Abstract The turbulent/non-turbulent interface in a zero-pressure-gradient turbulent boundary layer at high Reynolds number ( $\mathit{Re}_\tau =14\, 500$ ) is examined using particle image velocimetry. An experimental set-up is utilized that employs multiple high-resolution cameras to capture a large field of view that extends $2\delta \times 1.1\delta $ in the streamwise/wall-normal plane with an unprecedented dynamic range. The interface is detected using a criteria of local turbulent kinetic energy and proves to be an effective method for boundary layers. The presence of a turbulent/non-turbulent superlayer is corroborated by the presence of a jump for the conditionally averaged streamwise velocity across the interface. The steep change in velocity is accompanied by a discontinuity in vorticity and a sharp rise in the Reynolds shear stress. The conditional statistics at the interface are in quantitative agreement with the superlayer equations outlined by Reynolds (J. Fluid Mech., vol. 54, 1972, pp. 481–488). Further analysis introduces the mass flux as a physically relevant parameter that provides a direct quantitative insight into the entrainment. Consistency of this approach is first established via the equality of mean entrainment calculations obtained using three different methods, namely, conditional, instantaneous and mean equations of motion. By means of ‘mass-flux spectra’ it is shown that the boundary-layer entrainment is characterized by two distinctive length scales which appear to be associated with a two-stage entrainment process and have a substantial scale separation.

http://absimage.aps.org/image/DFD12/MWS_DFD12-2012-001385.pdf

The Turbulent/Non-turbulent Interface and Entrainment in a Boundary Layer

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.

/pdf/uncertainty-quantification-in-particle-image-velocimetry-44buxu5nve.pdf

Uncertainty quantification in particle image velocimetry

Wall turbulence is a ubiquitous phenomenon in nature and engineering applications, yet predicting such turbulence is difficult due to its complexity. High-Reynolds-number turbulence arises in most practical flows, and is particularly complicated because of its wide range of scales. Although the attached-eddy hypothesis postulated by Townsend can be used to predict turbulence intensities and serves as a unified theory for the asymptotic behaviours of turbulence, the presence of coherent structures that contribute to the logarithmic behaviours has not been observed in instantaneous flow fields. Here, we demonstrate the logarithmic region of the turbulence intensity by identifying wall-attached structures of the velocity fluctuations ( structures. These findings suggest that the identified structures are prime candidates for Townsend’s attached-eddy hypothesis and that they can serve as cornerstones for understanding the multiscale phenomena of high-Reynolds-number boundary layers.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2243925528E22AE6C4125288B89953DE/S0022112018007279a.pdf/div-class-title-wall-attached-structures-of-velocity-fluctuations-in-a-turbulent-boundary-layer-div.pdf

Wall-attached structures of velocity fluctuations in a turbulent boundary layer

The spectra and correlations of the velocity fluctuations in turbulent channels, especially above the buffer layer, are analysed using new direct numerical simulations with friction Reynolds numbers up to Re at very large ones.

Scaling of the energy spectra of turbulent channels

A parametric study of the factors contributing to peak-locking, a known bias error source in particle image velocimetry (PIV), is conducted using synthetic data that are processed with a state-of-the-art PIV algorithm. The investigated parameters include: particle image diameter, image interpolation techniques, the effect of asymmetric versus symmetric window deformation, number of passes and the interrogation window size. Some of these parameters are found to have a profound effect on the magnitude of the peak-locking error. The effects for specific PIV cameras are also studied experimentally using a precision turntable to generate a known rotating velocity field. Image time series recorded using this experiment show a linear range of pixel and sub-pixel shifts ranging from 0 to ±4 pixels. Deviations in the constant vorticity field (ω z ) reveal how peak-locking can be affected systematically both by varying parameters of the detection system such as the focal distance and f-number, and also by varying the settings of the PIV analysis. A new a priori technique for reducing the bias errors associated with peak-locking in PIV is introduced using an optical diffuser to avoid undersampled particle images during the recording of the raw images. This technique is evaluated against other a priori approaches using experimental data and is shown to perform favorably. Finally, a new a posteriori anti peak-locking filter (APLF) is developed and investigated, which shows promising results for both synthetic data and real measurements for very small particle image sizes.

https://iopscience.iop.org/article/10.1088/0957-0233/27/10/104005/pdf

Peak-locking reduction for particle image velocimetry

Time-resolved planar particle image velocimetry was used to analyse the structuring of a turbulent boundary layer into uniform momentum zones (UMZs). The instantaneous peak-detection method employed by Adrian et al. (J. Fluid Mech., vol. 422, 2000, pp. 1–54) and de Silva et al. (J. Fluid Mech., vol. 786, 2016, pp. 309–331) is extended to account for temporal coherence of UMZs. The resulting number of zones detected appears to follow a normal distribution at any given instant. However, the extreme cases in which the number of zones is either very high or very low, are shown to be linked with two distinct flow states. A higher than average number of zones is associated with a large-scale event in the log region which creates increased small-scale activity within that region. Conversely, a low number of zones corresponds to a large-scale event in the log region and decreased turbulent activity away from the wall. The residence times, within the measurement plane, of zones belonging to the latter scenario are shown to be on average four times larger than those of zones present during higher than average zone structuring states. For both cases, greater residence times are observed for zones of higher momentum that are generally closer to the free stream.

