Particle Image Velocimetry Algorithm Research Articles

Uncertainty quantification for velocity measurement with 2D2C particle image velocimetry

Abstract In this paper, a theoretical model of dimensionless instantaneous and average velocity measurement uncertainty quantification with 2D2C particle image velocimetry (PIV) is established under the framework of generally adopted international uncertainty quantification standards. The effectiveness of the model is verified using uniform flow field testing data. Combined with semi-quantitative analysis of the theoretical model, uncertainty control suggestions for PIV measurements are given. The major sources affecting the uncertainty of instantaneous velocity measurements are the reference velocity, particle instantaneous pixel displacement, and their correlation term. For average velocity measurement uncertainty quantification, the uncertainty of particle average pixel displacement is effectively controlled by taking a large number of particle images. Thus, three single-component terms — the calibration factor, particle average pixel displacement and reference velocity — and two correlation terms — the particle average pixel displacement–calibration factor and the particle average pixel displacement–reference velocity — all make an important contribution to the average velocity measurement uncertainty. To reduce the uncertainty of PIV velocity measurement, one can reduce the reference velocity measurement uncertainty, optimize the PIV algorithm and improve the calibration factor by applying a high spatial resolution imaging system in experiments. In addition, reducing the reference velocity measurement uncertainty and improving the spatial resolution are key feasible methods.

Towards High-Speed And High-Resolution Real-Time Optical Flow Particle Image Velocimetry

One of the major advantages of Optical Flow PIV (Particle Image Velocimetry) algorithms over Cross-Correlation PIV is their scalability leading to potentially very high computational speeds. This is confirmed in this study using different GPUs (Graphics Processor Unit) and different image sizes. The other advantage is the possibility of obtaining dense velocity fields of up to one vector per pixel. It is well known that particle seeding plays a crucial role in the results of standard particle image velocimetry based on cross-correlation algorithms. Its influence on the quality of the optical flow algorithm is not as well established. In this article the influence of particle concentration is quantified by introducing a criterion considering the proportion of “active” pixels in a snapshot. It is shown that it is possible to optimize particle concentration to maximize the percentage of active pixels, leading to better spatial resolution, down to one vector per pixel. The principle is validated on a vortex-free flow and applied to the complex 3D flow downstream a backward-facing step.

A Particle Based Approach For Improved Resolution PIV And TOMO-PIV Based On The Coherent Point Drift And The Affine Least-Squares Transformation

Particle Image Velocimetry (PIV) is a widely used method for flow diagnostics, but there is still potential for improvement, particularly in terms of velocity gradient estimation and computational cost when considering three-dimensional problems. This paper presents a framework that combines a Particle Tracking Velocity (PTV) approach with local gradient-based Eulerian reconstruction to improve PIV performance. The approach uses the Coherent Point Drift (CPD) method for particle pairing and introduces the Affine Least-Squares Transformation (ALST) for local deformation gradient estimation. The CPD method consists of pairing particles whose positions at two successive instants have been obtained from the images. The ALST estimates local deformation gradients, allowing the Eularian reconstruction of the velocity field. The effectiveness of the proposed method compared to traditional PIV algorithms is demonstrated by synthetic test cases in both 2D and 3D configurations. In 2D cases, the CPD+ALST approach outperforms standard PIV methods, especially in capturing local velocity gradients. In 3D cases, comparisons with TOMO-PIV show the improved performance of CPD+ALST in the context of locally large velocity gradients. However, the linear nature of ALST makes it less efficient than quadratic binning techniques. The study demonstrates the potential of CPD+ALST to improve velocity field reconstruction in complex flows.

