To improve the performance of particle image velocimetry in measuring instantaneous velocity fields, direct cross-correlation of image fields can be used in place of auto-correlation methods of interrogation of double- or multiple-exposure recordings. With improved speed of photographic recording and increased resolution of video array detectors, cross-correlation methods of interrogation of successive single-exposure frames can be used to measure the separation of pairs of particle images between successive frames. By knowing the extent of image shifting used in a multiple-exposure and by a priori knowledge of the mean flow-field, the cross-correlation of different sized interrogation spots with known separation can be optimized in terms of spatial resolution, detection rate, accuracy and reliability.

Theory of cross-correlation analysis of PIV images : Image analysis as measuring technique in flows

The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

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The Structure of Turbulent Shear Flow

A survey is given of the major developments in three-dimensional velocity field measurements using the tomographic particle image velocimetry (PIV) technique. The appearance of tomo-PIV dates back seven years from the present review (Elsinga et al 2005a 6th Int. Symp. PIV (Pasadena, CA)) and this approach has rapidly spread as a versatile, robust and accurate technique to investigate three-dimensional flows (Arroyo and Hinsch 2008 Topics in Applied Physics vol 112 ed A Schroder and C E Willert (Berlin: Springer) pp 127–54) and turbulence physics in particular. A considerable number of applications have been achieved over a wide range of flow problems, which requires the current status and capabilities of tomographic PIV to be reviewed. The fundamental aspects of the technique are discussed beginning from hardware considerations for volume illumination, imaging systems, their configurations and system calibration. The data processing aspects are of uppermost importance: image pre-processing, 3D object reconstruction and particle motion analysis are presented with their fundamental aspects along with the most advanced approaches. Reconstruction and cross-correlation algorithms, attaining higher measurement precision, spatial resolution or higher computational efficiency, are also discussed. The exploitation of 3D and time-resolved (4D) tomographic PIV data includes the evaluation of flow field pressure on the basis of the flow governing equation. The discussion also covers a-posteriori error analysis techniques. The most relevant applications of tomo-PIV in fluid mechanics are surveyed, covering experiments in air and water flows. In measurements in flow regimes from low-speed to supersonic, most emphasis is given to the complex 3D organization of turbulent coherent structures.

Tomographic PIV: principles and practice

The linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend’s attached eddies. Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies in the original theory, providing direct evidence on the existence of Townsend’s attached eddies. It is shown that a single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length between and , where is half the height of the channel, the former is found to be self-similar along and , while the latter is self-similar along and where is the wall-normal direction. The scaling suggests that the smallest attached eddy would be a near-wall coherent motion in the form of a streak and quasi-streamwise vortices aligned to that, whereas the largest one would be an outer motion with a very-large-scale motion (VLSM) and large-scale motions (LSMs) aligned to that. The attached eddies in between, the size of which is proportional to their distance from the wall, contribute to the logarithmic region and fill the space caused by the length scale separation. The scaling is also found to yield behaviour consistent with the emergence of spectra in a number of previous studies. Finally, a further discussion is provided, in particular on Townsend’s inactive motion and several recent theoretical findings.

Statistical structure of self-sustaining attached eddies in turbulent channel flow

Known structures and self-sustaining mechanisms of wall turbulence are reviewed and explored in the context of the scale interactions implied by the nonlinear advective term in the Navier–Stokes equations. The viewpoint is shaped by the systems approach provided by the resolvent framework for wall turbulence proposed by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in which the nonlinearity is interpreted as providing the forcing to the linear Navier–Stokes operator (the resolvent). Elements of the structure of wall turbulence that can be uncovered as the treatment of the nonlinearity ranges from data-informed approximation to analysis of exact solutions of the Navier–Stokes equations (so-called exact coherent states) are discussed. The article concludes with an outline of the feasibility of extending this kind of approach to high-Reynolds-number wall turbulence in canonical flows and beyond.

The engine behind (wall) turbulence: perspectives on scale interactions

A combination of cross-wire probes with an array of flush-mounted skin-friction sensors are used to study the three-dimensional conditional organisation of large-scale structures in a high-Reynolds-number turbulent boundary layer. Previous studies have documented the amplitude modulation of small-scale motions in response to conditionally averaged large-scale events, but the data are largely restricted to the streamwise component of velocity alone. Here, we report results based on all three components of velocity and find that the small-scale spanwise and wall-normal fluctuations (v and w) and the instantaneous Reynolds shear stress ( uw) are modulated in a very similar manner to that previously noted for the streamwise fluctuations (u). The envelope of the small scale fluctuations for all velocity components is well described by the large-scale component of the u fluctuation. These results also confirm the conditional existence of roll modes associated with the very large-scale or ‘superstructure’ motions.

