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

Aerodynamics of high cadence cycling

A novel study on assessing the drag penalty due to hull roughness from a recently cleaned and painted ship hull is reported. Here we estimate the rough surface drag penalty by measuring the velocity profile directly over the hull of an operating ship under steady cruising using a Laser Doppler Anemometer (LDA). The novel technique is non-intrusive and requires only optical accessand does not require a full hull-penetration. For this experiment a small glass window is placed on the double-bottom hull of an operating ship, allowing the LDA to measure the velocity gradient in the turbulent boundary layer formed over the hull (during steady sailing) across some traversable distance from close to the hull surface, to at least the end of the logarithmic region. Preliminary initial results show that there is an approximate 37% increase in skin-friction drag for a recently cleaned ship-hull compared to the hydrodynamically smooth surface

In-situ turbulent boundary layer measurements over freshly cleaned ship-hull under steady cruising

Our work builds on the investigation of Marusic et al. [7] who examined the streamwise evolution of a turbulent boundary layer from different types of spanwise homogeneous trips. Here we introduce a spanwise three dimensionality at the trip by employing a series of miniature vortex generators placed immediately downstream of the original spanwise homogeneous trip in a high Reynolds number boundary layer facility. The resultant modified boundary layer is surveyed using hot-wire anemometry to examine its streamwise evolution. Further, a series of targeted Particle Image Velocimetry measurements are conducted to examine the modified structural composition of the flow. The results exhibit the presence of streamwise counter-rotating roll-modes over a large streamwise extent, which appear to be strongest after a certain characteristic length downstream of their introduction. Comparisons are drawn between the observed evolution of a turbulent boundary layers with a spanwise three dimensionality and the evolution model of Perry et al. [8], which is formulated for spanwise homogeneous flows. Preliminary findings reveal that the spanwise periodic modes introduced at the inception point (trip) of a turbulent boundary layer can persist for a substantial streamwise extent. Further, even at the furthest downstream station surveyed (x > 1000 vortex generator heights) little or no recovery towards the canonical state was observed for some evolution parameters, perhaps suggesting that three-dimensionality can alter the asymptotic state, or at least significantly delay recovery to the canonical state.

Developing turbulent boundary layers with spanwise periodic trips

This study examines the pronounced periodicity of large-scale coherent structures in turbulent boundary layers, which are of the order of the boundary layer thickness (δ) and reside in the logarithmic and wake regions. To this end, a series of multi-camera planar particle image velocimetry (PIV) measurements are conducted in a streamwise/spanwise and streamwise/wall-normal planes at a friction Reynolds number of Reτ ≈ 2500. The experiments are configured to capture a large field-of-view with velocity fields that cover a streamwise extent in excess of 15δ. The resulting vector fields reveal large-scale streamwise and spanwise organisation instantaneously, which is often lost when only examining mean statistics. By extracting the dominant streamwise and spanwise Fourier modes of the large-scale motions, a clearer picture of these structural organisations and coherence is presented. A targeted inspection of these dominant modes reveal that these features remain coherent over a significant fraction of the boundary layer thickness in the wall-normal direction, but only a fraction of them have coherence that extends to the wall (wall-coherent). Further, the spatial extents and the population density of these wall-coherent and wall-incoherent modes are characterised, with the former conforming to the attached eddy arguments of Townsend (1976) and the subsequent attached eddy models. Collectively, through the evidence gathered here, we provide a conceptual picture of the representative large-scale structures in turbulent boundary layers, which are likely to have implications on the type of representative structures to be used in structure-based models for these flows.

Periodicity of large-scale coherence in turbulent boundary layers

This paper examines the recovery of a turbulent boundary layer that has undergone a sudden streamwise transition from a rough-walled to a smooth-walled surface. Despite studies over the past few decades these flows are yet to be fully understood. In particular, these attempts have been hampered by reliability issues in determining the local wall-shear stress after the transition [1], where many existing tools for measuring the wall-shear stress fail due to non-equilibrium, non-canonical conditions. Here, we utilise a collection of experimental databases at Reτ ≈ 3500 with direct measures of the wall-shear stress to understand the recovery to equilibrium conditions to the new surface. Our results reveal that for distances less than 0.5δ0 (where δ0 is the boundary layer thickness at the roughness transition) downstream of the rough-to-smooth transition the wall-shear stress for the current configuration exhibits variation in the spanwise direction. Further, the mean velocity in the buffer region and beyond appears to take several boundary layer thicknesses downstream of the roughness change to recover to the equilibrium state. Through a spectral analysis of the energetic modes of the flow, we also observe that the recovery of small-scale streamwise velocity fluctuations in the near-wall region is achieved over shorter downstream distances compared to the larger scales.

R. Baidya

Papers

Aerodynamics of high cadence cycling

In-situ turbulent boundary layer measurements over freshly cleaned ship-hull under steady cruising

Developing turbulent boundary layers with spanwise periodic trips

Periodicity of large-scale coherence in turbulent boundary layers

Recovery of a turbulent boundary layer following a rough-to-smooth step-change in the wall condition