\rm{DM}} \lesssim 0.1~\rm{cm}^2/\rm{g}$. [abridged]

Super-resolution reconstruction of turbulent velocity fields using a generative adversarial network-based artificial intelligence framework

A general super-resolution reconstruction strategy was proposed for turbulent velocity fields using a generative adversarial network-based artificial intelligence framework. Two advanced neural networks, i.e., super-resolution generative adversarial network (SRGAN) and enhanced-SRGAN (ESRGAN), were first applied in fluid mechanics to augment the spatial resolution of turbulent flow. As a validation, the flow around a single-cylinder and a more complicated wake flow behind two side-by-side cylinders were experimentally measured using particle image velocimetry. The spatial resolution of the coarse flow field can be successfully augmented by 42 and 82 times with remarkable accuracy. The reconstruction performances of SRGAN and ESRGAN were comprehensively investigated and compared, including an analysis of the recovered instantaneous flow field, statistical flow quantities, and spatial correlations. The results convincingly demonstrated that both models can reconstruct the high-spatial-resolution flow field accurately even in an intricate flow configuration, and ESRGAN can provide a better reconstruction result than SRGAN in the mean and fluctuation flow field.

Simultaneous reconstruction of temperature and velocity fields using nonlinear acoustic tomography

Acoustic tomography developed and investigated before can only recover either the temperature or the velocity field from the time-of-flight measurements along a single direction of sonic rays. However, the sonic propagation time is a nonlinear function of temperature and velocity; thus, in principle, the measurements allow us to reconstruct both simultaneously. In order to achieve this, we propose a modality of acoustic tomography based on the recently proposed concept of nonlinear tomography, which can take full advantage of the aforementioned nonlinear dependences. Proof-of-concept numerical demonstrations are presented using representative two-dimensional temperature and flow velocity phantoms. The obtained simulative results confirmed the feasibility of nonlinear acoustic tomography in recovering the distributions of temperature and velocity fields.

Beyond BAO: Improving cosmological constraints from BOSS data with measurement of the void-galaxy cross-correlation

We present a measurement of the anisotropic void-galaxy cross-correlation function in the CMASS galaxy sample of the BOSS DR12 data release. We perform a joint fit to the data for redshift space distortions (RSD) due to galaxy peculiar velocities and anisotropies due to the Alcock-Paczynski (AP) effect, for the first time using a velocity field reconstruction technique to remove the complicating effects of RSD in the void centre positions themselves. Fits to the void-galaxy function give a 1% measurement of the AP parameter combination $D_A(z)H(z)/c = 0.4367\pm 0.0045$ at redshift $z=0.57$, where $D_A$ is the angular diameter distance and $H$ the Hubble parameter, exceeding the precision obtainable from baryon acoustic oscillations (BAO) by a factor of ~3.5 and free of systematic errors. From voids alone we also obtain a 10% measure of the growth rate, $f\sigma_8(z=0.57)=0.501\pm0.051$. The parameter degeneracies are orthogonal to those obtained from galaxy clustering. Combining void information with that from BAO and galaxy RSD in the same CMASS sample, we measure $D_A(0.57)/r_s=9.383\pm 0.077$ (at 0.8% precision), $H(0.57)r_s=(14.05\pm 0.14)\;10^3$ kms$^{-1}$Mpc$^{-1}$ (1%) and $f\sigma_8=0.453\pm0.022$ (4.9%), consistent with cosmic microwave background (CMB) measurements from Planck. These represent a factor \sim2 improvement in precision over previous results through the inclusion of void information. Fitting a flat cosmological constant $\Lambda$CDM model to these results in combination with Planck CMB data, we find up to an 11% reduction in uncertainties on $H_0$ and $\Omega_m$ compared to use of the corresponding BOSS consensus values. Constraints on extended models with non-flat geometry and a dark energy of state that differs from $w=-1$ show an even greater improvement.

Time-resolved turbulent velocity field reconstruction using a long short-term memory (LSTM)-based artificial intelligence framework

This paper focuses on the time-resolved turbulent flow reconstruction from discrete point measurements and non-time-resolved (non-TR) particle image velocimetry (PIV) measurements using an artificial intelligence framework based on long short-term memory (LSTM). To this end, an LSTM-based proper orthogonal decomposition (POD) model is proposed to establish the relationship between velocity signals and time-varying POD coefficients obtained from non-TR-PIV measurements. An inverted flag flow at Re = 6200 was experimentally measured using TR-PIV at a sampling rate of 2000 Hz for the construction of training and testing datasets and for validation. Two different time-step configurations were employed to investigate the robustness and learning ability of the LSTM-based POD model: a single-time-step structure and a multi-time-step structure. The results demonstrate that the LSTM-based POD model has great potential for time-series reconstruction since it can successfully recover the temporal revolution of POD coefficients with remarkable accuracy, even in high-order POD modes. The time-resolved flow fields can be reconstructed well using coefficients obtained from the proposed model. In addition, a relative error reconstruction analysis was conducted to compare the performance of different time-step configurations further, and the results demonstrated that the POD model with multi-time-step structure provided better reconstruction of the flow fields.

