PIV Data Research Articles

Estimating Velocity Correlations Using Single Pixel PIV

In this work, we analyze the possibility of determining correlations of turbulent velocity fluctuations from PIV data with improved spatial resolution. The analysis is based on the method presented by Oldenziel et al. (2023), where a joint probability density function of the velocity at two locations is calculated from the single-pixel ensemble correlation for these locations. Synthetic PIV images are used to discuss the occurrence of random and systematic errors and to derive the number of image pairs required for a determination of the correlation coefficient with desired uncertainty, depending on the particle image density. Compared to classical window correlation, the presented method can improve the spatial resolution by about one order of magnitude if a very large number of PIV image pairs are available and/or many statistically independent points with identical flow properties can be used. As an example of application, we show the spatial distribution of a two-point correlation in a compressible turbulent boundary layer flow for a reference point near the wall.

Validating Volumetric Measurements Using Helium-Filled Soap Bubbles in a Turbulent Boundary Layer And Wake Of An Axisymmetric Body Of Revolution

This study focuses on the validation of a volumetric measurement technique to characterize the turbulent boundary layers (TBL) and wake of a slender axisymmetric body. Specifically, Lagrangian Particle Tracking (LPT) was employed to analyse a TBL subjected to an adverse pressure gradient (APG) and transverse curvature at the tail of an axisymmetric body, with a Reynolds number based on model length of 3.95×10 6 . For the LPT method, a seeding rake with 100 nozzles was used to disperse helium-filled soap bubbles (HFSB), which served as tracers. These tracers were illuminated by high-powered LED arrays, allowing their motion to be captured by three high-speed cameras at acquisition rates up to 20 kHz. A key aspect of this research was using shadowgraphy to measure the diameter of the bubbles exiting the nozzles and obtaining their statistical variations across the various nozzles in the seeding rake. The study identified that the diameter of bubbles averaged 0.45 mm, indicating a state of near-neutral buoyancy. The LPT results were then obtained using the shake-the-box (STB) tracking alogirthm, while ensemble bin-averaging of the scattered particle tracks was used to obtain turbulence statistics on a regular grid. To validate the LPT results, comparisons were made with time-resolved 2D Particle Image Velocimetry (TR-PIV) and highly resolved hot-wire anemometry. This comparative analysis revealed good agreement of the mean profiles across the methodologies, highlighting the robustness and accuracy of the LPT technique. While the turbulence levels in the outer layer were well captured by the LPT, some discrepancies were observed near the wall in both PIV and LPT data, indicating limitations in capturing small-scale phenomena. The implications of these findings, particularly in understanding the complex 3D flow effects of such TBLs and the resulting wake flow field are discussed.

A Software Tool For Automated Analysis And Characterization Of Raw PIV Images

The time to process large PIV data sets can be expensive and the resultant velocity fields are a strong function of the quality of the particle images used. For new and even experienced users of PIV, determination of the quality of a particle image data set can be challenging and time consuming especially for a large number of data sets. This is compounded with new high-speed camera systems that are capable of collecting terabytes of data quickly. A software tool is described here that allows the user to make informed decisions on the general quality of the data sets and what pre-processing image data steps are needed. The software provides statistical feedback on such parameters as particle count, particle size, particle intensity for not only a single image but also a complete data set. Using this software allows the user to make informed decisions and generate and document the quality of the data collected. Based on this, a robust PIV processing algorithm can be developed.