Reach-Scale Mapping of Surface Flow Velocities from Thermal Images Acquired by an Uncrewed Aircraft System along the Sacramento River, California, USA

An innovative payload containing a sensitive mid-wave infrared camera was flown on an uncrewed aircraft system (UAS) to acquire thermal imagery along a reach of the Sacramento River, California, USA. The imagery was used as input for an ensemble particle image velocimetry (PIV) algorithm to produce near-continuous maps of surface flow velocity along a reach approximately 1 km in length. To assess the accuracy of PIV velocity estimates, in situ measurements of flow velocity were obtained with an acoustic Doppler current profiler (ADCP). ADCP measurements were collected along pre-planned cross-section lines within the area covered by the imagery. The PIV velocities showed good agreement with the depth-averaged velocity measured by the ADCP, with R2 values ranging from 0.59–0.97 across eight transects. Velocity maps derived from the thermal image sequences acquired on consecutive days during a period of steady flow were compared. These maps showed consistent spatial patterns of velocity vector magnitude and orientation, indicating that the technique is repeatable and robust. PIV of thermal imagery can yield velocity estimates in situations where natural water-surface textures or tracers are either insufficient or absent in visible imagery. Future work could be directed toward defining optimal environmental conditions, as well as limitations for mapping flow velocities based on thermal images acquired via UAS.

A two‐dimensional, reach‐scale implementation of space‐time image velocimetry (STIV) and comparison to particle image velocimetry (PIV)

AbstractImage‐based algorithms have become a powerful tool for estimating flow velocities in rivers. In this study, we generalize the space‐time image velocimetry (STIV) framework for reach‐scale application rather than along a cross section. The new algorithm provides information on both the magnitude and orientation of velocity vectors, and we refer to the algorithm as two‐dimensional STIV, or 2D‐STIV. The workflow involves setting up a grid, using centreline tangent vectors as initial estimates of flow direction, and then extracting space‐time images (STIs) along search lines radiating from each grid node. The autocorrelation function is used to infer the inclination of streak lines present in STIs, which represents the advection of water surface features. Information on flow direction is obtained by evaluating various candidate search lines and identifying that which yields the highest velocity. This search can be performed exhaustively or via optimization. We applied the new 2D‐STIV algorithm to three test cases, one simulated data set and two natural channels, and compared image‐derived velocities to modelled or measured values. We also applied two established particle image velocimetry (PIV) algorithms to the same data sets. 2D‐STIV performed as well as the two PIV algorithms for simulated images. For a natural river with distinct water surface features, 2D‐STIV was effective for much of the channel but also led to a more patchy, irregular velocity field than the two PIV algorithms. For a site lacking obvious surface features, exhaustive 2D‐STIV led to velocity estimates uncorrelated with field data while the optimization‐based version produced erratic flow directions. 2D‐STIV also required greater image sequence durations, higher frame rates, and generally longer computational run times. Overall, ensemble PIV was the most reliable algorithm.

A framework to facilitate development and testing of image‐based river velocimetry algorithms

AbstractImage‐based methods have compelling, demonstrated potential for characterizing flow fields in rivers, but algorithms like particle image velocimetry (PIV) must be further tested and improved to enable more effective use of these techniques. This paper presents a framework designed for this exact purpose: Simulating Hydraulics and Images for Velocimetry Evaluation and Refinement (SHIVER). The approach involves coupling a hydrodynamic model with a synthetic particle generator to advect particles between frames, as dictated by local velocity vectors and thus construct a plausible image sequence specific to the reach of interest. The resulting time series can then be used as input to a velocimetry algorithm to compare image‐derived estimates with known (modelled) velocities to perform an exhaustive, spatially distributed accuracy assessment. As an example application of SHIVER, we examined the effects of interrogation area (IA) size, frame rate, flow velocity, and image sequence duration on the performance of a standard PIV algorithm. This analysis indicated that image‐derived velocities were generally in close agreement with those from the flow model (root mean square error <10% and mean bias <3%), except when small IAs were coupled with low frame rates. Velocity estimates were most accurate for the lowest modelled discharge ( at baseflow) and became less reliable as the mean flow velocity increased ( for an intermediate discharge and at bankfull). Accuracy was essentially independent of image sequence duration, implying that long occupations might not be necessary. Errors were concentrated along channel margins, where PIV‐based velocities tended to be greater than those from the flow model. Small IAs led to underpredictions of velocity, while larger IAs led to overpredictions. SHIVER is highly modular and could be updated to make use of different hydrodynamic models or image simulators. The framework could also facilitate more thorough sensitivity analyses and comparison of various velocimetry algorithms.

