Full Velocity Field Research Articles

Prediction of Turbulent Boundary Layer Flow Dynamics with Transformers

Time-marching of turbulent flow fields is computationally expensive using traditional Computational Fluid Dynamics (CFD) solvers. Machine Learning (ML) techniques can be used as an acceleration strategy to offload a few time-marching steps of a CFD solver. In this study, the Transformer (TR) architecture, which has been widely used in the Natural Language Processing (NLP) community for prediction and generative tasks, is utilized to predict future velocity flow fields in an actuated Turbulent Boundary Layer (TBL) flow. A unique data pre-processing step is proposed to reduce the dimensionality of the velocity fields, allowing the processing of full velocity fields of the actuated TBL flow while taking advantage of distributed training in a High Performance Computing (HPC) environment. The trained model is tested at various prediction times using the Dynamic Mode Decomposition (DMD) method. It is found that under five future prediction time steps with the TR, the model is able to achieve a relative Frobenius norm error of less than 5%, compared to fields predicted with a Large Eddy Simulation (LES). Finally, a computational study shows that the TR achieves a significant speed-up, offering computational savings approximately 53 times greater than those of the baseline LES solver. This study demonstrates one of the first applications of TRs on actuated TBL flow intended towards reducing the computational effort of time-marching. The application of this model is envisioned in a coupled manner with the LES solver to provide few time-marching steps, which will accelerate the overall computational process.

Hierarchical thermal modeling and surrogate-model-based design optimization framework for cold plates used in battery thermal management systems

The continued advancement of battery-powered electric vehicles (EVs) towards higher energy and power densities poses significant thermal challenges for batteries. This work proposes a generalized design optimization framework for battery thermal management systems (BTMS), responding to the need for EVs with enhanced battery thermal performance, safety, and lifetime. This framework combines hierarchical thermal modeling and surrogate-model-based design optimization, explicitly tailored for liquid-cooled cold plates commonly used in EV BTMS. The hierarchical thermal modeling component decouples the battery cell, battery module, and cold plate models to reduce computational modeling costs while preserving the relative thermal performance of different cold plate designs. The design optimization component leverages our pioneer deep encoder–decoder hierarchical (DeepEDH) convolutional neural network surrogate modeling methodology to predict the cold plate’s full pressure, velocity, and temperature fields. Computationally efficient DeepEDH neural networks replace costly transient thermal simulations of cold plates and compute the objectives for evolutionary optimization using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). This work’s novel modeling and optimization framework produces optimal cold plate designs that consider battery-module-specific design features, including distributed battery cell heat generation, packaging materials, and heat-spreading characteristics. The proposed framework is evaluated through a cold plate design for modular BTMS, thoroughly assessing the impact of optimization objectives, flow path constraints, modeling assumptions, and design variable choices. The results demonstrate the effectiveness of the combined hierarchical thermal modeling and design optimization framework, with the optimized cold plates achieving reductions of 6.26K, 6.29K (22.7%), and 16.16Pa (18.7%) for maximum temperature, maximum temperature difference, and pressure loss, respectively. Moreover, compared to other methodologies that apply direct optimization without hierarchical and surrogate models, our approach significantly reduces the computational cost — from approximately 4800h to 13.5h. Our generalized multi-objective optimization framework is an effective and efficient design tool that can be leveraged to advance thermal management innovations for next-generation battery systems.

Study on Non-Spherical Deformation Velocity of a Single Cavitation Bubble

Cavitation bubbles commonly exist in shipbuilding engineering, ocean engineering, mechanical engineering, chemical industry, and aerospace. Asymmetric deformation of the bubble occurs near the boundary and then has strong destructiveness, such as high amplitude loading. Therefore, the research on non-spherical deformation is of great significance, and the objective of this paper is to investigate the non-spherical collapse dynamics of laser-induced cavitation bubbles when near different boundaries. In this study, experimental data, such as the bubble pulsation process and bubble surface velocity distribution, were obtained by high-speed camera techniques and full-field velocity calculations. Near the different boundaries, the results show that the bubbles appeared to have different collapse shapes, such as near-hemispherical, near-ellipsoidal, near-cone, and near-pea shapes, and the surface velocity distribution is extremely non-uniform. When the bubble near the free surface or rigid boundary collapses, the smaller the stand-off r is, the more obvious the repulsive effect of the free surface or the attractive effect of the rigid boundary is. As the stand-off r decreases, the larger the Bjerknes force and the bubble surface velocity difference and the more pronounced the non-spherical shape becomes.