Object Registration Techniques For 3D Particle Tracking

Image based 3D particle tracking is currently the most widely used technique for volumetric velocity measurements. Inspecting the flow-field around an object is however, hampered by the latter, obstructing the view across it. In this study, the problem of measurement limitations due to the above is addressed. The present work builds upon the recent proposal from Wieneke and Rockstroh (2024), whereby the information of the occluded lines of sight can be incorporated into the particle tracking algorithm. The approach, however, necessitates of methods that accurately evaluate the shape and position of the object within the measurement domain. Methods of object marking and the following 3D registration of a digital object model (CAD) are discussed. For the latter, the Iterative Closest Point (ICP) registration algorithm is adopted. The accuracy of object registration is evaluated by means of experiments, where marking approaches that include physical and optically projected markers are discussed and compared. Three objects with growing level of geometrical complexity are considered: a cube, a truncated wing and a scaled model of a sport cyclist. The registered CAD representations of the physical objects are included in aerodynamic experiments, and the flow field is measured by means of large-scale particle tracking using helium filled soap bubbles. Three operating regimes are studied and compared: monolithic, partitioned and object-aware (OA) monolithic. The results indicate that object registration enables a correct reconstruction of particle tracers and strongly reduces the domain clipping typical of the monolithic approach. Furthermore, the dynamical use of all views in the OA monolithic method offers clear benefits compared to the partitioned approach, namely a lower occurrence of ghost particles. Finally, the combined visualization of the object and the surrounding flow pattern offers means of insightful data inspection and interpretation, along with posing a basis for PIV data assimilation at the fluid-solid interface.

Improved Impingement Cooling Using Flow Enhancing Structural Elements

This investigation is part of a study seeking to improve impingement cooling in internal combustion turbomachinery using flow modifying elements within the cooling channel. A simplified geometry of a jet impingement cooling configuration is chosen for well-defined numerical simulations and complementary experiments. The generic cooling channel setup features of a square cross-section that is closed on one end and is supplied by 9 inline jets that are directed toward a heated plate. Using RANS, the presence of an arc-conic placed immediately downstream of each jet nozzle was found to increase the heat transfer and prompted the present experimental study to elucidate the fluid mechanical mechanisms leading to the improved performance. Central to the study is an extensive data base of time-resolved 2d-2c PIV data for both channel configurations, with and without installed arc-conics, on a field of view that simultaneously captures up to 3 jets. Using two-point correlations, an interaction or modal coupling between the jets is not observed, suggesting that each jet may be treated individually. The arc-conics tend to stabilize the jets by capturing and redirecting the bulk cross-flow, thereby increasing the self-similarity of the jet impingement pattern, in particular toward the channel exit. Modal analysis using both proper orthogonal decomposition (POD) and spectral proper orthogonal decomposition (SPOD) capture the dynamics of the flow, ideally to achieve a dimensionality reduction for reduced order modeling. However, the fully turbulent flow with highly stochastic dynamics exhibits only weak spatial or temporal signatures, with the energy content spread across a large number of modes. Among the dominant modes are pulsations of the jet onto the surface along with spanwise sweeping motions. The stabilization of the jet by the arc-conic results in a more defined impingement flow with the signature of the jet’s shear layer visible in the higher modes of the energy spectrum and is considered the main mechanism of improved heat transfer.

Optimizing Flow Conditions and Fish Passage Success in Vertical Slot Fishways: Lessons from Fish Behavior Observations

This study investigates the behavior of chubs (Squalius cephalus) of mid-body length (9.7–15.6 cm) with respect to turbulent flow conditions in a pool representing an experimental vertical slot fishway. Velocity and turbulence were characterized using PIV data. The influence of turbulent flow on fish behavior was assessed through the number of successful fish passage attempts, the associated passage times, and the spatial distribution of fish in the pool. Turbulence conditions were modified by the addition of one or three vertical rigid cylinders inside the pool. The results show that these adaptations may facilitate the passage of chubs. Results provide valuable insights and information to understand the relationship between fish behavior and hydraulic conditions, especially in the context of improving the design of fishways.