/pdf/time-evolution-of-uniform-momentum-zones-in-a-turbulent-mrvo6exjvl.pdf

Time evolution of uniform momentum zones in a turbulent boundary layer

Streamwise velocity and wall-shear stress are acquired simultaneously with a hot-wire and an array of azimuthal/spanwise-spaced skin friction sensors in large-scale pipe and boundary layer flow facilities at high Reynolds numbers. These allow for a correlation analysis on a per-scale basis between the velocity and reference skin friction signals to reveal which velocity-based turbulent motions are stochastically coherent with turbulent skin friction. In the logarithmic region, the wall-attached structures in both the pipe and boundary layers show evidence of self-similarity, and the range of scales over which the self-similarity is observed decreases with an increasing azimuthal/spanwise offset between the velocity and the reference skin friction signals. The present empirical observations support the existence of a self-similar range of wall-attached turbulence, which in turn are used to extend the model of Baars et al. (J. Fluid Mech., vol. 823, p. R2) to include the azimuthal/spanwise trends. Furthermore, the region where the self-similarity is observed correspond with the wall height where the mean momentum equation formally admits a self-similar invariant form, and simultaneously where the mean and variance profiles of the streamwise velocity exhibit logarithmic dependence. The experimental observations suggest that the self-similar wall-attached structures follow an aspect ratio of in the streamwise, spanwise and wall-normal directions, respectively.

/pdf/simultaneous-skin-friction-and-velocity-measurements-in-high-1wi8dup0tc.pdf

Simultaneous skin friction and velocity measurements in high Reynolds number pipe and boundary layer flows

A quantification metric is provided to determine the degree to which a particle image velocimetry data set is pixel-locked. The metric is calculated by integrating the histogram equalization transfer function and normalizing by the worst-case scenario to return the percentage pixel-locked. When this metric is calculated for each position in the vector field, it is shown that pixel-locking is non-uniform across the field. Hence, pixel-locking adjustments should be made on a vector-by-vector basis rather than uniformly across a field, although the latter is the common practice. A methodology is provided to compensate for the effects of pixel-locking on a vector-by-vector basis. This includes applying a Gaussian filter directly to the images, processing the images with window deformation, ensuring the vector fields are in pixel displacements, applying histogram equalization calculated at each vector coordinate, and mapping the adjusted vector fields to physical space.

/pdf/quantification-and-adjustment-of-pixel-locking-in-particle-rhciijkrj3.pdf

Quantification and adjustment of pixel-locking in particle image velocimetry

This study presents findings from a first-of-its-kind measurement campaign that includes simultaneous measurements of the full velocity and vorticity vectors in both pipe and boundary layer flows under matched spatial resolution and Reynolds number conditions. Comparison of canonical turbulent flows offers insight into the role(s) played by features that are unique to one or the other. Pipe and zero pressure gradient boundary layer flows are often compared with the goal of elucidating the roles of geometry and a free boundary condition on turbulent wall flows. Prior experimental efforts towards this end have focused primarily on the streamwise component of velocity, while direct numerical simulations are at relatively low Reynolds numbers. In contrast, this study presents experimental measurements of all three components of both velocity and vorticity for friction Reynolds numbers 휏 ranging from 5000 to 10 000. Differences in the two transverse Reynolds normal stresses are shown to exist throughout the log layer and wake layer at Reynolds numbers that exceed those of existing numerical data sets. The turbulence enstrophy profiles are also shown to exhibit differences spanning from the outer edge of the log layer to the outer flow boundary. Skewness and kurtosis profiles of the velocity and vorticity components imply the existence of a ‘quiescent core’ in pipe flow, as described by Kwon et al. (J. Fluid Mech., vol. 751, 2014, pp. 228–254) for channel flow at lower 휏 , and characterize the extent of its influence in the pipe. Observed differences between statistical profiles of velocity and vorticity are then discussed in the context of a structural difference between free-stream intermittency in the boundary layer and ‘quiescent core’ intermittency in the pipe that is detectable to wall distances as small as 5 % of the layer thickness.

/pdf/a-comparative-study-of-the-velocity-and-vorticity-structure-1qs6v4q39a.pdf

R. J. Hearst

Papers

Time evolution of uniform momentum zones in a turbulent boundary layer

Simultaneous skin friction and velocity measurements in high Reynolds number pipe and boundary layer flows

Quantification and adjustment of pixel-locking in particle image velocimetry

A comparative study of the velocity and vorticity structure in pipes and boundary layers at friction Reynolds numbers up to 10(4)