INSIGHT INTO COHERENCE STRUCTURE IN LOGARITHMIC REGION OF WALL TURBULENCE WITH DETACHED EDDY BY USING CONDITIONALLY AVERAGED TWO-CAMERA PIV MEASUREMENTS

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 ($u_{i}$) through the direct numerical simulation of a moderate-Reynolds-number boundary layer ($Re_{\unicode[STIX]{x1D70F}}\approx 1000$). The wall-attached structures are self-similar with respect to their heights ($l_{y}$), and in particular the population density of the streamwise component ($u$) scales inversely with $l_{y}$, reminiscent of the hierarchy of attached eddies. The turbulence intensities contained within the wall-parallel components ($u$ and $w$) exhibit the logarithmic behaviour. The tall attached structures ($l_{y}^{+}>100$) of $u$ are composed of multiple uniform momentum zones (UMZs) with long streamwise extents, whereas those of the cross-stream components ($v$ and $w$) are relatively short with a comparable width, suggesting the presence of tall vortical structures associated with multiple UMZs. The magnitude of the near-wall peak observed in the streamwise turbulent intensity increases with increasing $l_{y}$, reflecting the nested hierarchies of the attached $u$ 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.

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On the logarithmic region in wall turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.511 ◽

2013 ◽

Vol 716 ◽

Cited By ~ 306

Author(s):

Ivan Marusic ◽

Jason P. Monty ◽

Marcus Hultmark ◽

Alexander J. Smits

Keyword(s):

Wall Turbulence ◽

Turbulent Shear ◽

Recent Experimental Data ◽

Turbulent Shear Flow ◽

Number Range ◽

The Past ◽

Logarithmic Region ◽

The Mean ◽

Logarithmic Functions ◽

Considerable Discussion

AbstractConsiderable discussion over the past few years has been devoted to the question of whether the logarithmic region in wall turbulence is indeed universal. Here, we analyse recent experimental data in the Reynolds number range of nominally$2\times 1{0}^{4} \lt {\mathit{Re}}_{\tau } \lt 6\times 1{0}^{5} $for boundary layers, pipe flow and the atmospheric surface layer, and show that, within experimental uncertainty, the data support the existence of a universal logarithmic region. The results support the theory of Townsend (The Structure of Turbulent Shear Flow, Vol. 2, 1976) where, in the interior part of the inertial region, both the mean velocities and streamwise turbulence intensities follow logarithmic functions of distance from the wall.

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Investigation of Flow and Mass Transfer on a Flat Plate Downstream of a Shear Inducing Moving Wall

2010 14th International Heat Transfer Conference, Volume 2 ◽

10.1115/ihtc14-22394 ◽

2010 ◽

Author(s):

Kalyanjit Ghosh ◽

R. J. Goldstein

Keyword(s):

Boundary Layer ◽

Mass Transfer ◽

Reynolds Number ◽

Energy Content ◽

Turbulent Energy ◽

Wall Turbulence ◽

Freestream Velocity ◽

Moving Wall ◽

Wall Boundary Layer ◽

Logarithmic Region

The effects of an opposing (upstream-moving) wall-shear on a two-dimensional turbulent boundary layer are investigated. The shear at the boundary is imparted by a moving belt, flush with the wall. Boundary layer measurements are reported for four surface-to-freestream velocity ratios (0, −0.38, −0.51, −0.63) with the Reynolds number (based on the momentum thickness) between 922 and 1951. Velocity profiles downstream of the moving surface show an increased velocity deficit near the wall, which is more pronounced at higher (negative) belt velocity. Streamwise turbulence values downstream of the belt show the growth of a second peak in the logarithmic region of the boundary layer in addition to the normally-observed peak in the buffer region. This suggests the presence of larger length-scale turbulent eddies at locations away from the wall in the boundary layer. Spectral measurements indicate that the turbulent energy content is distributed over a wide portion of the logarithmic region. Mass transfer measurements using naphthalene sublimation provide the variation of Stanton with Reynolds number on the plate downstream of the moving belt. It shows little difference from the stationary belt case, which suggests that increased wall turbulence is balanced by an increase in the boundary layer thickness.

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Scaling of second- and higher-order structure functions in turbulent boundary layers

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.122 ◽

2015 ◽

Vol 769 ◽

pp. 654-686 ◽

Cited By ~ 46

Author(s):

C. M. de Silva ◽

I. Marusic ◽

J. D. Woodcock ◽

C. Meneveau

Keyword(s):

Large Scale ◽

Scaling Laws ◽

Strong Support ◽

Structure Functions ◽

Higher Order ◽

Wall Turbulence ◽

Inertial Subrange ◽

Order Structure ◽

Logarithmic Scaling ◽

Logarithmic Region

The statistical properties of wall turbulence in the logarithmic region are investigated using structure functions of the streamwise velocity. To this end, datasets that span several orders of magnitude of Reynolds numbers are used, up to$Re_{{\it\tau}}=O(10^{6})$, providing uniquely large scale separations for scrutinising previously proposed scaling laws. For the second-order structure functions strong support is found simultaneously for power-law scalings in the Kolmogorov inertial subrange and for logarithmic scaling at larger scales within the inertial range ($z<r\ll {\it\delta}$, where$z$is the distance from the wall,$r$the scale, and${\it\delta}$the boundary layer thickness). The observed scalings are shown to agree between the datasets, which include both temporal and spatial velocity signals and span from laboratory to atmospheric flows, showing a degree of universality in the results presented. An examination of higher even-order structure functions also shows support for logarithmic scaling behaviour for$z<r\ll {\it\delta}$, provided that the Reynolds number is sufficiently high. These findings are interpreted by generalising the work of Meneveau & Marusic (J. Fluid Mech., vol. 719, 2013) and introducing bridging relations between higher-order moments of velocity fluctuations and structure functions. Further, a physical model based on the attached-eddy hypothesis is utilised to derive various properties of the structure functions for the energy-containing scales of the logarithmic region. The descriptions derived from the model are shown to be supported by the experimental data.