Experimental and numerical study of mixed convection heat transfer in a vented cavity partially filled with a porous medium: Effects of reynolds and rayleigh numbers on Nusselt number and flow regimes

This article presents a comprehensive investigation of mixed convection flow and heat transfer within a vented, partially side-heated cubical cavity, incorporating a porous medium with low-conductivity square-shaped inclusions. The study encompasses an extensive range of Rayleigh numbers (106 < Ra < 6 × 106) and Reynolds numbers (200 < Re < 4000) while maintaining a fixed Prandtl number of Pr = 0.71. This investigation spans over three decades in Richardson numbers (Ri = Ra/(Re2 Pr)), aiming to discern the interplay between the Nusselt number, Nu, and the Richardson number. Our understanding of Nusselt number dependencies is enhanced by combining PIV measurements of heat transfer and velocity fields with temperature field data. The study uses both experimental and numerical PIV data, incorporating porous media representation to reveal heat transfer scaling with both Reynolds and Rayleigh numbers. Computational Fluid Dynamics (CFD) methods are used to explore the complex physical behavior under different flow conditions. Three distinct flow and heat transfer regimes have been identified, predicated upon the Richardson number. For Ri < 25, the flow structure and Nusselt number exhibit similarities with pure forced convection, where the Nusselt number scales as Nu ∼ Re0.6, independent of the Rayleigh number. Conversely, for Ri > 70, natural convection dominates the vicinity of the heating wall, rendering the Nusselt number less sensitive to Reynolds number variations and predominantly dictated by the Rayleigh number. Notably, the intermediate regime, ranging from 25 < Ri < 70, witnesses a competition between upward-directed natural convection flow at the heating wall and downward-directed forced flow, culminating in a minimum effective Nusselt number.

Influence of the turbulence model on the numerical predictions of cold turbulent flow in a heavy-duty gas turbine DLN combustor

The influence of different turbulence models on the numerical predictions of cold turbulent flow in a 300 MW F-class DLN combustor was investigated in this study. PIV and PLIF test data were obtained and used for comparison. The simulation results obtained using the LES method exhibited a high level of agreement with the experimental results regarding the velocity distribution and recirculation zone scale. Of the RANS models, only the results from the RNG k-ε and Realizable k-ε are comparable to the experimental data and are suitable for rapid simulation of the combustor flow field. Conversely, the Standard k-ε, SST k-ω, and RSM model results display notable differences from the experiment. Regarding the mixing simulation in the combustor, the LES method was the closest to the experiment. The RANS models roughly reflect the same mixing trend as the experiment, despite the tracer gas diffusing much slower than in the experiment.

Towards Reduced Order Models via Robust Proper Orthogonal Decomposition to capture personalised aortic haemodynamics

Data driven, reduced order modelling has shown promise in tackling the challenges associated with computational and experimental haemodynamic models. In this work, we focus on the use of Reduced Order Models (ROMs) to reconstruct velocity fields in a patient-specific dissected aorta, with the objective being to compare the ROMs obtained from Robust Proper Orthogonal Decomposition (RPOD) to those obtained from the traditional Proper Orthogonal Decomposition (POD). POD and RPOD are applied to in vitro, haemodynamic data acquired by Particle Image Velocimetry and compare the decomposed flows to those derived from Computational Fluid Dynamics (CFD) data for the same geometry and flow conditions. In this work, PIV and CFD results act as surrogates for clinical haemodynamic data e.g. MR, helping to demonstrate the potential use of ROMS in real clinical scenarios. The flow is reconstructed using different numbers of POD modes and the flow features obtained throughout the cardiac cycle are compared to the original Full Order Models (FOMs).Robust Principal Component Analysis (RPCA), the first step of RPOD, has been found to enhance the quality of PIV data, allowing POD to capture most of the kinetic energy of the flow in just two modes similar to the numerical data that are free from measurement noise. The reconstruction errors differ along the cardiac cycle with diastolic flows requiring more modes for accurate reconstruction. In general, modes 1–10 are found sufficient to represent the flow field. The results demonstrate that the coherent structures that characterise this aortic dissection flow are described by the first few POD modes suggesting that it is possible to represent the macroscale behaviour of aortic flow in a low-dimensional space; thus significantly simplifying the problem, and allowing for more computationally efficient flow simulations or machine learning based flow predictions that can pave the way for translation of such models to the clinic.