Physics-agnostic and physics-infused machine learning for thin films flows: modelling, and predictions from small data

Numerical simulations of multiphase flows are crucial in numerous engineering applications, but are often limited by the computationally demanding solution of the Navier–Stokes (NS) equations. The development of surrogate models relies on involved algebra and several assumptions. Here, we present a data-driven workflow where a handful of detailed NS simulation data are leveraged into a reduced-order model for a prototypical vertically falling liquid film. We develop a physics-agnostic model for the film thickness, achieving a far better agreement with the NS solutions than the asymptotic Kuramoto–Sivashinsky (KS) equation. We also develop two variants of physics-infused models providing a form of calibration of a low-fidelity model (i.e. the KS) against a few high-fidelity NS data. Finally, predictive models for missing data are developed, for either the amplitude, or the full-field velocity and even the flow parameter from partial information. This is achieved with the so-called ‘gappy diffusion maps’, which we compare favourably to its linear counterpart, gappy POD.

Exploring Physics of Acoustic Flow Control Over Airfoils Toward Potential Application to High Work and Lift Turbines

Abstract In this study, acoustic actuation was applied experimentally to massively separated flows on simplified hump geometries, which mimic the pressure distribution over high-work-and-lift low Reynolds airfoils. The acoustic excitation demonstrated significant control over flow separation, resulting in higher relative lift enhancement than standard, localized actuation techniques with similar momentum coefficients. Full-field velocity measurements were used to examine the transient behavior of the actuated flow in order to explain the physical mechanism of separation control. The velocity measurements revealed the presence of a viscous wall mode that organized the vorticity upstream of the separation point. A spatio-temporal correlation analysis found that the generation of these wall modes in the attached flow was the dominant cause of the subsequent reorganization of the separating shear layer and the change in separation dynamics. The importance of wall modes to acoustic flow control mechanism has important implications for the design of new acoustic control strategies for high-speed turbomachinery. Along these lines, the ramifications of this phenomena are explored over geometries, which are designed to approximate flow fields in high-speed turbomachinery. At the conducive Strouhal number, which scale linearly with the square root of Reynolds numbers, up to 22% lift enhancement is observed for excitation amplitudes in the range of ∼128 dB, typical to the engine environment. Of the many diverse flow control techniques, acoustics can be effectively employed in low Reynolds turbine blades, which are prone to flow separation in the off-design conditions with the ever increasing demand for higher flow turning.

Comparison of different data-assimilation approaches to augment RANS turbulence models

Reynolds-averaged Navier–Stokes (RANS) simulations are the most widespread approach to predict turbulent flows typical of industrial problems. Despite its success, the inherent simplifications and assumptions used to model the unknown Reynolds stresses are sources of inaccuracies. With this in mind, data-assimilation (DA) techniques can be used to minimize errors between the predicted and the exact flow fields by optimizing a space-dependent correction term. This correction term can be subsequently fed into machine learning algorithms to enhance RANS turbulence models. The main objective of this work is to assess the performance of several correction terms to match a full mean-flow velocity field, provided by averaged DNS simulations, and analyze the pros and cons of each when used subsequently in a machine-learning based RANS framework. Three configurations were chosen to perform the analysis: the converging-diverging channel at Re=12600, the flow over periodic hills at Re=2800, and the square cylinder at Re=22000. Six different correction terms were considered and discussed in this paper. Assimilations based on eddy-viscosity corrections, albeit constrained by the Boussinesq hypothesis, were able to correct the velocity field even for flows exhibiting large recirculation regions. However, the precise choice of the correction term employed has a major impact in the optimization process. On the other hand, when correction is applied as source terms in the momentum equations, better fit of the corrected mean-flow field is achieved.

