A statistical tool called design of experiments (DOEs) is introduced for uncertainty quantification in particle image velocimetry (PIV). DOE allows to quantify the total uncertainty as well as the systematic uncertainties arising from various experimental factors. The approach is based on measuring a quantity (e.g. time-averaged velocity or Reynolds stresses) several times by varying the levels of the experimental factors which are known to affect the value of the measured quantity. Then, using Analysis of Variances, the total variance in the measured quantity is computed and hence the total uncertainty. Moreover, the analysis provides the individual variances for each of the experimental factors, leading to the estimation of the systematic uncertainties from each factor and their contributions to the total uncertainty. The methodology is assessed for planar PIV measurements of the flow over a NACA0012 airfoil at 15 degrees angle of attack considering five experimental factors, namely camera aperture, inter-frame time separation, interrogation window size, laser sheet thickness and seeding density. Additionally, the methodology is applied to the investigation by stereoscopic PIV of the flow at the outlet of a ducted Boundary Layer Ingesting propulsor. The total uncertainty in the time-averaged velocity as well as the constituent systematic uncertainties due to the experimental factors, namely camera aperture, inter-frame time separation, interrogation window size and stereoscopic camera angle, are quantified.@en

Particle Image Velocimetry (PIV) is a leading technique that allows flow velocity measurements in two- and three- dimensional domains. PIV is a full-field, non-intrusive and quantitative technique. However, due to the complexity of the measurement chain, PIV results are often affected by errors from various sources. It is therefore necessary to identify these errors and quantify the uncertainties. The available PIV uncertainty quantification (UQ) approaches are limited in estimating systematic uncertainties in the measurements and mostly focus on the random uncertainty. In order to exploit full benefits of PIV, the knowledge of the full uncertainty comprising both random and systematic uncertainties is necessary. The present work proposes a comprehensive PIV-UQ framework which not only quantifies the systematic uncertainties but is also universal as it can potentially be used for any measurement irrespective of the measurement setup (e.g. planar PIV, tomographic PTV, large scale PIV or microscopic PTV) or the output quantity (e.g. mean velocity or higher order statistics). @en

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.@en

A novel approach is devised for the quantification of systematic uncertainty due to peak locking in particle image velocimetry (PIV), which also leads to correction of the peak-locking errors. The approach, applicable to statistical flow properties such as time-averaged velocity and Reynolds stresses, relies on image recordings with multiple time separations Δt and a least-squares regression of the measured quantities. In presence of peak locking, the measured particle image displacement is a non-linear function of Δt due to the presence of measurement errors which vary non-linearly with the sub-pixel particle image displacement. Additionally, the measured displacement fluctuations are a combination of the actual flow fluctuations and the measurement error. When the image recordings are acquired with multiple Δt's, a least-squares regression among the statistical results yields a correction where systematic errors due to peak locking are significantly diminished. The methodology is assessed for planar PIV measurements of the flow over a NACA0012 airfoil at 10 degrees angle of attack. Reference measurements with much larger Δt than the Δt's of the actual measurements, such that relative peak-locking errors are negligible for the former, are used to assess the validity of the proposed approach. @en

A novel approach is devised for the quantification of the systematic uncertainty due to peak locking in particle image velocimetry (PIV), which also leads to correction of the peak-locking errors. The approach relies on a linear regression of the measured displacements from multiple Δt acquisitions (Δt being the time separation between two frames of an image pair). In presence of peak locking, the measured particle image displacement is not a linear function of Δt as the measurement error varies non-linearly with the sub-pixel particle image displacement. In the proposed approach, image acquisition is conducted with multiple Δt’s, and then a linear regression is carried out among the measured time-averaged displacements at different Δt’s, yielding a regression displacement. When the Δt’s are selected properly, the latter represents a correction to the measured displacement where systematic errors due to peak locking are significantly diminished. The expression of the standard uncertainty in the regression displacement is provided. The regression displacement (and velocity) can also be used to quantify the systematic uncertainty due to peak locking in the measured time-averaged displacements (and velocities). The methodology is first assessed with synthetic data and then applied to planar PIV experiments on a uniform flow and an airfoil wake flow. Reference measurements with much larger Δt than the Δt’s of the actual measurements (such that relative peak-locking errors are negligible for the former) are used to validate the proposed approach in both the experiments. Uncertainty coverages for the estimated uncertainties in the velocities measured in the experiments of the uniform flow and the wake flow are of 67% and 59%, respectively, which are comparable to 68% confidence level at which the uncertainties are computed. This proves the validity of the proposed multi-Δt approach for peak-locking uncertainty quantification. @en

A novel approach is devised for the quantification of the systematic uncertainty due to peak locking in particle image velocimetry (PIV), which also leads to correction of the peak-locking errors. The approach relies on a linear regression of the measured displacements from multiple Δt acquisitions (Δt being the time separation between two frames of an image pair). In presence of peak locking, the measured particle image displacement is not a linear function of Δt as the measurement error varies non-linearly with the sub-pixel particle image displacement. In the proposed approach, image acquisition is conducted with multiple Δt’s, and then a linear regression is carried out among the measured time-averaged displacements at different Δt’s, yielding a regression displacement. When the Δt’s are selected properly, the latter represents a correction to the measured displacement where systematic errors due to peak locking are significantly diminished. The expression of the standard uncertainty in the regression displacement is provided. The regression displacement (and velocity) can also be used to quantify the systematic uncertainty due to peak locking in the measured time-averaged displacements (and velocities). The methodology is first assessed with synthetic data and then applied to planar PIV experiments on a uniform flow and an airfoil wake flow. Reference measurements with much larger Δt than the Δt’s of the actual measurements (such that relative peak-locking errors are negligible for the former) are used to validate the proposed approach in both the experiments. Uncertainty coverages for the estimated uncertainties in the velocities measured in the experiments of the uniform flow and the wake flow are of 67% and 59%, respectively, which are comparable to 68% confidence level at which the uncertainties are computed. This proves the validity of the proposed multi-Δt approach for peak-locking uncertainty quantification. @en