Investigation of the Sound Source Regions in Open and Closed Organ Pipes

The airflow in the mouth of an open and closed flue organ pipe of corresponding geometrical proportions is studied. The phase locked particle image velocimetry with subsequent analysis by the biorthogonal decomposition is employed in order to compare the flow mechanisms and related features. The most significant differences lie in the mean velocity distribution and rapidity of the jet lateral motion. Remarks on the pressure estimation from PIV data and its importance for the aeroacoustic source terms are made and a specific example is discussed.

Vapor concentration and bimodal distributions of turbulent fluctuations in cavitating flow around a hydrofoil

The article presents results of a statistical analysis of the original PIV data for the cavitating flow around the 2D symmetric hydrofoil mimicking a guide vane of a Francis turbine which were previously reported in Timoshevskiy et al. (2020). We employ the procedure of statistical vector filtration (Heinz et al., 2004) to eliminate vector outliers from the measured velocity fields, which allows us to retrieve genuine spatial distributions of higher-order statistical moments of velocity fluctuations, and the method of vapor phase detection (Pervunin et al., 2021) to extract time-averaged fields of vapor in the cavitating flow. The spatial distributions of the probability of vapor phase occurrence allowed us to unambiguously distinguish the extension of the flow area occupied by the dispersed phase (cavitation) together with the time-averaged concentration of the vapor phase in the three characteristic regimes of the cavitating flow as well as different features of cavitation evolution, including the location and length of an attached cavity and the place of detachments of cloud cavities in the case of unsteady cloud cavitation. The development of cavitation is also reflected in the fields of higher-order statistical moments of turbulent fluctuations by the example of coefficients of asymmetry and excess. With a transition to unsteady cloud cavitation, the distribution of velocity fluctuations transforms, taking a nonequilibrium shape, with an increase in magnitudes of the asymmetry and excess coefficients over a significant flow area. In a region of the attached cavity, around the place of formation of vapor clouds and downstream, where the cloud cavities are carried away by the flow, the distribution of velocity fluctuations becomes bimodal. Through visual inspection of the raw PIV images, realizations related to two characteristic phases of the cavity oscillation cycle were extracted, providing quasi-phase-averaged data. As a result, the bimodal shape of the distributions in certain areas of the unsteady cavitating flow was demonstrated to be most probably linked with periodic detachments and downstream advection of the vapor clouds as the predominant fundamental process determining the flow structure and dynamics.

Numerical evaluation of wind direction effects on the turbulence aerodynamics of a ship airwake

The airwake characteristics around a ship body are an important consideration for helicopter pilots during shipboard operations, as airwake can lead to the formation of massively turbulent flow over the ship deck. Therefore, this study conducted a delayed detached eddy simulation (DDES) to investigate the impact of the bow part of the ship and the wind direction on the turbulent flow characteristics of the ship deck airwake. Numerical simulations were performed for two different ship models (1:12.5) of the Simple Frigate Shape 1 and 2 (SPF1 and SFS2) to analyze the influence of the bow part on the deck flow-field. Seven different orientations of wind direction angle (HW, RW15, RW30, RW45, RW60, RW75, and RW90) were numerically simulated for SFS1. The time-averaged velocity and pressure fields computed by the DDES approach were validated in comparison to those of the experimental data measured by the PIV data and Kulite pressure sensors, respectively, at various locations over the ship deck. The numerical data revealed that, while the deck flow-field is not influenced by the bow of the ship, the airwake flow is significantly affected by the wind direction angle. Specifically, as the wind direction angle is increased, the turbulent kinetic energy is also increased and the flow-field becomes more asymmetric. Moreover, the spectral analysis and time/space assessment of the flow field showed more pressure fluctuations and a higher level of unsteadiness over the ship deck with a larger wind direction angle, which are important parameters in shipboard operations.