Experimental study of flow field and transition characteristics in rod bundle channel

Utilizing the particle image velocimetry (PIV) technique, this study investigates the fully developed flow field and turbulence statistics in a 5×5 rod bundle across 22 cases, with Reynolds numbers ranging from 310 to 12296.Time-averaged, statistical, and spectral analyses were performed on the full field and instantaneous velocity vectors obtained through PIV measurements to examine the velocity distribution, turbulence characteristics, and spectral features in different subchannels under various Reynolds numbers. In conjunction with a differential pressure transmitter, the flow properties and fluid transitions were also explored.The experimental results reveal that the relative velocity gradient in the rod bundle channel is more significant at lower Reynolds numbers. As the Reynolds number increases, the relative velocity distribution becomes more uniform. A comparison of experimental results from different planes indicates that the fluctuation velocity in the gap subchannel is greater than that in the inner subchannel, suggesting that tightly arranged rods can generate higher turbulence intensity. Furthermore, the transition observed through the friction factor in the rod bundle channel is less distinct than those in pipes, with the transition Reynolds number being approximately 900. A low Reynolds number effect is present in the rod bundle channel, where the dimensionless fluctuation velocity decreases as the Reynolds number increases. Upon reaching the transition Reynolds number, the area-averaged dimensionless fluctuation velocity abruptly rises. By examining the turbulence intensity variations at different positions within the rod bundle, it becomes evident that the transition Reynolds numbers vary across different subchannel positions. Ultimately, the experimental data can be employed to validate the applicability of turbulence models for different Reynolds numbers.

Reconstructing the cosmological density and velocity fields from redshifted galaxy distributions using V-net

The distribution of matter that is measured through galaxy redshift and peculiar velocity surveys can be harnessed to learn about the physics of dark matter, dark energy, and the nature of gravity. To improve our understanding of the matter of the Universe, we can reconstruct the full density and velocity fields from the galaxies that act as tracer particles. In this paper, we usethe simulated halos as proxies for the galaxies. We use a convolutional neural network, a V-net, trained on numerical simulations of structure formation to reconstruct the density and velocity fields. We find that, with detailed tuning of the loss function, the V-net could produce better fits to the density field in the high-density and low-density regions, and improved predictions for the probability distribution of the amplitudes of the velocities. However, the weights will reduce the precision of the estimated β parameter. We also find that the redshift-space distortions of the halo catalogue do not significantly contaminate the reconstructed real-space density and velocity field. We estimate the velocity field β parameter by comparing the peculiar velocities of halo catalogues to the reconstructed velocity fields, and find the estimated β values agree with the fiducial value at the 68% confidence level.

Reconstructing turbulent velocity and pressure fields from under-resolved noisy particle tracks using physics-informed neural networks

Volume-resolving imaging techniques are rapidly advancing progress in experimental fluid mechanics. However, reconstructing the full and structured Eulerian velocity and pressure fields from sparse and noisy particle tracks obtained experimentally remains a significant challenge. We introduce a new method for this reconstruction, based on Physics-Informed Neural Networks (PINNs). The method uses a Neural Network regularized by the Navier-Stokes equations to interpolate the velocity data and simultaneously determine the pressure field. We compare this approach to the state-of-the-art Constrained Cost Minimization method [1]. Using data from direct numerical simulations and various types of synthetically generated particle tracks, we show that PINNs are able to accurately reconstruct both velocity and pressure even in regions with low particle density and small accelerations. PINNs are also robust against increasing the distance between particles and the noise in the measurements, when studied under synthetic and experimental conditions.

