Accurate Velocity Field Research Articles

Large-scale flow field super-resolution via local-global fusion convolutional neural networks

Particle image velocimetry (PIV) techniques have a limited field of view of the flow field and can only capture high-resolution flow fields in localized areas. To obtain a larger measurement range, multiple cameras must be used to capture the flow field simultaneously and then stitch the parts together. However, this method can be expensive. We propose the local-global fusion convolutional neural network (LGF-CNN) for reconstructing large-field flow fields with high spatial resolution based only on two flow data types: local small-field high spatial resolution wake velocity fields and global large-field low spatial resolution velocity fields. The core of the model consists of convolutional neural network (CNN) architecture to learn the mapping relationship between the small field of view with high spatial resolution and the large field of view with low spatial resolution. Using the effectively trained LGF-CNN model, we demonstrate its ability to reconstruct high-resolution velocity fields around the circular cylinder. The LGF-CNN is rigorously validated on a number of representative datasets, including simulated data for Reynolds numbers of 200 and 500, as well as experimental data for a Reynolds number of 3.3 × 104 with the steady jet at the rear stagnation point of the cylinder. The results demonstrate the ability of LGF-CNN to generate accurate velocity fields with high spatial resolution, including reliable detection of high-frequency components. The proposed method could reduce the number of cameras required for large-field, high spatial resolution PIV measurements, thereby reducing experimental costs.

Comparative evaluation of electrical resistance tomography, positron emission particle tracking and high-speed imaging for analysing horizontal particle-liquid flow in a pipe

We evaluate three experimental techniques - electrical resistance tomography (ERT), positron emission particle tracking (PEPT) and high-speed imaging (HSI) – for analysing the local particle velocity field and spatial distribution in a horizontal particle-liquid pipe flow under varying conditions of solid concentration. A new ERT methodology is devised for estimating particle velocity, circumventing the limitations of the conventional cross-correlation technique. Furthermore, an enhanced HSI approach is introduced and systematically compared with PEPT and ERT. Results show that, under all conditions, PEPT provides the most accurate particle velocity field followed by HSI, whilst ERT yields the most accurate concentration field, followed by HSI. The enhanced HSI emerges as a simple cost-effective option compared to PEPT and ERT. A combined measurement approach using PEPT for local particle velocity and ERT for local concentration, however, delivers the best comprehensive two-phase flow characterization, highlighting potential synergies between these methods for complex flow studies.

Deep-learning optical flow for measuring velocity fields from experimental data.

Deep learning-based optical flow (DLOF) extracts features in adjacent video frames with deep convolutional neural networks. It uses those features to estimate the inter-frame motions of objects. We evaluate the ability of optical flow to quantify the spontaneous flows of microtubule (MT)-based active nematics under different labeling conditions, and compare its performance to particle image velocimetry (PIV). We obtain flow velocity ground truths either by performing semi-automated particle tracking on samples with sparsely labeled filaments, or from passive tracer beads. DLOF produces more accurate velocity fields than PIV for densely labeled samples. PIV cannot reliably distinguish contrast variations at high densities, particularly along the nematic director. DLOF overcomes this limitation. For sparsely labeled samples, DLOF and PIV produce comparable results, but DLOF gives higher-resolution fields. Our work establishes DLOF as a versatile tool for measuring fluid flows in a broad class of active, soft, and biophysical systems.

Three-Dimensional Velocity Field Interpolation Based on Attention Mechanism

The establishment of a three-dimensional velocity field is an essential step in seismic exploration, playing a crucial role in understanding complex underground geological structures. Accurate 3D velocity fields are significant for seismic imaging, observation system design, precise positioning of underground geological targets, structural interpretation, and reservoir prediction. Therefore, obtaining an accurate 3D velocity field is a focus and challenge in this field of study. To achieve intelligent interpolation of the 3D velocity field more accurately, we have built a network model based on the attention mechanism, JointA 3DUnet. Based on the traditional U-Net, we have added triple attention blocks and channel attention blocks to enhance dimension information interaction, while adapting to the different changes of geoscience data in horizontal and vertical directions. Moreover, the network also incorporates dilated convolution to enlarge the receptive field. During the training process, we introduced transfer learning to further enhance the network’s performance for interpolation tasks. At the same time, our method is a deep learning interpolation algorithm based on an unsupervised model. It does not require a training set and learns information solely from the input data, automatically interpolating the missing velocity data at the missing positions. We tested our method on both synthetic and real data. The results show that, compared with traditional intelligent interpolation methods, our approach can effectively interpolate the three-dimensional velocity field. The SNR increased to 36.22 dB, and the pointwise relative error decreased to 0.89%.