Transient phase in shear zone formation in sands

An experimental study has been made to study the emergence of narrow shear zones (“shear bands”), in uniformly graded quartzitic sand under dry conditions using the model setup of orthogonal cutting. A fixed region of interest around the stationary tool is imaged using a high-resolution and high-speed camera and further analyzed using Particle Image Velocimetry (PIV) algorithm to obtain the flow (velocity) fields. The velocity field maps of the near tool tip region demonstrate sharp change in the motion of sand particles along with the formation of a “dead zone” – a region of material stagnation or no flow. This extent of the dead zone was found to fluctuate in time for a given cutting speed, and no significant effect of the cutting speed (or strain rate) is observed in the propagation of dead zone size. The dynamic repose angle of the evolving sand pile in front of the tool increases initially and then attains a steady value of around 40°. The regions of intense straining in the sands were revealed in the effective strain rate fields. The shear localization was seen to emerge from the tooltip and propagate toward the free surface. The inclination angle of these bands evolves periodically with time and showed a decreasing trend due to an increase in the surcharge. The oscillatory force signatures suggested that every undisturbed ensemble of sands, on reaching the tool vicinity, undergoes material softening (dilation) followed by hardening(compaction), which is also reflected in the periodic formation and destruction of shear bands.

Analysis of Flow Field Characteristics of the Propane Jet Combustion Flame

In order to effectively prevent fire accidents and improve fire management capability, this paper describes the independent designs and builds of an experimental low-cost particle image velocimetry platform for a propane jet combustion flame using traditional mutual correlation theory. The particle image velocimetry (PIV) algorithm is written based on MATLAB software, allowing it to realise image preprocessing, multi-level grid window deformation inter-correlation calculations, and other functions. Fluid flow velocity and vorticity are used as entry points to study the flame combustion mechanism. The air flow field and vorticity above the propane jet flame are analysed. The results show that, from the level of fluid flow velocity, the maximum fluid flow velocity in the test area does not exceed 0.23 m/s, and the maximum transverse fluid flow velocity is close to 0.15 m/s. Additionally, the longitudinal fluid flow velocity is opposite the upper and lower portions of the longitudinal flow velocity, and there is a swirling phenomenon in the propane flame jet. From the vorticity level, the closer to the centre of the jet in the vortex plane, the faster the air flow speed, and simultaneously, in the upper and lower parts of the vortex, the air flow travels in the opposite direction and is of equal size. The particle image velocimetry platform that was independently designed in this study can efficiently characterise the dynamic flow field and the flow characteristics of complex combustion chambers, simultaneously ensuring high efficiency and reducing research costs. It provides a measurement method and experimental basis for the development of fire extinguishing equipment and numerical simulation, while also helping us to carry out a series of subsequent studies on fire extinguishing mechanisms.

ANDROMEDE — A software platform for optical surface velocity measurements

Methods and algorithms for measuring stream surface velocities have been continuously developed over the past five years to adapt to specific flow typologies. The free software ANDROMEDE allows easy use and comparison of these methods with image processing capabilities designed for measurements in natural environments and with unmanned aerial vehicles. Conventional particle tracking velocimetry, optical flow and particle image velocimetry algorithms, as well as filtering and statistical analysis methods, are available on a single platform. The code is written in Python, exploits available Python libraries, and allows accessible open-source code development. The validation of the integrated algorithms is presented on three case studies that represent the targeted applications: the study of currents for eco-hydraulics, the measurement of low water flows and the diagnosis of hydraulic structures. The field measurements are in very good agreement with the optical measurements and demonstrate the usefulness of the tool for rapid flow diagnosis for all the intended applications.