A New Approach to Evaluate 3D Flow Fields Using an Off-Axis 2D PIV System: Investigation of a Tubular Reactor Equipped with Kenics Static Mixers

In this work, an off-axis 2D Particle Image Velocimetry system is used to obtain the 3D flow field at the outlet of a tubular reactor equipped with Kenics static mixers. The 3D flow fields are obtained exploiting the out-of-plane velocity component and considering the symmetrical features of the flow generated by the static mixers. The raw results show that the velocity vectors, measured on a cross section perpendicular to the tube axis by 2D-PIV with the camera located at 24° from the measurement plane, are affected by the axial component of the flow. However, taking into account the symmetry of the flow field with respect to the tubular reactor axis and evaluating the effect of the out of plane velocity component, the correct 2D velocity vectors on the plane and also the velocity component in the axial direction can be calculated from the raw 2D PIV data. The consistency of the methodology is demonstrated by comparison of the results with the flow field measured in a smaller tubular reactor of similar geometry and Reynolds number with a symmetrical 2D-PIV system, with the camera located perpendicularly to the laser plane. Then, the 3D features of the flow are analyzed to characterize the effects of the different combinations of static mixer configurations on the fluid dynamics of the system in turbulent conditions. The results show that, as the pressure drop increases, a more uniform velocity distribution is achieved.Graphical

Gappy spectral proper orthogonal decomposition

Experimental spatio-temporal flow data often contain gaps or other types of undesired artifacts. To reconstruct flow data in the compromised or missing regions, a data completion method based on spectral proper orthogonal decomposition (SPOD) is developed. The algorithm leverages the temporal correlation of the SPOD modes with preceding and succeeding snapshots, and their spatial correlation with the surrounding data at the same time instant. For each gap, the algorithm first computes the SPOD of the remaining, unaffected data. In the next step, the compromised data are projected onto the basis of the SPOD modes. This corresponds to a local inversion of the SPOD problem and yields expansion coefficients that permit the reconstruction in the affected regions. This local reconstruction is successively applied to each gap. After all gaps are filled in, the procedure is repeated in an iterative manner until convergence. This method is demonstrated on two examples: direct numerical simulation of laminar flow around a cylinder, and time-resolved PIV data of turbulent cavity flow obtained by Zhang et al. (2019) [47]. Randomly added gaps correspond to 1%, 5%, and 20% of data loss. Even for 20% data corruption, and in the presence of measurement noise in the experimental data, the algorithm recovers 97% and 80% of the original data in the corrupted regions of the simulation and PIV data, respectively. These values are higher than those achieved by established methods like gappy POD and Kriging.

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%.

Feasibility Of Multi-Aperture µPTV For Wall Shear Stress Measurements

We present a feasibility study on 3d 3c micro PTV for boundary layer flows using a single high-speed camera with a microscope lens. Multi-aperture µPTV (MA-µPTV) relies on the “defocusing” concept (Willert &amp; Gharib, 1992) and determines the wall distance of a particle from the size of projected particle image triplets generated by placing an triplet aperture on the entrance pupil of a microscope objective. Illumination with a high-speed pulsed laser is introduced through the same window used for imaging. The calibration of the orientation and size of the particle image triplets is described and accounts for variation of both with lateral image position and wall distance. Geometrically constrained templates of 2d Gaussians are used to provide least square fitting of triple image intensities, thereby iteratively improving the initial centers and depth position of each particle. In addition to Gaussian weighting, the convolution of a Gaussian and a Lorentzian is studied, that latter of which is considered promising for modeling defocused particle images at large distances from the focus. Lagrangian particle tracks are reconstructed from 3d particle positions using state-of-the-art tracking procedures. Comparative profile-PIV measurements provide reference measurements including estimates of the wall shear stress. A comparison with PIV flow statistics is possible by bin-averaging the velocities of the particle tracks in the wall-normal direction. Mean wall shear rates obtained from MA-µPTV and using single-line cross-correlation on the PIV data are in good agreement and within the uncertainty of the flow parameters. Statistics from bin-averaged velocities of all tracked particles indicate consistency with profile-PIV and agree well with DNS data up to wall distances of 30 wall units.