Multidecadal and climatological surface current simulations for the southwestern Indian Ocean at 1∕50° resolution

Abstract. The Western INDian Ocean Simulation (WINDS) is a regional configuration of the Coastal and Regional Ocean Community Model (CROCO) for the southwestern Indian Ocean. WINDS has a horizontal resolution of 1/50∘ (∼2 km) and spans a latitudinal range of 23.5∘ S–0∘ N and a longitudinal range from the East African coast to 77.5∘ E. We ran two experiments using the WINDS configuration: WINDS-M, a full 28-year multidecadal run (1993–2020); and WINDS-C, a 10-year climatological control run with monthly climatological forcing. WINDS was primarily run for buoyant Lagrangian particle tracking applications, and horizontal surface velocities are output at a temporal resolution of 30 min. Other surface fields are output daily, and the full 3D temperature, salinity, and velocity fields are output every 5 d. We demonstrate that WINDS successfully manages to reproduce surface temperature, salinity, currents, and tides in the southwestern Indian Ocean, and it is therefore appropriate for use in regional marine dispersal studies for buoyant particles or other applications using high-resolution surface ocean properties.

Three-dimensional full-field velocity measurements in shock compression experiments using stereo digital image correlation.

Shock compression plate impact experiments conventionally rely on point-wise velocimetry measurements based on laser-based interferometric techniques. This study presents an experimental methodology to measure the free surface full-field particle velocity in shock compression experiments using high-speed imaging and three-dimensional (3D) digital image correlation (DIC). The experimental setup has a temporal resolution of 100ns with a spatial resolution varying from 90 to 200μm/pixel. Experiments were conducted under three different plate impact configurations to measure spatially resolved free surface velocity and validate the experimental technique. First, a normal impact experiment was conducted on polycarbonate to measure the macroscopic full-field normal free surface velocity. Second, an isentropic compression experiment on Y-cut quartz-tungsten carbide assembly is performed to measure the particle velocity for experiments involving ramp compression waves. To explore the capability of the technique in multiaxial loading conditions, a pressure shear plate impact experiment was conducted to measure both the normal and transverse free surface velocities under combined normal and shear loading. The velocities measured in the experiments using digital image correlation are validated against previous data obtained from laser interferometry. Numerical simulations were also performed using established material models to compare and validate the experimental velocity profiles for these different impact configurations. The novel ability of the employed experimental setup to measure full-field free surface velocities with high spatial resolutions in shock compression experiments is demonstrated for the first time in this work.

High Dimensional Data Reduction in Modal Analysis with Stochastic Subspace Identification

Subspace system identification methods are widely used in output-only vibration analysis of civil structures, known as operational modal analysis. With the advent of new sensor technologies, such as video camera-based full field displacement or velocity measurements, the number of measured outputs is quickly increasing. In this paper, we propose principal component analysis-based data size reduction methods for efficient application of subspace methods, while preserving the high spatial resolution of the identified mode shapes for detailed modal analysis.

Estimation of venous sinus pressure drop in patients with idiopathic intracranial hypertension using 4D-flow MRI.

We aimed to explore a non-invasive estimate of pressure drop in patients who undergo venous sinus stenting to treat idiopathic intracranial hypertension (IIH). This prospective study included 28 IIH patients scheduled for venous stenting. 4D-flow MRI was acquired 24-48 h before venous manometry. Manometry-obtained pressure drop (Mp) was dichotomized into low (Lp: 0-8 mmHg) and high (Hp: 8-30 mmHg) groups. Hemodynamic indices were compared between Lp and Hp. Trans-stenotic pressure drop was estimated by work-energy equation, simplified Bernoulli equation, vorticity magnitude, and velocity difference between inlet and outlet and was compared with Mp. Measurement agreement, correlation, and accuracy were evaluated using the κ coefficient, Pearson's r, and confusion matrix-derived accuracy. Among 28 patients (mean age 38.8 ± 12.7), 19 (67.9%) were female. Work-energy equation-estimated pressure drop (WEp) had strong correlation (r = 0.91, 95% confidence interval [CI]: 0.81-0.96, p < 0.001) and high agreement (intraclass correlation coefficient = 0.90, 95% CI: 0.78-0.95, p < 0.001) with Mp. WEp classified Lp and Hp with an accuracy of 0.96. The κ value between WEp and Mp was 0.92 (95% CI: 0.78-1.00). In the work-energy equation, the viscosity energy term (Ve) had the largest weights, and the ratio of Ve to the summation of the three energy terms was 0.93 ± 0.07. Ve had strong correlation with mVort (r = 0.93, 95% CI: 0.85-0.97, p < 0.001), and mean vorticity magnitude was significantly elevated in Hp compared to that in Lp (259.8 vs. 174.9 mL/s, p < 0.001). Trans-stenotic pressure drop in IIH can be estimated using the work-energy equation with favorable accuracy. • Trans-stenotic pressure drop in patients with idiopathic intracranial hypertension can be estimated accurately with the work-energy equation using the 4D-flow MRI full velocity field. • Compared with traditional venous sinus manometry, the 4D-flow MRI-derived pressure drop is totally non-invasive and cost-saving. • 4D-flow MRI may help neurointerventionalist to select IIH patients suitable for venous sinus stenting.