High level GPU-accelerated 2D PIV framework in Python

The Particle Image Velocimetry (PIV) method is widely used for optical measurment of flow velocity fields. This paper demonstrates the possibilities of using high-level libraries for GPU-accelerated PIV data analysis in Python. The Torch PIV library for the analysis of 2D PIV experiments based on the deep learning framework PyTorch with CUDA support was developed. The library implements a multi pass cross-correlation FFT PIV algorithm with an interrogation window shift. The chosen implementation does not require compilation from the user, has a compact codebase, is able to run both on the CPU and the GPU depending on the user choice, and also it is as flexible as the Python module. In this work, the performance of the CPU version of the developed method was compared with existing open source implementations. It is shown that the main functions of the developed module can be executed on the GPU at the speed of CUDA implementations. The developed library is tested on synthetic images and experimental data. Program SummaryProgram title: TorchPIV.CPC Library link to program files: https://doi.org/10.17632/yw43vjc36h.1.Developer's repository link: https://github.com/NikNazarov/TorchPIV.Licensing provisions: MIT license.Programming language: Python.Nature of problem: PIV experiments often require analyzing a large number of images in order to determine the statistical characteristics of the flow. GPUs are actively used in this field to speed up the data analysis process. Open-source software solutions to this problem usually require build and are difficult to integrate into the analysis pipelines.Solution method: The main feature of the developed module is its flexibility and simple distribution. The module is cross-platform, and installation does not require compilation from the user. The developed library can be imported as an ordinary Python module, at the same time it allows to get a significant performance gain when analyzing PIV experiments by using NVIDIA GPUs. Implementation in pure Python allows the module to serve as a backend for more complex experimental data processing systems. The core library of this method is one of the most reliable and widespread in the field of machine learning.

An Improved Convolutional Neural Network for Particle Image Velocimetry

With the wide application of Particle Image Velocimetry (PIV) technology in various engineering and research fields, the requirements for the accuracy, computational efficiency, and robustness of PIV algorithms are increasing. Although traditional algorithms have wide applicability, they suffer from low accuracy, large computational cost, and poor robustness. Recently, deep learning algorithms have provided new solutions, especially, convolutional neural networks with different structures, which have achieved good performance on synthetic PIV datasets. This paper proposes a structural improvement scheme for PIV convolutional neural network models. Experiments verify that the proposed method can significantly optimize the performance of the model on synthetic PIV datasets, providing a novel approach for improving other convolutional neural networks for PIV analysis.

Applying Super High Resolution Fluorescence Microscope and Advanced Smart Cloud Algorithm in Real-Time Quantitative Processing and Analysis of Electroconvection

In an electrochemical cell at high current densities, electroconvection plays a critical role in determining the morphology of electrodeposited metals. The resultant dendrite formation leads to risky battery performance failure. Over the past decades, though intensive theoretical analysis and experimental effort have been done, the detailed structure and dynamics of electroconvection remain unknown, because experimental observations lacked the resolution to expose the fundamental, hierarchical spatial structure of these flows, while the data processing algorithms were not fully established for large sample size. To address this shortcoming, we built an advanced optical electrochemical cell that fits in situ imaging with a super-resolution fluorescence microscope. By observing and recording real-time motions of electrolytes, electroconvection flows have been interrogated at unprecedented, high temporal and spatial resolution. As a complement to the visualization studies, a cloud-computing analysis algorithm was developed by combining a higher resolution Particle Image Velocimetry algorithm and a machine learning model to enable velocity distribution data over the entire optical field of view at nanoscale or microscale spatial resolution. Consequently, detailed velocity maps are obtained across the optical electrochemical cell, allowing us to quantitatively measure and analyze the initiation and evolution of the hierarchical microstructures inside the electroconvection in a unidirectional electric field. With these powerful tools, we further studied the effect of polymer viscoelasticity on electroconvection and electrodeposition. The addition of an ultrahigh molar mass polyethylene oxide to the electrolytes transforms the materials to a viscoelastic fluid state that changes the electroconvection dependence on time and voltage and induces a smooth electrodeposition on the metal anode by unique polymer rheological properties. Especially, the relaxation of long polymer chains in electrolyte provides a promising manner to prevent dendrite growth. We further analyzed these observations using direct numerical simulations for Newtonian and viscoelastic fluid models, and the quantitative analysis of experimental results indicates good consistency with simulation predictions.