Analytic reconstruction of a two-dimensional velocity field from an observed diffusive scalar

Inverting an evolving diffusive scalar field to reconstruct the underlying velocity field is an underdetermined problem. Here we show, however, that for two-dimensional incompressible flows, this inverse problem can still be uniquely solved if high-resolution tracer measurements, as well as velocity measurements along a curve transverse to the instantaneous scalar contours, are available. Such measurements enable solving a system of partial differential equations for the velocity components by the method of characteristics. If the value of the scalar diffusivity is known, then knowledge of just one velocity component along a transverse initial curve is sufficient. These conclusions extend to the shallow-water equations and to flows with spatially dependent diffusivity. We illustrate our results on velocity reconstruction from tracer fields for planar Navier–Stokes flows and for a barotropic ocean circulation model. We also discuss the use of the proposed velocity reconstruction in oceanographic applications to extend localized velocity measurements to larger spatial domains with the help of remotely sensed scalar fields.

POD-based reduced order model for flows induced by rigid bodies in forced rotation

This paper deals with the construction of reduced order models (ROMs) for the simulation of the interaction between a fluid and a rigid body with imposed rotation velocity. The approach is a follows. First, we derive a monolithic description of the fluid–structure interaction by extending the Navier–Stokes equations from the fluid domain to the solid domain (rotor) similarly to the fictitious-domain approach. Second, we build a ROM by a proper orthogonal decomposition (POD) of the resulting multi-phase flow. This method consists in (i) constructing an optimal albeit empirical spatial basis for a very small subspace of the solution space, and (ii) projecting the governing equations on this reduced basis. Third, we cope with the reconstruction of the high-dimensional velocity field needed to evaluate the imposed velocity constraint by a POD of the rigid body membership function. This provides a substantial computation time saving compared to existing approaches. Fourth, we use a novel approach to interpolate between available POD bases to build the proposed POD-ROM for a range of parameters values. The complete procedure is applied to a simple configuration and proves efficient in the reconstruction of the velocity in both the fluid domain and the solid domain, while substantially reducing the computational cost.

A Predictive Model for the Streamwise Velocity in the Near‐Neutral Atmospheric Surface Layer

AbstractFor the reconstruction of the streamwise velocity field in the high‐Reynolds‐number (Reτ ≈ Ο(106)) near‐neutral atmospheric surface layer (ASL), a predictive model was proposed in our work. In our model, the streamwise velocity time series at each height are predicted by the superposition of mean velocity, small‐scale turbulent signals, and large‐scale turbulent signals. All the parameters used by our model have clear physical meaning. In addition, the parameters can be directly determined by the experiment that is easy to be achieved in the ASL. The model can predict the streamwise velocity between 0.9 and 30 m in the near‐neutral ASL based only on single‐point‐measured large‐scale streamwise velocity signal. For example, mean velocity, turbulence intensity, and power spectrum of streamwise velocity can be predicted by the new model. Furthermore, the streamwise velocity time series predicted by the new model have a good correlation with the directly measured results, especially for large‐scale structures. It indicates that our model can be used to reconstruct the streamwise velocity field in the logarithmic region of the near‐neutral ASL, and our model is an important complement to the Marusic‐Mathis‐Hutchins model.

The informativeness of roof tremor hazard analysis based on seismic measurements and analytical modelling

Rock bursts are a common hazard in Polish hard-coal mines. Their magnitude depends on the state of stress in the mining area, and on underground mining-induced seismicity. Both long-term and ongoing as-sessments of the capacity of the rock mass to generate tremors are based on geological and mining surveys, rock property measurements (in laborato-ries and in-situ) and observations involving signs of rock mass pressure, supported by available concepts applicable to geomechanical and geophys-ical measurements. These include seismic measurements, including profil-ing, scanning, passive/active geotomography and analytical techniques. This paper presents a comparative analysis involving exemplary results provided by both seismic and analytical methods for a selected panel in one of Upper Silesian Coal Basin (USCB) mines. For the purposes of our seismic measurements, we employed seismic tomography for the ge-otomographic reconstruction of velocity fields. Subsequently, we com-pared the results with the results of analytical modelling of rock stresses that relied on classical engineering solutions applicable to problems of me-chanics of deformable bodies. The tremor hazard analysis was based on observations of changes in P-wave velocity distributions in the coal seam environment relative to the evolution of the vertical stress concentration factor at the level of a potentially seismogenic roof layer.