A mixed pressure-velocity formulation to model flow in heterogeneous porous media with physics-informed neural networks

Current implementations of Physics Informed Neural Networks (PINNs) can experience convergence problems in simulating fluid flow in porous media with highly heterogeneous domains. The objective of this work is to develop an accurate implementation of PINNs to model fluid flow in heterogeneous porous media that avoids alternative approaches in the literature that tend to impose unphysical continuity of the hydraulic conductivity field. The proposed implementation is inspired by the mixed formulation of the governing equations, which separates the mass continuity equation and Darcy's law. This methodology has been used with the mixed finite element method and is known to provide accurate pressure and velocity fields in highly heterogeneous domains. In this work, a similar methodology is applied to PINNs, where the training loss function is based on the decoupled continuity equation and Darcy's law. The separation of the continuity equation and Darcy's law allows for calculating the residual term in the learning loss function without evaluating the spatial derivatives of the discontinuous hydraulic conductivity and associated non-differentiable functions. This approach provides more accurate automatic differentiation of the neural networks for pressure and velocity fields. The new implementation of PINNs can be applied to simulate flow in porous media, regardless of the type and level of heterogeneity with a discontinuous hydraulic conductivity distribution. A variety of structures of the new implementation are investigated. Numerical experiments show that the structure based on different neural networks for the pressure and each component of the velocity field provides the highest accuracy with equivalent training time as other structures. The proposed methodology presents a novel approach to broaden the scope of PINNs in modeling fluid flow in porous media, while preserving the precise representation of the domain's discontinuous features.

Assessing the impact of turbulent kinetic energy boundary conditions on turbulent flow simulations using computational fluid dynamics

Computational fluid dynamics has been widely used to study hemodynamics, but accurately determining boundary conditions for turbulent blood flow remains challenging. This study aims to investigate the effect of patient-specific turbulence boundary conditions on the accuracy of turbulent flow simulation. Using a stenosis model with 50% severity in diameter, the post-stenosis turbulence flow region was simulated with different planes to obtain inlet boundary conditions and simulate downstream flows. The errors of simulated flow fields obtained with turbulence kinetic energy (TKE) boundary data and arbitrary turbulence intensity were compared. Additionally, the study tested various TKE data resolutions and noise levels to simulate experimental environments. The mean absolute error of velocity and TKE was investigated with various turbulence intensities and TKE mapping. While voxel size and signal-to-noise ratio of the TKE data affected the results, simulation with SNR > 5 and voxel size < 10% resulted in better accuracy than simulations with turbulence intensities. The simulation with appropriate TKE boundary data resulted in a more accurate velocity and turbulence field than those with arbitrary turbulence intensity boundary conditions. The study demonstrated the potential improvement of turbulent blood flow simulation with patient-specific turbulence boundary conditions, which can be obtained from recent measurement techniques.

Dimensionality reduction for regularization of sparse data-driven RANS simulations

Data assimilation can reduce the model-form errors of RANS simulations. A spatially distributed corrective parameter field can be introduced into the closure model, whose optimal values can be efficiently found by an adjoint method and gradient-based optimization. When assimilating experimental data, which in most cases are sparsely distributed or based on a low-resolution grid, the inverse problem is highly underdetermined and thus ambiguous. Therefore, to reduce the ambiguity, regularization is required. Established regularization approaches such as total variation and Sobolev gradient methods can produce smooth and physically meaningful velocity fields in many cases. However, if the measurements are located close to walls, spiky and unphysical wall shear stress profiles can occur. A new regularization strategy based on a piecewise linear approximation of the corrective field is proposed. This method is shown to lead to a very accurate free stream velocity field and smooth wall shear stress profiles. The resulting skin friction drag error for the case of flow over periodic hills was around 1.38% which is seven times lower than the error obtained with the Sobolev gradient and two orders of magnitude lower than that obtained with the other two methods.

