Uncertainty quantification in particle image velocimetry

Particle image velocimetry (PIV) has become the chief experimental technique for velocity field measurements in fluid flows. The technique yields quantitative visualizations of the instantaneous flow patterns, which are typically used to support the development of phenomenological models for complex flows or for validation of numerical simulations. However, due to the complex relationship between measurement errors and experimental parameters, the quantification of the PIV uncertainty is far from being a trivial task and has often relied upon subjective considerations. Recognizing the importance of methodologies for the objective and reliable uncertainty quantification (UQ) of experimental data, several PIV-UQ approaches have been proposed in recent years that aim at the determination of objective uncertainty bounds in PIV measurements. This topical review on PIV uncertainty quantification aims to provide the reader with an overview of error sources in PIV measurements and to inform them of the most up-to-date approaches for PIV uncertainty quantification and propagation. The paper first introduces the general definitions and classifications of measurement errors and uncertainties, following the guidelines of the International Organization for Standards (ISO) and of renowned books on the topic. Details on the main PIV error sources are given, considering the entire measurement chain from timing and synchronization of the data acquisition system, to illumination, mechanical properties of the tracer particles, imaging of those, analysis of the particle motion, data validation and reduction. The focus is on planar PIV experiments for the measurement of two- or three-component velocity fields. Approaches for the quantification of the uncertainty of PIV data are discussed. Those are divided into a-priori UQ approaches, which provide a general figure for the uncertainty of PIV measurements, and a-posteriori UQ approaches, which are data-based and aim at quantifying the uncertainty of specific sets of data. The findings of a-priori PIV-UQ based on theoretical modelling of the measurement chain as well as on numerical or experimental assessments are discussed. The most up-to-date approaches for a-posteriori PIV-UQ are introduced, highlighting their capabilities and limitations. As many PIV experiments aim at determining flow properties derived from the velocity fields (e.g. vorticity, time-average velocity, Reynolds stresses, pressure), the topic of PIV uncertainty propagation is tackled considering the recent investigations based on Taylor series and Monte Carlo methods. Finally, the uncertainty quantification of 3D velocity measurements by volumetric approaches (tomographic PIV and Lagrangian particle tracking) is discussed.Aerodynamic

Uncertainty quantification in particle image velocimetry and advances in time-resolved image and data analysis

Particle Image Velocimetry (PIV) is a well-established technique for the measurement of the flow velocity in a two or three-dimensional domain. As in any other technique, PIV data is affected by measurement errors, defined as the difference between the measured velocity and its actual value, which is unknown. Aim of uncertainty quantification is estimating an interval that contains the (unknown) actual error magnitude with a certain probability. The present work introduces a novel methodology for the uncertainty quantification of PIV data. The method relies upon the concept of image matching: the PIV recordings are matched based on the measured velocity field. The positional disparity between paired particle images is then computed to retrieve the measurement uncertainty. Both the numerical assessment via Monte Carlo simulations and the experimental assessment show that the image matching approach allows estimating the measurement uncertainty in good agreement with the actual error value. Furthermore, advanced methodologies for time-resolved image and data analysis are investigated. Those methodologies include: the enhancement of the image quality via a temporal filter applied to the PIV images; a multi-frame processing algorithm (pyramid correlation) that improves precision and robustness of PIV measurements; a post processing approach based on the solution of the Navier-Stokes equations for estimating the velocity field in regions where no experimental data is available.Aerodynamics, Wind Energy, Flight Performance and Propulsion (AWEP)Aerospace Engineerin

Special issue on uncertainty quantification in particle image velocimetry and Lagrangian particle tracking

Aerodynamic

Elimination of unsteady background reflections in PIV images by anisotropic diffusion

A novel approach is introduced that allows the elimination of undesired laser light reflections from particle image velocimetry (PIV) images. The approach relies upon anisotropic diffusion of the light intensity, which is used to generate a background image to be subtracted from the original image. The intensity is diffused only along the edges and not across the edges, thus allowing one to preserve, in the background image, the shape of boundaries as laser light reflections on solid surfaces. Due to its ability to produce a background image from a single snapshot, as opposed to most methods that make use of intensity information in time, the technique is particularly suitable for elimination of reflections in PIV images of unsteady models, such as transiting objects, propellers, flapping and pitching wings. The technique is assessed on an experimental test case which considers the flow in front of a propeller, where the laser light reflections on the model's surface preclude accurate determination of the flow velocity. Comparison of the anisotropic diffusion approach with conventional techniques for suppression of light reflections shows the advantages of the former method, especially when reflections need to be removed from individual images.Aerodynamic