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Assessment of dual plane PIV measurements in wall turbulence using DNS data

Experiments in Fluids ◽

10.1007/s00348-006-0168-z ◽

2006 ◽

Vol 41 (2) ◽

pp. 265-278 ◽

Cited By ~ 30

Author(s):

Neelakantan Saikrishnan ◽

Ivan Marusic ◽

Ellen K. Longmire

Keyword(s):

Wall Turbulence ◽

Piv Measurements ◽

Dual Plane

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Comparing the Aerodynamic Behaviour of Real Footballs to a Smooth Sphere Using Tomographic PIV

Proceedings ◽

10.3390/proceedings2020049150 ◽

2020 ◽

Vol 49 (1) ◽

pp. 150

Author(s):

Matthew Ward ◽

Martin Passmore ◽

Adrian Spencer ◽

Andy Harland ◽

Henry Hanson ◽

...

Keyword(s):

Particle Image ◽

Vertical Axis ◽

Force Balance ◽

Piv Measurements ◽

Tomographic Piv ◽

The Real ◽

Magnus Effect ◽

Image Velocimetry ◽

Insight Into ◽

Smooth Sphere

Many studies have investigated the forces acting on a football in flight and how these change with the introduction or modification of surface features; however, these rarely give insight into the underlying fluid mechanics causing these changes. In this paper, force balance and tomographic particle image velocimetry (PIV) measurements were taken on a smooth sphere and a real Telstar18 football at a range of airspeeds. This was done under both static and spinning conditions utilizing a lower support through the vertical axis of the ball. It was found that the presence of the seams and texturing on the real ball were enough to cause a change from a reverse Magnus effect on the smooth ball to a conventional Magnus on the real ball in some conditions. The tomographic PIV data showed the traditional horseshoe-shaped wake structure behind the sphere and how this changed with the type of Magnus effect. It was found that the positioning of these vortices compared well with the measured side forces.

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Influence of the Reynolds number on the vortical structures in the logarithmic region of turbulent boundary layers

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.491 ◽

2013 ◽

Vol 716 ◽

pp. 5-50 ◽

Cited By ~ 26

Author(s):

Sophie Herpin ◽

Michel Stanislas ◽

Jean Marc Foucaut ◽

Sebastien Coudert

Keyword(s):

Reynolds Number ◽

Coherent Structures ◽

Flow Region ◽

Wall Turbulence ◽

Statistical Characteristics ◽

Present Contribution ◽

Vortical Structures ◽

Stereo Particle Image Velocimetry ◽

Logarithmic Region ◽

The Subject

AbstractNear-wall turbulence is a subject of prime importance for turbulence modelling. Coherent structures were hypothesized early by Theodorsen in this flow region and have been the subject of intensive research ever since. The overall organization of these coherent structures has now been well assessed. Vortical structures appear to play a key role in this organization. Their characteristics and scaling have been studied by many authors as listed in the Introduction. The present contribution to the subject relies on high-resolution stereo particle image velocimetry (PIV) to study these structures. High-quality measurements are performed in a thick turbulent boundary layer at different values of the Reynolds number. The data quality is first assessed by comparing the statistics to those of hot-wire anemometry and direct numerical simulation data. The agreement between the two appears satisfactory. The PIV data are then processed in order to extract the vortex characteristics in a streamwise plane and in a spanwise plane. The statistical characteristics of these vortices are analysed in detail as a function of wall distance. The scaling of the data appears to be universal when the Kolmogorov scales are used. These results are analysed and discussed in terms of their probability density functions. This leads to a question regarding the Kolmogorov cascade in this region of the flow.

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Alignment Trends of a Decomposed SGS Stress Tensor Determined From Holographic PIV Measurements

Volume 1: Fora, Parts A and B ◽

10.1115/fedsm2002-31261 ◽

2002 ◽

Author(s):

Bo Tao ◽

Joseph Katz ◽

Charles Meneveau

Keyword(s):

Joint Probability ◽

Statistical Geometry ◽

Clear Trend ◽

Square Duct ◽

Piv Measurements ◽

Vorticity Vector ◽

Modal Behavior ◽

Alignment Angle ◽

Joint Probability Density ◽

Insight Into

Based on the holographic PIV measurements in the core region of a square duct at ReH ≈ 1.2×105, the tensorial alignment of the deviatoric subgrid-scale (SGS) stress (τij) is shown to have a bi-modal behavior (Tao et al., 2001, 2002). To gain further insight into the statistical geometry of τij, we employ the Germano decomposition, τij = Lij + Cij + Rij (Leonard, 1974; Germano, 1986), and compute the decomposed stress elements directly from the velocity data. Their alignment trends are then investigated using joint probability density functions (pdf), similar to those in Tao et al. (2002). The alignment between the Leonard stress, Lij, and the filtered strain-rate (S˜ij) is found to exhibit a similar bi-modal trend, but the alignment angle between the corresponding eigenvectors is around 40° instead of 32°. The alignment between the SGS Reynolds stress, Rij and S˜ij, on the other hand, is found to be consistent with an eddy viscosity configuration. In contrast, the alignment between the cross stress, Cij, and S˜ij is more complicated and does not exhibit any significant trend. Furthermore, previously reported alignment trends of the vorticity vector, ω˜i, relative to τij, are primarily due to the contribution from Lij. The orientation of ω˜i relative to Cij shows less robust alignment trends, and there is no clear trend in the alignment of ω˜i relative to Rij.

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