Visibility analysis of boundary layer transition

We study the transition to turbulence in a flat plate boundary layer by means of visibility analysis of velocity time-series extracted across the flow domain. By taking into account the mutual visibility of sampled values, visibility graphs are constructed from each time series. The latter are, thus, transformed into a geometrical object, whose main features can be explored using measures typical of network science that provide a reduced order representation of the underlying flow properties. Using these metrics, we observe the evolution of the flow from laminarity to turbulence and the effects exerted by the free-stream turbulence. Different from other methods requiring an extensive amount of spatiotemporal data (e.g., full velocity field) or a set of parameters and thresholds arbitrarily chosen by the user, the present network-based approach is able to identify the onset markers for transition by means of the streamwise velocity time-series alone.

A data-driven stochastic model for velocity field and phase distribution in stirred particle-liquid suspensions

A computationally efficient Lagrangian stochastic model driven by short 3D experimental trajectories determined by a technique of positron emission particle tracking, has been developed to study two-phase particle-liquid flow in a mechanically agitated vessel and unravel the complex behaviour of both phases. Using a small set of trajectory driver data, the stochastic model is used in conjunction with a particle-wall collision model to simulate the full velocity field and spatial distribution of particles. The performance of a first and a second order model is evaluated in particle suspensions of various concentrations. Both models are able to predict local phase velocities to a high degree of accuracy. Predictions of spatial particle distribution are reasonable by the first order model but very accurate by the second order model. Furthermore, the latter is able to accurately predict the two-phase velocity field and spatial phase distribution under flow conditions outside the experimental range. • Deterministic multiphase flow models are challenging and computationally costly • A stochastic model accurately predicts 3D two-phase flow field in a stirred vessel • The stochastic model is driven by a small set of Lagrangian input data • The stochastic model is capable of extrapolating flow predictions • The stochastic model is highly computationally efficient

Dense velocity, pressure and Eulerian acceleration fields from single-instant scattered velocities through Navier–Stokes-based data assimilation

In this study, a reconstruction procedure to infer full 3D instantaneous velocity and pressure fields from sparse velocity measurements is proposed, here focusing on the case of scattered data as provided by particle tracking velocimetry (PTV). A key characteristic of the present approach is that it only relies on single-instant velocity measurements, and does not require any time-resolved or acceleration information. It is based on a strong enforcement of the Navier–Stokes equations where the partial time derivative of the velocity field, namely Eulerian acceleration, is considered as a control vector to minimize the discrepancies between the single-instant measurements and the reconstructed flow. Eulerian acceleration is thus a byproduct of the present methodology in addition to the identification of the full velocity and pressure fields. The reconstruction performances of the proposed Navier–Stokes-based data-assimilation approach for single-instant velocity measurements (NS-DA-SIM) are assessed using a numerical dataset for the 3D flow past a cylinder. Comparisons with existing data assimilation methodologies allow to further illustrate the merits of the present approach. The latter is finally applied to the instantaneous reconstruction of an experimental air jet flow from volumetric PTV data, confirming its robustness and high efficacy.