Fast and accurate flow measurement through dual-camera light field particle image velocimetry and ordered-subset algorithm

Light field particle image velocimetry (LF-PIV) can measure the three-dimensional (3D) flow field via a single perspective and hence is very attractive for applications with limited optical access. However, the flow velocity measurement via single-camera LF-PIV shows poor accuracy in the depth direction due to the particle reconstruction elongation effect. This study proposes a solution based on a dual-camera LF-PIV system along with an ordered-subset simultaneous algebraic reconstruction technique (OS-SART). The proposed system improves the spatial resolution in the depth direction and reduces the reconstruction elongation. The OS-SART also reduces the computational time brought by the dual-camera LF-PIV. Numerical reconstructions of the particle fields and Gaussian ring vortex field are first performed to evaluate the reconstruction accuracy and efficiency of the proposed system. Experiments on a circular jet flow are conducted to further validate the velocity measurement accuracy. Results indicate that the particle reconstruction elongation is reduced more than 10 times compared to the single-camera LF-PIV and the reconstruction efficiency is improved at least twice compared to the conventional SART. The accuracy is improved significantly for the ring vortex and 3D jet flow fields compared to the single-camera system. It is therefore demonstrated that the proposed system is capable of measuring the 3D flow field fast and accurately.

Three-dimensional color particle image velocimetry based on a cross-correlation and optical flow method

Rainbow particle image velocimetry (PIV) can restore the three-dimensional velocity field of particles with a single camera; however, it requires a relatively long time to complete the reconstruction. This paper proposes a hybrid algorithm that combines the fast Fourier transform (FFT) based co-correlation algorithm and the Horn–Schunck (HS) optical flow pyramid iterative algorithm to increase the reconstruction speed. The Rankine vortex simulation experiment was performed, in which the particle velocity field was reconstructed using the proposed algorithm and the rainbow PIV method. The average endpoint error and average angular error of the proposed algorithm were roughly the same as those of the rainbow PIV algorithm; nevertheless, the reconstruction time was 20% shorter. Furthermore, the effect of velocity magnitude and particle density on the reconstruction results was analyzed. In the end, the performance of the proposed algorithm was verified using real experimental single-vortex and double-vortex datasets, from which a similar particle velocity field was obtained compared with the rainbow PIV algorithm. The results show that the reconstruction speed of the proposed hybrid algorithm is approximately 25% faster than that of the rainbow PIV algorithm.

Characterization of a debris flow event using an affordable monitoring system

This study presents monitoring data of a debris flow event in the Central Italian Alps. The debris flow occurred on August 16, 2021 in the Blè basin (Val Camonica valley, Lombardia Region) and was recorded by a monitoring station installed just few weeks before. The monitoring system was deployed to document the hydrologic response of the catchment to rainfall, and was designed to be lightweight, relatively cheap, and easy to deploy in the field. To this purpose, we combined video cameras with geophysical sensors (geophones and infrasound) and optimized the power supply system. The data recorded during the event allowed to identify the triggering rainfall, document the flow behaviour, and estimate surface flow velocity and flow rate using Particle Image Velocimetry algorithms. Moreover, the seismic signal generated by the debris flow revealed a peculiar frequency spectrum compared to regular streamflow. These results show that even a relatively simple monitoring system may provide valuable data on real debris flow events.

Correlation-based algorithms for accurate PIV measurement near the slip boundary

Accurate particle image velocimetry (PIV) measurement near the wall is of great significance in many fields. However, it is challenging for conventional PIV algorithms to deal with the near-wall flow, especially under the slip boundary condition. In general, the conventional window correlation method cannot accurately calculate the flow velocity at any location that is less than half the size of the interrogation window away from the boundary. For steady or periodic flow, the single-pixel ensemble correlation method can estimate the velocity very near the wall, but numerous image pairs are required, which comes at a great computational cost. In this paper, a new method based on window deformation is proposed to estimate the velocity profile of near-wall flows. Furthermore, a multi-pixel ensemble correlation method is proposed based on the single-pixel method, which improves accuracy and significantly reduces the computational cost relative to the single-pixel method. Both methods are validated by synthetic particle images and experiments. The present work extends the PIV methodology for accurately measuring near-wall flows, especially under the slip boundary condition, which will benefit research on the boundary layer, drag reduction, microfluidics, etc.

