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

Particle image velocimetry (PIV) has evolved to be the dominant method for velocimetry in experimental fluid mechanics and has contributed to many advances in our understanding of turbulent and complex flows. In this article we review the achievements of PIV and its latest implementations: time-resolved PIV for the rapid capture of sequences of vector fields; tomographic PIV for the capture of fully resolved volumetric data; and statistical PIV, designed to optimize measurements of mean statistical quantities rather than instantaneous fields. In each implementation, the accuracy and spatial resolution are limited. To advance the method to the next level, we need a completely new approach. We consider the fundamental limitations of two-pulse PIV in terms of its dynamic ranges. We then discuss new paths and developments that hold the promise of achieving a fundamental reduction in uncertainty.

Particle Image Velocimetry for Complex and Turbulent Flows

Detailed instantaneous velocity fields of a jet in crossflow have been measured with stereoscopic particle image velocimetry (PIV). The jet originated from a fully developed turbulent pipe flow and entered a crossflow with a turbulent boundary layer. The Reynolds number based on crossflow velocity and pipe diameter was 2400 and the jet to crossflow velocity ratios were R=3.3 and R=1.3. The experimental data have been analysed by proper orthogonal decomposition (POD). For R=3.3, the results in several different planes indicate that the wake vortices are the dominant dynamic flow structures and that they interact strongly with the jet core. The analysis identifies jet shear-layer vortices and finds that these vortical structures are more local and thus less dominant. For R=1.3, on the other hand, jet shear-layer vortices are the most dominant, while the wake vortices are much less important. For both cases, the analysis finds that the shear-layer vortices are not coupled to the dynamics of the wake vortices. Finally, the hanging vortices are identified and their contribution to the counter-rotating vortex pair (CVP) and interaction with the newly created wake vortices are described.

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A turbulent jet in crossflow analysed with proper orthogonal decomposition

Transverse jets and their control

Conditionally sampled measurements with particle image velocimetry (PIV) of a turbulent round submerged liquid jet in a laboratory have been taken at Re = 2 × 103 between 60 and 100 nozzle diameters from the nozzle in order to investigate the dynamics and transport processes at the continuous and well-defined bounding interface between the turbulent and non-turbulent regions of flow. The jet carries a fluorescent dye measured with planar laser-induced fluorescence (LIF), and the surface discontinuity in the scalar concentration is identified as the fluctuating turbulent jet interface. Thence the mean outward ‘boundary entrainment’ velocity is derived and shown to be a constant fraction (about 0.07) of the the mean jet velocity on the centreline. Profiles of the conditional mean velocity, mean scalar and momentum flux show that at the interface there are clear discontinuities in the mean axial velocity and mean scalar and a tendency towards a singularity in mean vorticity. These actual or asymptotic discontinuities are consistent with the conditional mean momentum and scalar transport equations integrated across the interface. Measurements of the fluxes of turbulent kinetic energy and enstrophy are consistent with computations by Mathew & Basu (Phys. Fluids, vol. 14, 2002, pp. 2065–2072) in showing that for a jet flow (without forcing) the entrainment process is dominated by small-scale eddying at the highly sheared interface (‘nibbling’), with large-scale engulfing making a small (less than 10%) contribution consistent with concentration measurements showing that the interior of the jet is well mixed. (Turbulent jets differ greatly from the free shear layer in this respect.) To explain the difference between velocity and scalar profiles, their conditional mean gradients are defined in terms of a local eddy viscosity and eddy diffusivity and the momentum and scalar fluxes inside the interface. Since the eddy diffusivity is larger than the eddy viscosity, the scalar profile is flatter inside the interface so that the scalar discontinuity is relatively greater than the mean velocity discontinuity. Theoretical arguments, following Hunt, Eames & Westerweel (in Proc. of the IUTAM Symp. on Computational Physics and New Perspectives in Turbulence, ed. Y. Kaneda, vol. 4, 2008, pp. 331–338, Springer), are proposed for how the vortex sheet develops, how the internal structure of the interface layer relates to the inhomogeneous rotational and irrotational motions on each side and why the dominant entrainment process of jets and wakes differs from that of free shear layers.

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Momentum and scalar transport at the turbulent/non-turbulent interface of a jet

The governing equations for the two-point velocity correlations in the far field of the axisymmetric jet are examined and it is shown that these equations can have equilibrium similarity solutions for jets with finite Reynolds number that retain a dependence on the growth rate of the jet. The two-point velocity correlation can be written as the product of a scale that depends on the downstream position of the two points and a function that only depends on the similarity variables. Physically, this result implies that the turbulent processes producing and dissipating energy at the different scales of motion, as well as transferring energy between the different scales of motion, are in equilibrium as the flow evolves downstream. A particularly interesting prediction from the analysis is that the two-point similarity solutions depend only on the separation distance between the points in the streamwise similarity coordinate (i.e. v=xi'-xi), that is, the logarithm of the streamwise coordinate itself (i.e. xi=ln x(1), where x, is measured from a virtual origin). Thus, the measures of the turbulence are homogeneous in the streamwise similarity coordinate. The predictions from the similarity analysis for the streamwise two-point velocity correlation were compared with combined hot-wire and LDA measurements on the centreline of a round jet at a Reynolds number of 33000, and with two-point velocity correlations computed from PIV measurements in a round jet at a Reynolds number of 2000 performed by Fukushima et al. In both cases, the measured two-point velocity correlations in the streamwise direction collapsed when they were scaled in the manner predicted by the similarity analysis. The results provide further evidence that the equilibrium similarity hypothesis does describe the development of the flow in fully developed turbulent round jets and that the two-point correlations are statistically homogeneous in the streamwise similarity coordinate.

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Two-point similarity in the round jet

Measurements with particle image velocimetry have been carried out in a scale model of the Annex 20 room. Data were taken in a plane near the inlet. The flow consisted of a wall jet (Re=5,000) and a low-velocity region below the jet. POD was used to analyze dominant flow structures. The analysis showed that the flow some of the time has flow structures very different from the mean velocity field. A time-resolved data series was projected onto the orthonormal basis derived from the POD for analysis of the time variation of the POD amplitudes.

POD analysis of flow structures in a scale model of a ventilated room

Both Particle Image Velocimetry (PIV) and Large Eddy Simula tion (LES) provides instantaneous velocity fields which can contain dynamical fl ow structures that occur systematically. Turbulent flows also contain random flow structure s, and therefore there is a need for tools that can identify the systematic dynamic flow structur es. We show how Proper Orthogonal Decomposition (POD) based on snapshots (instantaneous flow realizations) can be used for this purpose. As a test case, we use PIV measurements and LES calcu lations on the same turbulent jet in cross flow. The Reynolds number based on the crossflow ve locity and pipe diameter is 2400 and the jet to crossflow velocity ratio is R = 3.3. The POD is able to identify two dynamic flow structures: jet shear-layer vortices and wake vortices . A good agreement for the dynamical content is found between PIV and LES.

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Jakob Martin Pedersen

Papers

A turbulent jet in crossflow analysed with proper orthogonal decomposition

Momentum and scalar transport at the turbulent/non-turbulent interface of a jet

Two-point similarity in the round jet

POD analysis of flow structures in a scale model of a ventilated room

POD as tool for comparison of PIV and LES data