A Patch-Based Flow Field Reconstruction Method for Particle Image Velocimetry Data of Multistage Centrifugal Pumps

Abstract Particle image velocimetry (PIV) technology, which performs the full-field velocity measurement on the laser plane, plays a crucial role in studying complex flow structures in multistage centrifugal pumps. In particle image cross-correlation analysis, the flow field could be corrupted with outliers due to the background Gaussian imaging noise, insufficient illumination caused by optical obstruction, and particle slip caused by centrifugal forces. In this study, we propose a patch-based flow field reconstruction (PFFR) method for PIV data of multistage centrifugal pumps. Since natural images contain a large number of mutually similar patches at different locations, the instantaneous PIV data with a symmetric property is segmented to multiple patches. The flow field reconstruction is achieved by low-rank sparse decomposition, which exploits the information about similar flow characteristics present in patches. Furthermore, we illustrated the proposed PFFR on a large eddy simulation vorticity field and experimental data of a multistage centrifugal pump to evaluate its effectiveness. We also performed the three other data analysis methods. The results show that the proposed PFFR has a strong reconstruction ability to improve data reliability for the instantaneous flow field with outliers. When the outliers account for 20% of the total flow vectors, the average normalized root-mean-square error of PFFR-reconstructed data is 0.143, which is lower than the three other data methods by 21.9%–48.1%. The structural similarity is 0.702, which is higher than the three other data methods by 2.1%–9%.

Numerical study of statistically developed gas-liquid intermittent flows by the lens of three-dimensional simulations

Two-phase intermittent flows are characterized by an alternation between a region almost fully occupied by liquid (a liquid plug) and another one composed by a gas bubble. This type of flow is frequently found in industry, particularly in the transportation of oil and gas through pipelines. Their dynamics is commonly modeled with a one-dimensional approach, since long pipelines are employed, making 2D or 3D simulations unfeasible. The models always require an assessment of wall and interfacial friction factors, which are usually obtained by empirical correlations. In this work, from full 3D velocity fields across statistically developed slug unit cells, flow parameters needed for 1D models were determined. For that, several three-dimensional numerical simulations were performed using the open source platform OpenFOAM®. The two-phase flow was determined within a computational domain corresponding to a single slug unit cell, with periodic boundary conditions under imposed pressure gradient and overall void fraction, employing the Volume of Fluid (VOF) method. Both laminar and turbulent flows were studied. Turbulence was modeled with the k-ω Shear Stress Transport (SST) model. The axial velocity profile along the cross section, as well as slug parameters, were compared with available experimental data, showing a quite good agreement. From the results validated by experimental data, friction factors and momentum flux parameters were determined, allowing the development of corrections to improve the available 1D models.

Recognition of a quasi-static region in a granular bed impacted with a sphere

Various characteristics such as stationary, laminar, and turbulent flow exist in the granular flow and it is critical to recognize the flow features based on the full-field velocity measurement to reveal the complex motion of granular flow. We propose a Dilated Convolution UNet++ (DC-UNet++) framework modeling of flow field images, which can recognize the features within the region in sphere impact on granular beds without using Particle Image Velocimetry (PIV). When compared with the results of the thresholding method, the accuracy of feature recognition using this model is improved by 8.3%. The accuracy of feature recognition reaches 73.44% for the flow field of transparent glass beads, which is difficult to analyze using PIV. This suggests that DC-UNet++ has a wide range of applications for granular materials that are difficult to handle using PIV and is a new tool for developing a feature recognition model for granular flow.

Optical flow tracking velocimetry of near-field explosions

To better understand the complex dynamics and physics associated with the rapid expansion of the detonation product fireball following an explosion, it is imperative to have a full description of its associated velocity field. Typical experimental techniques rely on simple single-point measurements captured from pressure transducers or Hopkinson pressure bars. In this technical design note, we aim to improve the current state-of-the-art by introducing a means to determine full velocity fields from high-speed video using optical flow tracking velocimetry. We demonstrate the significance of this method from our results by comparing velocity fields derived from high-speed video and a validated numerical model of the same case. A wider use of this technique will allow researchers to elucidate spatial and temporal features of explosive detonations, which could not be obtained thus far using single-point measurements.