Near Wake Analysis of a Two-Man Bobsleigh Scaled Model

The flow field in the near wake of a 1:5.5 bobsleigh model was investigated by means of stereoscopic particle image velocimetry. The time-averaged flow field revealed two counter-rotating vortices and a strong downwash between them. From the velocity field, the aerodynamic drag was retrieved invoking the conservation of momentum. This approach enabled relating the aerodynamic loads with the flow structures responsible of the loads. Measurements were repeated with different front-cowling rotations between 0° and 20°. It was found that small nose rotations allowed a drag reduction by approximately 5%, whereas for nose rotations exceeding 10° the drag coefficient remained approximately constant.Aerodynamic

Investigation of the Ahmed body cross-wind flow topology by robotic volumetric PIV

Robotic volumetric PIV is employed to investigate the time-averaged three-dimensional near-wake flow topology of the Ahmed body in steady cross-wind conditions. The model selected for this study is a 1:2 replica of the reference Ahmed body with 25° slant angle. The measurements are conducted at free-stream velocity of 12 m/s, resulting in a Reynolds number of 1.15×105 based on the model’s height. Yaw angles of 0°, 4° and 8° are considered. The results show that the position and strength of the C-pillar vortices are significantly influenced by the presence of a yaw angle. The yaw angles cause an increase in the strength of the windward C-pillar vortex, with a consequent upward displacement; conversely, the strength of the leeward vortex decreases, and the position of its core moves downwards and inboard. At the larger yaw angle, the presence of a ground streamwise vortex is detected which co-rotates with the windward C-pillar vortex and is located between the latter and the ground.Aerodynamic

On the Cyclist's Drag Crisis

The distribution of the critical velocity (point of minimum aerodynamic drag) is determined along the body of a time-trial cyclist by flow measurement in the model's near-wake.AerodynamicsAerodynamics, Wind Energy & Propulsio

Aeroacoustic analysis of a NACA 0015 airfoil with Gurney flap based on time-resolved PIV measurements

The present study investigates the feasibility of high-lift devices noise prediction based on measurements of time-resolved particle image velocimetry (TR-PIV). The model under investigation is a NACA 0015 airfoil with Gurney flap with height of 6% chord length. The velocity fields around and downstream the Gurney flap are measured by PIV and are used for the PIV-based noise predictions. The predictions are assessed via microphone measurements. Since the Gurney flap height is much smaller than the emitted acoustic wavelength, the source of noise can be considered compact and the integral implementation of Curle's analogy based on the unsteady aerodynamic loads can be followed. The results are compared with the simultaneous microphone measurements in terms of time histories and power spectra. The integral formulation of Curle's analogy yields acoustic sound pressure levels in good agreement with the simultaneous microphone measurements for the tonal component. All the calculated far-field noise power spectra reproduce the peak at vortex shedding frequency, which also agrees well with the microphone measurements.AerodynamicsWind Energ

On the wake deflection of vertical axis wind turbines by pitched blades

Wake losses are a critical consideration in wind farm design. The ability to steer and deform wakes can result in increased wind farm power density and reduced energy costs and can be used to optimize wind farm designs. This study investigates the wake deflection of a vertical axis wind turbine (VAWT) experimentally, emphasizing the effect of different load distributions on the wake convection and mixing. A trailing vortex system responsible for the wake topology is hypothesized based on a simplified vorticity equation that describes the relationship between load distribution and its vortex generation; the proposed vorticity system and the resulting wake topology are experimentally validated in the wind tunnel via stereoscopic particle image velocimetry measurements of the flow field at several wake cross-sections. Variations in load distribution are accomplished by a set of fixed blade pitches. The experimental results not only validate the predicted vorticity system but also highlight the critical role of the streamwise vorticity component in the deflection and deformation of the wake, thus affecting the momentum and energy recoveries. The evaluation of the various loading cases demonstrates the significant effect of the wake deflection on the wind power available to a downwind turbine, even when the distance between the two turbines is only three diameters.Flow Physics and TechnologyWind EnergyAerodynamic