Wind field reconstruction from lidar measurements at high-frequency using machine learning

The increase in wind turbine size during recent years has led to a situation where the wind speed measured at hub height is no longer a sufficient representation of the power available to be extracted by a turbine. Light Detection and Ranging (“Lidar”) wind sensing devices can measure wind speeds in a volume in front of the sensor, offering affordable and improved estimation of wind turbine power performance and loading. However, a Lidar can only measure the component of the wind velocity in the direction of the beam. This makes reconstruction of the wind velocity field from raw Lidar measurements a challenge, and current methods contain assumptions which cause inaccuracies in complex terrain and in wind turbine wakes. In addition, data availability is reduced in specific weather conditions, such as very cold climates and dense fog. A novel Machine Learning method is developed here, based on Gaussian Process regression, to remove these assumptions when producing full 3D wind fields from Lidar measurements. This approach is naturally robust to overfitting and predicts uncertainty derived from data density and machine error, without needing physical information about the local terrain. Initial validation by comparison of a Windcube Lidar with a meteorological mast, on a site with simple conditions, shows excellent performance which meets the threshold for commercial use. The method also infers data during measurement gaps, offering the potential for 100% data availability. Instantaneous 2D wake measurements in a plane can be made, which when validated and further developed will offer a breakthrough in understanding of wind farm interactions and turbine loading.

A space–time integral minimisation method for the reconstruction of velocity fields from measured scalar fields

Scalar image velocimetry (SIV) is the technique to extract velocity vectors from scalar field measurements. The usual technique involves minimising a cost functional, that penalises the deviation from the scalar conservation equation. This approach requires the measured scalar field to be sufficiently resolved and relatively noise free, such that space and time derivatives of the measured scalar field can be accurately evaluated. We quantify these requirements for a synthetic two-dimensional (2-D) turbulent flow field by evaluating the velocity reconstruction accuracy as a function of the temporal and spatial resolution and the noise level. We propose an improved SIV scheme, that reconstructs not only the velocity field but also the scalar field, which does not require approximating the space and time derivatives of the measured scalar field. Improved velocity reconstruction is demonstrated for the 2-D synthetic field. We furthermore apply the scheme to interferograms of the thickness field of a falling soap film, where 2-D turbulence is generated by an array of cylindrical obstacles. The statistics of the reconstructed velocity field are within 10 % of laser Doppler velocimetry measurements.

Rockburst hazard assessment based on seismic tomography and analytical modelling - a case study

In accordance with the formal regulations currently in force in Poland, the criteria for rockburst hazard assessment with respect to coal deposits include the records of seismic events and their impacts, de-stressing of the entire seam or its parts and expert opinions of mine operation engineers. Effectiveness of the de-stressing can be verified by geophysical test data whilst the expert opinions are mostly based on mathematical modelling using specialist software or dedicated simulation algorithms. This study collates and synthesises the results of tests carried out in a seam section in a colliery within the Upper Silesia Coal Basin, obtained by the outlined methods. Geophysical survey results are interpreted basing on seismic tomography procedures utilising the geo-tomography techniques for velocity field reconstruction in data processing. For comparison, the stress state modelling data are provided, based on conventional engineering solutions applicable to mechanics of deformable media. The actual assessment of the rockburst threat level is based on observations of distributions of the longitudinal wave velocity in relation to the actual value of the vertical component of stress concentration within the coal seam.

A measurement device for electromagnetic flow tomography

Electromagnetic flow meters have succesfully been used in many industries to measure the mean flow velocity of conductive liquids. This technology works reliably in single phase flows with axisymmetric flow profiles but can be inaccurate with asymmetric flows, which are encountered, for example, in multiphase flows, pipe elbows and T-junctions. Some computational techniques and measurement devices with multiple excitation coils and measurement electrodes have recently been proposed to be used in cases of asymmetric flows. In earlier studies, we proposed a computational approach for electromagnetic flow tomography (EMFT) for estimating velocity fields utilizing several excitation coils and a set of measurement electrodes attached to the surface of the pipe. This approach has been shown to work well with simulated data but has not been tested extensively with real measurements. In this paper, an EMFT system with four excitation coils and 16 measurement electrodes is introduced. The system is capable of using both square wave and sinusoidal coil current excitations and all the coils can be excited individually, also enabling parallel excitations with multiple frequencies. The studies undertaken in the paper demonstrate that the proposed EMFT system, together with the earlier introduced velocity field reconstruction approach, is capable of producing reliable velocify field estimates in a laboratory environment with both axisymmetric and asymmetric single phase flows.