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Amplitude modulation of all three velocity components in turbulent boundary layers

An assessment of self-similarity in the inertial sublayer is presented by considering the wall-normal velocity, in addition to the streamwise velocity component. The novelty of the current work lies in the inclusion of the second velocity component, made possible by carefully conducted subminiature ×-probe experiments to minimise the errors in measuring the wall-normal velocity. We show that not all turbulent stress quantities approach the self-similar asymptotic state at an equal rate as the Reynolds number is increased, with the Reynolds shear stress approaching faster than the streamwise normal stress. These trends are explained by the contributions from attached eddies. Furthermore, the Reynolds shear stress cospectra, through its scaling with the distance from the wall, are used to assess the wall-normal limits where self-similarity applies within the wall-bounded flow. The results are found to be consistent with the recent prediction from the work of Wei et al. [“Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows,” J. Fluid Mech. 522, 303–327 (2005)], Klewicki [“Reynolds number dependence, scaling, and dynamics of turbulent boundary layers,” J. Fluids Eng. 132, 094001 (2010)], and others that the self-similar region starts and ends at z+∼O(δ+) and O(δ+), respectively. Below the self-similar region, empirical evidence suggests that eddies responsible for turbulent stresses begin to exhibit distance-from-the-wall scaling at a fixed z+ location; however, they are distorted by viscous forces, which remain a leading order contribution in the mean momentum balance in the region z+≲O(δ+), and thus result in a departure from self-similarity.

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Distance-from-the-wall scaling of turbulent motions in wall-bounded flows

We examine the behaviour of turbulent boundary layers over surfaces composed of spanwise-alternating smooth and rough strips, where the width of the strips varies such that, where is the boundary-layer thickness averaged over one spanwise wavelength of the heterogeneity. The experiments are configured to examine the influences of spanwise variation in wall shear stress over a large range. Hot-wire anemometry and particle image velocimetry (PIV) reveal that the half-wavelength governs the diameter and strength of the resulting mean secondary flows and hence the observed isovels of the mean streamwise velocity. Three possible cases are observed: limiting cases (either or), where the secondary flows are confined near the wall or near the roughness change, and intermediate cases (), where the secondary flows are space filling and at their strongest. These secondary flows, however, exhibit a time-dependent behaviour which might be masked by time averaging. Further analysis of the energy spectrogram and fluctuating flow fields obtained from PIV show that the secondary flows meander in a similar manner to that of large-scale structures occurring naturally in turbulence over smooth walls. The meandering of the secondary flows is a function of and is most prominent when.

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The effect of spanwise wavelength of surface heterogeneity on turbulent secondary flows

Here, we report the measurements of two-dimensional (2-D) spectra of the streamwise velocity (u) in a high-Reynolds-number turbulent boundary layer. A novel experiment employing multiple hot-wire probes was carried out at friction Reynolds numbers ranging from 2400 to 26 000. Taylor's frozen turbulence hypothesis is used to convert temporal-spanwise information into a 2-D spatial spectrum which shows the contribution of streamwise (λx) and spanwise (λy) length scales to the streamwise variance at a given wall height (z). At low Reynolds numbers, the shape of the 2-D spectra at a constant energy level shows λy/z ∼ (λx/z)1/2 behaviour at larger scales, which is in agreement with the existing literature at a matched Reynolds number obtained from direct numerical simulations. However, at high Reynolds numbers, it is observed that the square-root relationship tends towards a linear relationship (λy ∼ λx), as required for self-similarity and predicted by the attached eddy hypothesis.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/548E2EFD8F94B4ED6EBE200A3B5E5C18/S0022112017003597a.pdf/div-class-title-two-dimensional-energy-spectra-in-high-reynolds-number-turbulent-boundary-layers-div.pdf

Two-dimensional energy spectra in high-Reynolds-number turbulent boundary layers

A technique to enhance the reconstruction quality and consequently the accuracy of the velocity vector field obtained in Tomo-PIV experiments is presented here. The methodology involves detecting and eliminating spurious outliers in the reconstructed intensity field (ghost particles). A simulacrum matching-based reconstruction enhancement (SMRE) technique is proposed, which utilizes the characteristic shape and size of actual particles to remove ghost particles in the reconstructed intensity field. An assessment of SMRE is performed by a quantitative comparison of Tomo-PIV simulation results and DNS data, together with a comparison to Tomo-PIV experimental data measured in a turbulent channel flow at a matched Reynolds number (Reτ = 937) to the DNS study. For the simulation data, a comparative study is performed on the reconstruction quality based on an ideal reconstruction determined from known particle positions. The results suggest that a significant improvement in the reconstruction quality and flow statistics is achievable at typical seeding densities used in Tomo-PIV experiments. This improvement is further amplified at higher seeding densities, enabling the use of up to twice the typical seeding densities currently used in Tomo-PIV experiments. A reduction of spurious vectors present in the velocity field is also observed based on a median outlier detection criterion. The application of SMRE to Tomo-PIV experimental data shows an improvement in flow statistics, comparable to the improvement seen in simulations. Finally, due to the non-iterative nature of SMRE, the increase in processing time is marginal since only a single pass of the reconstruction algorithm is required.

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R. Baidya

Papers

Amplitude modulation of all three velocity components in turbulent boundary layers

Distance-from-the-wall scaling of turbulent motions in wall-bounded flows

The effect of spanwise wavelength of surface heterogeneity on turbulent secondary flows

Two-dimensional energy spectra in high-Reynolds-number turbulent boundary layers

Enhancing Tomo-PIV reconstruction quality by reducing ghost particles