The air entrainment and hydrodynamic shear of the liquid slosh in syringes

Understanding the interface motion and hydrodynamic shear induced by the liquid sloshing during the insertion stage of an autoinjector can help improve drug product administration. We perform experiments to investigate the interfacial motion and hydrodynamic shear due to the acceleration and deceleration of syringes. The goal is to explore the role of fluid properties, air gap size, and syringe acceleration on the interface dynamics caused by autoinjector activation. We used a simplified autoinjector platform to record the syringe and liquid motion without any view obstruction. Water and silicone oil with the same viscosity are used as the model fluids. Particle Image Velocimetry (PIV) is employed to measure the velocity field. Simultaneous shadowgraph visualization captures the air entrainment. Our in-house PIV and image processing algorithms are used to quantify the hydrodynamic stress and interfacial area to investigate the effects of various autoinjector design parameters and fluid types on liquid sloshing. The results indicate that reducing the air gap volume and syringe acceleration/deceleration mitigate the interface area and effective shear. Moreover, the interfacial area and induced hydrodynamic stress decrease with the Fr=U/aD, where U is the interface velocity, a is the maximum syringe acceleration, and D is the syringe diameter.

Optimization in PIV algorithm for visualizing vortices in bubble wake

The PIV (Particle image velocimetry) is the most commonly used method for flow field observation because of its high efficiency and non-interference to the flow field. This study aims to clarify the optimal parameter conditions used in the cross-correlation algorithm of PIV for flow fields with vortices. The influence factors on the error of the cross-correlation algorithm are analyzed and discussed using a synthetic flow field, including the seeding conditions, the velocity gradient and vortex size. It is confirmed that the minimum particle number density per interrogation window is about 10, which generally limits the minimum size of the window. For a vortex, when the vortex size is fixed, the velocity gradient corresponding to the characteristic velocity both controls the lower and upper limitation of window size. For a relatively small vortex, generally a window not larger than the vortex size is asked. Then, a strategy to improve the observation based on the existing equipment is discussed and applied to visualize a rising bubble wake based on LIF (Laser-induced fluorescence) images.

On the Accuracy of Particle Image Velocimetry with Citizen Videos—Five Typical Case Studies

The application of image velocimetry to measure surface streamflow velocities requires meticulous preparation, including surveying and securing both the existence of floating features on the water surface, and, as in every hydrometry method, appropriate hydraulic conditions (e.g., uniform flow, turbulent velocity profile, etc.). Though these requirements can be easily satisfied when all stages involved in image velocimetry are prepared and executed by specialists, this is not guaranteed when the video footage is recorded by citizens. This kind of spontaneously obtained data are frequently the only available information of extreme flood events; therefore, and despite their non-scientific origin and standardization, these data are very important for hydrology. In this study, we evaluate image velocimetry under a variety of conditions, including conditions resembling citizen videos. Furthermore, we conclude on the manual analysis as a means of verification of the accuracy of the velocity estimations. An interesting finding from the case study with non-uniform flow conditions was that the surface velocities occurring at the middle section of the river, estimated using large-scale particle image velocimetry algorithms, exhibited a significant error, whereas the manual estimation was more accurate. This finding calls for further investigation and a more careful approach in similar conditions.

Two-Dimensional Flow Field Measurement Method for Sediment-Laden Flow Based on Optical Flow Algorithm

This paper proposes a novel particle image velocimetry (PIV) technique to generate an instantaneous two-dimensional velocity field for sediment-laden fluid based on the optical flow algorithm of ultrasound imaging. In this paper, an ultrasonic PIV (UIV) system is constructed by integrating a medical ultrasound instrument and an ultrasonic particle image velocimetry algorithm. The medical ultrasound instrument with a phased sensor array is used to acquire acoustic echo signals of particles in water and generate two-dimensional underwater ultrasound images. Based on the optical flow field, the instantaneous velocity of the particles in water corresponding to the pixels in the ultrasonic particle images is derived from the grayscale change between adjacent images under the L-K local constraint based on the optical flow field, and finally, the two-dimensional flow field is obtained. Through multiple sets of experiments, the proposed algorithm is verified. The experimental results are compared with those of the conventional cross-correlation algorithms. The results show that the L-K optical flow method can not only obtain the underwater velocity field accurately, but also has the advantages of good smoothness and extensive suitability, especially for the flow field measurement in sediment-laden fluid than conventional algorithms.