Investigating Effect of Geometric Differences on Fluid Behavior in Synthetic Jets

A synthetic jet is a flow that is created by an actuator vibrating at a specific frequency and amplitude. In this study the velocities and propagation of synthetic jets have been measured using both circular and single-wave orifice geometries. Axial velocity measurements in the direction of flow have been taken using the PCE 423 model hot wire anemometer. Also flow visualization has been performed using TiO2 surface oil visualization to determine velocity distributions in the radial direction. The measurements have been conducted at different H/D values, representing the ratio between the axial distance (H) and the orifice diameter (D). The excitation frequency has been varied between 4 Hz and 5 Hz with a sinusoidal signal type. The results have shown that circular orifice geometry have higher velocities in the axial direction. However, When the axial velocity was measured at 4 Hz, it has been observed that the single wave geometry provided results close to a circle at H/D = 13 and 14 values, and at 5 Hz for H/D = 12 and 13 values. This suggests that the geometric shape is not very important at high H/D ratios. In addition, the axial velocity values for a single wave orifice geometry show almost the close results for both excitation frequency values. The flow visualization results have indicated that the single-wave orifice geometry with H/D=12 ratio perform better and provides a more accurate and well-distributed velocity field. In conclusion, the findings of this study suggest that synthetic jets could be potentially useful for industrial applications, especially in heat transfer applications with their extended flow field implications.

A pre-training model based on CFD for open-channel velocity field prediction with small sample data

Abstract Accurately obtaining the distribution of the open-channel velocity field in hydraulic engineering is extremely important, which is helpful for better calculation of open-channel flow and analysis of open-channel water flow characteristics. In recent years, machine learning has been used for open-channel velocity field prediction. However, effective training of data-driven models in machine learning heavily depends on the diversity and quantity of data. In this paper, a CFD-based pre-training neural network model (CFD–PNN) is proposed for accurate open-channel velocity field prediction, allowing the adaption to the task with small sample data. Also, a cross-sectional velocity field prediction method combining the computational fluid dynamics (CFD) and machine learning is established. By comparing CFD–PNN with six other neural network algorithm models and the CFD model, the results show that, in the case of small sample data, the CFD–PNN model can predict a more reasonable open-channel velocity field with higher prediction accuracy than other models. The average error of the velocity calculation for the trapezoidal open-channel cross-section is about 3.62%. Compared with other models, the accuracy is improved by 0.3–2.8%.

Contemporary Velocity Field for Turkey Inferred from Combination of a Dense Network of Long Term GNSS Observations

The Anatolia?Aegean domain represents a broad plate boundary zone, with the deformation accommodated by major faults bounding quasi-low deforming units. First-order features of this deformation were obtained in the form of a GNSS-derived velocity field. During the last decade, the accuracy of velocity solutions was improved, and the expansion of continuous networks increased spatial resolution. Nonetheless, an accurate representation of the deformation field requires interstation distances much lower than the locking depth of nearby faults, which has not yet been satisfied. The basis for creating a precise and accurate velocity field is uniform processing of the time series recorded both in the campaign and permanent GNSS stations, at once and for a single reference system. Although for Anatolia the data density has increased 6-fold since the landmark work of Reilinger et al. (2006), this crucial integration has not been made. We aim to fill this gap by analyzing the data and providing a uniform velocity solution. In this study, we processed the time series of 836 stations, of which 178 are published for the first time. With a period of up to 28 years, we present the most accurate velocity field with increased spatial and temporal resolution and homogeneity. We used the improved coverage of the velocity field to calculate strain accumulation on the North and East Anatolian Faults. Modelled slip rates vary between 20 and 26 mm/yr and 9.7 and 11 mm/yr for the North and East Anatolian faults, respectively. The data can better constrain the kinematics of continental deformation, provide accurate boundary conditions for dynamic models, and help test outstanding hypotheses about the kinematics of the Anatolia-Aegean domain.