Creating Data-Driven Turbulence Models Using PIV

Data-driven turbulence models have been created for a k-ε RANS model based on PIV data in a jet in crossflow. In the simpler of two implementations, the nominal value of the model coefficient Cµ was replaced with an optimized value calibrated to the PIV results. Despite being based on only four flow cases of a canonical configuration, the optimized model demonstrated superior performance over 48 flow cases of increasing complexity. A second, more sophisticated data-driven model has been created by mapping a spatially variable Cµ to flow state variables using machine learning of experimentally measured flow field properties of the turbulence. This second model has been implemented in a production RANS code but requires further improvements before it can return results deviating from either the nominal or calibrated Cµ models.

System Identification For Enhanced Flow Description From Multi-Pulse PIV

We propose a novel approach to obtain a time-resolved description from non-time-resolved PIV measurements. The method needs in input velocity and acceleration fields from ( at least) 3-pulse PIV data, without time r esolution. A sparse identification of nonlinear dynamics (based on the SINDy technique) is carried out to estimate the time history of coordinates in a low-dimensional space from Proper Orthogonal Decomposition (POD). The output is a reduced-order model of the dynamics which can be integrated to obtain time-resolved velocity fields using t he s napshots as i nitial c onditions. The t ime-resolved e volution of t he pressure fields is th en derived from the momentum equation. The time history of the velocity and pressure fields is obtained through a weighted Backward-Forward Integration (BFI) of the identified s ystem. Time super-sampling can be achieved by integration between consecutive non-time-resolved realizations. In alternative, simple one-directional time integration can be used for short-time prediction starting from individual snapshots. The algorithm is validated using a synthetic test case from 2D Direct Numerical Simulation of the wake of a fluidic pinball at a Reynolds number Re equal to 130, and PIV measurements of the wake of a NACA 0018 wing profile with Re = 4 800. We show that the method is able to reconstruct the flow dynamics for horizons of several convective times, provided that the basis for the data reduction is sufficiently c ompact. Our results suggest that manifold learning and data assimilation can be combined to obtain an enhanced flow description.

Simulation of Pressure–Velocity Correlations by Green’s Function Based on Reynolds Stress Model

Cost-effective wind energy harvesting by wind turbines in urban areas needs to strengthen the required flow field properties, such as mean velocity, turbulence, and its distribution. This paper conducts a series of CFD simulations to investigate the characteristics and related mechanisms of flow within the cavity, considering the force–turbulence interactions at the RANS scales. The pressure–velocity correlation term is formulated and solved by the elliptic relaxation equation to compensate for the Reynolds stress overestimation. Numerical simulations of flow over an open cavity with the proposed model are compared with corresponding PIV data. The results show that the mean velocity and the fluctuation velocity along the streamwise direction exist a slightly favorable pressure gradient. While the fluctuation velocity and fluctuation pressure show different correlation characteristics along the streamwise direction. Moreover, the pressure–velocity fluctuation correlation becomes obvious near the upper corner of the cavity due to the favorable pressure gradient. Hence, the leading and trailing locations of the cavity are both obvious favorable regions and further emphasis should be put on both high-accurate simulation methods and practical applications.

A novel ANN-CFD model for simulating flow in a vortex mixer

The study presents a novel ANN-CFD model for simulating flow in a vortex mixer (an unbaffled vessel stirred by a magnetic stirrer). Large eddy simulations (LES) are performed to simulate flow and turbulence considering presence of both air and liquid phases. The flow fields in air and liquid phases are coupled by applying suitable boundary conditions at the air–liquid interface represented by the vortex. The shape of the vortex is built-in in the computational domain and obtained by using an artificial neural network (ANN) model trained and validated with the data obtained from experiments carried out to capture the vortex shape under different parametric conditions. ANN-CFD model is validated with PIV data reported in literature. The ANN-CFD model reduces the computational time significantly by obviating the need of performing computationally very intensive interface tracking simulations. The model is used to understand hydrodynamics and turbulence characteristics of flow in the vortex mixer.