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A critical analysis of turbulence dissipation in near-wall flows, based on stereo particle image velocimetry and direct numerical simulation data
- William K. George, Michel Stanislas, Jean Marc Foucaut, Christophe Cuvier, Jean Philippe Laval
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- Journal:
- Journal of Fluid Mechanics / Volume 950 / 10 November 2022
- Published online by Cambridge University Press:
- 13 October 2022, A2
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An experiment was performed using stereo particle image velocimetry (SPIV) in the Laboratoire de Mécanique des Fluides de Lille boundary layer facility to determine all the derivative moments needed to estimate the average dissipation rate of the turbulence kinetic energy $\epsilon = 2 \nu \langle {\mathsf{s}}_{ij}{\mathsf{s}}_{ij} \rangle$, where ${\mathsf{s}}_{ij}$ is the fluctuating strain rate and $\langle ~\rangle$ denotes ensemble averages. Also measured were all the moments of the full average deformation rate tensor, as well as all of the first, second and third fluctuating velocity moments except those involving pressure. The Reynolds number was $Re_\theta = 7634$ or $Re_\tau = 2598$. The present paper gives the measured average dissipation, $\epsilon$ and the derivative moments comprising it. The results are compared with the earlier measurements of Balint, Wallace & Vukolavcevic (J. Fluid Mech., vol. 228, 1991, pp. 53–86) and Honkan & Andreopoulos (J. Fluid Mech., vol. 350, 1997, pp. 29–96) at lower Reynolds numbers and to new results from a plane channel flow DNS at comparable Reynolds number. Of special interest is the prediction by George & Castillo (Appl. Mech. Rev., vol. 50, 1997, pp. 689–729) and Wosnik, Castillo & George (J. Fluid Mech., vol. 421, 2000, pp. 115–145) that $\epsilon ^+ \propto {x_2^+}^{-1}$ for streamwise homogeneous flows and a nearly indistinguishable power law, $\epsilon \propto {x_2^+}^{\gamma -1}$, for boundary layers. In spite of the modest Reynolds number, the predictions seem to be correct. Then the statistical character of the velocity derivatives is examined in detail, and a particular problem is identified with the breakdown of local homogeneity inside $x_2^+ = 100$. A more general alternative for partially homogeneous turbulence flows is offered which is consistent with the observations. With the help of DNS, the spatial characteristics of the dissipation very near the wall are also examined in detail.
Space–time pressure–velocity correlations in a turbulent boundary layer
- Yoshitsugu Naka, Michel Stanislas, Jean-Marc Foucaut, Sebastien Coudert, Jean-Philippe Laval, Shinnosuke Obi
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- Journal:
- Journal of Fluid Mechanics / Volume 771 / 25 May 2015
- Published online by Cambridge University Press:
- 22 April 2015, pp. 624-675
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The spatio-temporal pressure–velocity correlation in a turbulent boundary layer is investigated so as to understand the link between pressure fluctuations and turbulent coherent structures. A new experimental set-up is developed to measure the pressure fluctuations at the wall and in the field and, simultaneously, the velocity field by stereoscopic particle image velocimetry. The present measurement area covers the whole boundary layer thickness, and the spatial resolution of the measurement is good enough to assess the representative length scales of the flow. The Reynolds number effect is quantified from the data at $\mathit{Re}_{{\it\theta}}=7300$, 10 000, 18 000. The spatio-temporal three-dimensional structures of the pressure–velocity correlations, $\boldsymbol{R}_{pu}$, $\boldsymbol{R}_{pv}$ and $\boldsymbol{R}_{pw}$, are evaluated. The wall pressure fluctuations are closely coupled with coherent structures which occupy a large region of the boundary layer in the wall-normal and spanwise directions and up to $10{\it\delta}/U_{e}$ in time, where ${\it\delta}$ and $U_{e}$ denote the boundary layer thickness and the free stream velocity. Reynolds number effects are mainly observed on the size and intensity of the pressure–velocity correlations. Conditioning the correlations on the pressure signal sign shows different types of flow phenomena linked to the positive and negative pressure events. For the wall pressure, positive pressure fluctuations appear to be correlated with the leading edge of a large sweeping motion of splatting type followed by a large ejection. The negative pressure fluctuations are linked to a localized ejection upstream, followed by a large sweeping motion downstream. For the pressure fluctuations in the field, in addition to the structures observed with the wall pressure, the pressure–velocity correlations exhibit a significant correlation in a region very extended in time. Such long structures appear to be independent of the one observed at the wall and to grow significantly in time with the Reynolds number when scaling with external variables. When conditioned by the pressure sign, clear ejection and sweeping motions are observed with associated streamwise vortical structures at a scale of the order of $0.2{\it\delta}$. These structures can be linked to the large-scale motion and very-large-scale motion previously observed by different authors and seem to organize in a scheme analogous to the near-wall cycle, but at a much larger scale.
Influence of the Reynolds number on the vortical structures in the logarithmic region of turbulent boundary layers
- Sophie Herpin, Michel Stanislas, Jean Marc Foucaut, Sebastien Coudert
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- Journal:
- Journal of Fluid Mechanics / Volume 716 / 10 February 2013
- Published online by Cambridge University Press:
- 25 January 2013, pp. 5-50
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Near-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.
Vortical structures in the turbulent boundary layer: a possible route to a universal representation
- MICHEL STANISLAS, LAURENT PERRET, JEAN-MARC FOUCAUT
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- Journal:
- Journal of Fluid Mechanics / Volume 602 / 10 May 2008
- Published online by Cambridge University Press:
- 25 April 2008, pp. 327-382
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A study of streamwise oriented vortical structures embedded in turbulent boundary layers is performed by investigating an experimental database acquired by stereoscopic particle image velocimetry (SPIV) in a plane normal both to the mean flow and the wall. The characteristics of the experimental data allow us to focus on the spatial organization within the logarithmic region for Reynolds numbers Reθ up to 15000. On the basis of the now accepted hairpin model, relationships and interaction between streamwise vortices are first investigated via computation of two-point spatial correlations and the use of linear stochastic estimation (LSE). These analyses confirm that the shape of the most probable coherent structures corresponds to an asymmetric one-legged hairpin vortex. Moreover, two regions of different dynamics can be distinguished: the near-wall region below y+=150, densely populated with strongly interacting vortices; and the region above y+=150 where interactions between eddies happen less frequently. Characteristics of the detected eddies, such as probability density functions of their radius and intensity, are then studied. It appears that Reynolds number as well as wall-normal independences of these quantities are achieved when scaling with the local Kolmogorov scales. The most probable size of the detected vortices is found to be about 10 times the Kolmogorov length scale. These results lead us to revisit the equation for the mean square vorticity fluctuations, and to propose a new balance of this equation in the near-wall region. This analysis and the above results allow us to propose a new description of the near-wall region, leading to a new scaling which seems to have a good universality in the Reynolds-number range investigated. The possibility of reaching a universal scaling at high enough Reynolds number, based on the external velocity and the Kolmogorov length scale is suggested.