DeepTRNet: Time-resolved reconstruction of flow around a circular cylinder via spatiotemporal deep neural networks

We propose spatiotemporal deep neural networks for the time-resolved reconstruction of the velocity field around a circular cylinder (DeepTRNet) based only on two flow data types: the non-time-resolved wake velocity field and sparse time-resolved velocity measurements at specific discrete points. The DeepTRNet consists of two operations, i.e., compact spatial representations extraction and sequential learning. We use the convolutional autoencoder (CAE) in DeepTRNet to extract compact spatial representations embedded in the non-time-resolved velocity field. The nonlinear CAE modes and corresponding CAE coefficients are thus obtained. Based on the nonlinear correlation analysis of the velocity field, we use the bidirectional recurrent neural networks (RNN) with the gated recurrent unit for mapping the sparse time-resolved velocity measurements to the CAE coefficients via sequential learning. The early stopping technique is used to train the DeepTRNet to avoid overfitting. With the well-trained DeepTRNet, we can reconstruct the time-resolved velocity field around the circular cylinder. The DeepTRNet is verified on the simulated datasets at two representative Reynolds numbers, 200 and 500, and the experimental dataset at Reynolds number 3.3 × 104 with the steady jet at the rear stagnation point of the cylinder. We systematically compare the DeepTRNet method and the RNN-proper orthogonal decomposition (POD) approach. The DeepTRNet can obtain the accurate time-resolved velocity field depending on the two data types mentioned above. The DeepTRNet method outperforms the RNN-POD method in the reconstruction accuracy, especially for the reconstruction of small-scale flow structures. In addition, we get the reliable velocity field even for the high-frequency components.

Field-based physical inference from peculiar velocity tracers

ABSTRACT We present a proof-of-concept Bayesian hierarchical modelling approach to reconstruct the initial cosmic matter density field constrained by peculiar velocity observations. Using a model for the gravitational evolution of dark matter to connect the initial conditions to late-time observations, it reconstructs the late-time density and velocity fields as natural byproducts. We implement this field-based physical inference approach by adapting the Bayesian Origin Reconstruction from Galaxies ($\small {\rm BORG}$) algorithm, which explores the high-dimensional posterior through the use of Hamiltonian Monte Carlo sampling. We test the self-consistency of the method using random sets of tracers, and assess its accuracy in a more complex scenario where peculiar velocity tracers are mock haloes drawn from $\small {\rm GADGET2}$ N-body simulations. We find that our framework self-consistently infers the initial conditions, density and velocity fields, and shows some robustness to model mis-specification. Compared with the approach of constrained Gaussian random fields/Wiener filtering, the hierarchical model produces more accurate final density and velocity field reconstructions. It also allows us to constrain the initial conditions by peculiar velocity observations, complementing in this aspect other field-based approaches based on alternative cosmological observables such as galaxy clustering or weak lensing.

Spatiotemporal Filtering for Continuous GPS Coordinate Time Series in Mainland China by Using Independent Component Analysis

Continuous Global Positioning Systems (GPS) coordinate time series with a high spatiotemporal resolution, and provide a great opportunity to study their noise models and common mode errors (CMEs), thus making it possible to detect and analyse spatiotemporal characteristics of tectonic and non-tectonic signals in time series, and further to estimate a reliable and accurate velocity field of crustal movement in a region by removing CMEs and using the optimal noise model. In this paper, we used GPS coordinate time series from the Crustal Movement Observation Network of China (CMONOC) with an approximate decadal period from 2010 to 2020, to construct optimal noise models by fitting them with several noise combinations according to the Akaike information criterion (AIC). We further adopted independent component analysis (ICA) to extract CMEs and analysed their spatiotemporal characteristics, and then evaluated their effects on noise models and velocity uncertainties, and finally estimated a decennial velocity field of crustal movement with a higher signal-to-noise ratio (SNR) by applying the CME filtering and considering the optimal noise model in Mainland China. Our results show that optimal noise models are dominated by white noise (WN) plus flicker noise (FN) for both east and north components, and WN plus power law noise (PN) with spectral index close to −1 for up component, respectively. ICA filtering can remove the highly spatially correlated CMEs and decrease the mean RMSEs of the residual time series by about 40–60%, providing a more accurate velocity field with a higher SNR in Mainland China, accordingly.

A Simple Analytical Model of a GaN MODFET to Study its DC and RF Performance

This work presents a theoretical study of a GaN MODFET considering accurate velocity field relation of GaN for a wide range of electric field. The analytical expression of different DC parameters such as drain current, mutual conductance and drain conductance of the device has been derived and their variation over different field regions has been investigated. This work has also been extended to study the RF parameters like cut-off frequency and maximum operating frequency of the device. The threshold voltage of the device is also derived and studied in terms of the thickness of the doped AlGaN layer and mole fraction of AlGaN. The mathematical model presented here is calibrated with the experimentally available results reported earlier and a good agreement has been observed.

A methodology for estimating accurate velocity field of NigNET based on new ITRF realization

This contribution presents a new velocity field describing the crustal motion of Nigeria from more than 5years continuous GNSS data at 8 of 14 permanent stations distributed across the country. GAMIT/GLOBK GNSS processing software was used for processing. The horizontal velocity field of NigNET stations which showed a North-East trend and the selected IGS stations were obtained from cleaned position time series of daily GNSS solutions. The velocity describe the horizontal and vertical motion the selected 8 GNSS stations assuming Flicker +White noise model, which optimally describes the geophysical error source of the adopted GNSS stations. Bland and Altman statistical method shows that residual velocity solutions of our study and others (in ITRF2008) and also MORVEL plate motion model are in agreement.

Combined temperature and velocity field measurements in thermal fluid systems with magnetic resonance velocimetry

Abstract A method for the combined measurement of velocity and temperature fields in water using magnetic resonance velocimetry (MRV) is presented. MRV can provide accurate volumetric, time-averaged temperature and velocity field data. However, the choice of the flow medium and other materials is limited due to the requirements placed on the magnetic properties. There are also limitations to the measurable fluid velocities and temperatures. The echo time TE, which typically defines the temperature sensitivity, is particularly important for temperature measurement in fluid flows. A longer TE means better temperature precision, but measurement errors are increased. In addition, material properties such as magnetic susceptibility and electrical conductivity are temperature-dependent and this can lead to systematic errors in the temperature results. The design of the MRV experiment must take all of these effects into account. Here, a measurement method is proposed that includes various corrective measures. The capabilities are demonstrated with two types of experiments, a pin-fin heat exchanger and a jet-in-crossflow experiment. The fluid in these systems is water with velocities of up to 1 m/s and a temperature between 20 °C and 50 °C. These experiments demonstrate the possibilities of performing quick parameter studies with MRV while achieving low measurement uncertainty and low systematic errors.

Experimental investigation of relative velocity field based on image rotation method in pump impeller

The continuous instantaneous flow field in pump impeller is vital for studying the mechanism of some complex flow phenomenon. In this paper, a high frequency PIV system with maximum sampling frequency 10 k Hz is built and used to measure the continuous flow field in impeller. In order to reduce the minimum sampling frequency required for PIV while ensuring the accuracy of flow field measurement, an image rotation method was proposed for calculating the relative velocity flow field in impeller. This method removed the particle displacement caused by impeller rotation in circumferential direction before the FFT calculation was performed. The relative velocity value calculated by velocity triangle method and image rotation method are compared and analyzed at different sampling line positions for different experimental conditions. The results show the image rotation method can not only obtain a more accurate velocity field near the blade area, but also has a lower requirement for the sampling frequency of the PIV system. The relative velocity error between two methods shows a trend of decreasing and then increasing when the sampling frequency decreases from 10 k Hz to 1 k Hz. Meanwhile, the relationship between the impeller speed and optimal sampling frequency range is established, which provides guidance for the selection of the appropriate PIV sampling frequency used for the measurement of the flow field in impeller.

Distortion correction of two-component two-dimensional PIV using a large imaging sensor with application to measurements of a turbulent boundary layer flow at $$\hbox {Re}_{\tau } = 2386$$

In the past decade, advances in electronics technology have made larger imaging sensors available to the experimental fluid mechanics community. These advancements have enabled the measurement of 2-component 2-dimensional (2C-2D) velocity fields using particle image velocimetry (PIV) with much higher spatial resolution than previously possible. However, due to the large size of the sensor, the lens distortion needs to be taken into account as it will now have a more significant effect on the measurement quality that must be corrected to ensure accurate high-fidelity 2C-2D velocity field measurements. In this paper, two dewarping models, a second-order rational function (R2) and a bicubic polynomial (P3) are investigated with regards to 2C-2D PIV measurements of a turbulent boundary layer (TBL) using a large imaging sensor. Two approaches are considered and compared: (i) dewarping the images prior to the PIV cross-correlation analysis and (ii) undertaking the PIV cross-correlation analysis using the original recorded distorted images then followed by using the mapping functions derived for image dewarping to provide the correct spatial location of the velocity measurement point. The results demonstrate that the use of P3 dewarping model to correct lens distortion yields better results than the R2 dewarping model. Furthermore, both approaches for the P3 dewarping model yield results which are statistically indistinguishable.

Super-resolution PIV using multi-frame displacement information

High-resolution (HR) fluid-flow velocity information is important to reliably analyze fluid measurements in particle image velocimetry (PIV), such as the boundary layer and turbulent flow. Efforts in PIV to enhance the resolution of flow fields are mainly based on single-frame information, which follows the velocity field estimation and may influence the final reconstruction accuracy. In this study, we propose a novel super-resolution (SR) reconstruction technology from another perspective, which consists of two parts: a multi-frame imaging system and a Bayesian-based multi-frame SR reconstruction algorithm. First, a splitbased imaging system is developed to obtain particle image pairs with fixed displacements. Subsequently, we present a Bayesian-based multi-frame SR (BMFSR) reconstruction algorithm to obtain an SR particle image. Multi-frame particle images collected by the developed system are used as the input low-resolution images for the following novel SR reconstruction algorithm. Synthetic and experimental particle images have been tested to verify the performance of the proposed technology, and the results are compared with the traditional and advanced reconstruction methods in PIV. The results and comparisons show that the proposed technology successfully achieves good performance in obtaining finer particle images and a more accurate velocity field.

Experimental Assessment of RANS Models for Wind Load Estimation over Solar-Panel Arrays

This paper reports a comparison between wind-tunnel measurements and numerical simulations to assess the capabilities of Reynolds-Averaged Navier-Stokes models to estimate the wind load over solar-panel arrays. The free airstream impinging on solar-panel arrays creates a complex separated flow at large Reynolds number, which is severely challenging for the current Reynolds-Averaged Navier-Stokes models. The Reynolds-Averaged Navier-Stokes models compared in this article are k-ϵ, Shear-Stress Transport k-ω, transition and Reynolds Shear Model. Particle Image Velocimetry measurements are performed to investigate the mean flow-velocity and turbulent-kinetic-energy fields. Pressure taps are located in the surface of the solar panel model in order to obtain static pressure measurements. All the Reynolds-Averaged Navier-Stokes models predict accurate average velocity fields when compared with the experimental ones. One of the challenging factor is to predict correctly the thickness of the turbulent wake. In this aspect, Reynolds Shear provides the best results, reproducing the wake shrink observed on the 3rd panel in the experiment. On the other hand, some other features, most notably the blockage encountered by the flow below the panels, are not correctly reproduced by any of the models. The pressure distributions over the 1st panel obtained from the different Reynolds-Averaged Navier-Stokes models show good agreement with the pressure measurements. However, for the rest of the panels Reynolds-Averaged Navier-Stokes fidelity is severely challenged. Overall, the Reynolds Shear model provides the best pressure estimation in terms of pressure difference between the front and back sides of the panels.