Search

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.

In a turbulent fluid, the time-reversal symmetry is explicitly broken by viscosity, and spontaneously broken in the inviscid limit. Recently, Drivas [J. Nonlinear Sci. 29, 65 (2019).JNSCEK0938-897410.1007/s00332-018-9476-8] proved the equivalence of two different local indicators of time irreversibility: (i) an Eulerian one, based on regularity properties of the velocity field [Duchon and Robert, Nonlinearity 13, 249 (2000).NONLE50951-771510.1088/0951-7715/13/1/312]; (ii) a Lagrangian one, based on symmetry properties of the trajectories under time reversal [Jucha et al., Phys. Rev. Lett. 113, 054501 (2014).PRLTAO0031-900710.1103/PhysRevLett.113.054501]. We test this equivalence in a turbulent Von Kármán experiment at a resolution of the order of the Kolmogorov scale using a high resolution 4D-PTV technique. We use the equivalence to perform the first joined Eulerian-Lagrangian exploration of the dynamics leading to time irreversibility, and find that it is linked with vortex interaction, suggesting a link between irreversibility and singularity.

A SPIV experiment using two orthogonal planes simultaneously was performed in the LML boundary layer facility to specifically measure all of the derivative moments needed to estimate the dissipation rate of the turbulence kinetic energy. The Reynolds number was $$Re_\theta = 7500$$ or $$Re_\tau = 2300$$ . A detailed analysis of the errors in derivative measurements was carried out, as well as applying and using consistency checks derived from the continuity equation. The random noise error was quantified and used to “denoise” the derivative moments. A comparison with a DNS channel flow at comparable Reynolds number demonstrated the capability of the technique. The results were further validated using the recent theory developed by George and Stanislas (Exp Fluids 62:188, 2021). An important result of the present work is the provision of reliable rules for an accurate assessment of the dissipation in future PIV experiments.

International audience; The denoising of Lagrangian trajectories based on regularized B-spline is investigated. The aim is to find systematic criteria for optimization of algorithms used in 4D-PTV in order to optimize the quality of 4D-PTV measurements of turbulent flows as well as high-order of turbulence statistics. We introduce and adapt to this context two innovative tuning strategies which are commonly used in the Tikhonov regularization of inverse problems based on -curve shape and Normalized Cumulative Periodogram (NCP). The corresponding strategies are tested on synthetic Lagrangian trajectories computed from Direct Numerical Simulation with additional white Gaussian noise. Error-based quantities like Signal-to-Noise Ratio as well as statistical Lagrangian quantities are investigated to compare the different strategies. We then apply the algorithm to experimental data from a 4D-PTV Lagrangian measurements in a turbulent Von Kármán flow. We show the ability of those strategies to optimize the quality of the signal compared to conventional methods. Moreover, the strategies are more adaptable to real experimental noise.

Coherent flow structures in turbulent boundary layers have been an active field of research for many decades, as they might be the key to reveal the mechanics of turbulence production and transport in turbulent shear flows. Renard and Deck (2016) proposed a theoretical decomposition for the mean skin-friction coefficient based on the mean kinetic energy budget in the streamwise direction. This decomposition, referred to as the Renard-Deck (RD) decomposition, decomposes the mean skin friction generation into three physical mechanisms in an absolute reference frame, namely, direct viscous dissipation, turbulent kinetic energy production, and spatial growth. In this study, the large scale motions (LSMs) are extracted using a proper orthogonal decomposition (POD) of the velocity field based on high-spatial-resolution two-dimensional – two-component particle image velocimetry (HSR 2C-2D PIV) of a zero-pressure-gradient turbulent boundary layer (ZPG-TBL), and their effect on the skin friction via RD decomposition.

Stereoscopic PIV (SPIV) is performed near the wall in a turbulent boundary layer at high Reynolds numbers (Reτ = 2272, 3840) in the streamwise-wallnormal plane. A novel method for denoising the statistics is proposed by the use to two independent SPIV systems to capture the same field of view, with the objective being that the random noise associated with the velocity fluctuations are not correlated between two independent PIV systems. The derivatives in the third (spanwise) direction are obtained by axisymmetry assumptions [George and Hussein (1991)] and continuity equation. The statistics are in agreement with that of DNS at comparable Reynolds number, from y + = 25 for lower Reτ experiment and from y + = 40 for higher Reτ experiment.

In the past decade, advances in electronics technology have made larger imaging sensors available to the experimental fluid mechanics community. These advancements have enabled the measurement of 2-component 2-dimensional (2C–2D) velocity fields using particle image velocimetry (PIV) with much higher spatial resolution than previously possible. However, due to the large size of the sensor, lens distortion needs to be accounted for and corrected to ensure accurate high-fidelity 2C–2D velocity field measurements, since it will now have a more significant effect on the measurement quality. In this paper, two dewarping models, a second-order rational function (R2) and a bicubic polynomial (P3) are investigated with regards to their performance, uncertainty and sensitivity and applied to correct 2C–2D PIV measurements of a high Reynolds number zero-pressure-gradient turbulent boundary layer using a large imaging sensor. Furthermore, two approaches are considered and compared, namely: (i) dewarping the images prior to 2C–2D cross-correlation digital PIV analysis and (ii) undertaking 2C–2D cross-correlation digital PIV analysis using the raw single-exposed PIV images followed by correcting the velocity vector positions to their correct locations determined using the dewarping function. The results demonstrate that the use of the P3 dewarping model to correct lens distortion yields better results than the R2 dewarping model and that, both approaches of applying the P3 dewarping model yield results that are statistically indistinguishable.

High-spatial-resolution (HSR) two-component, two-dimensional particle-image-velocimetry (2C-2D PIV) measurements of a zero-pressure-gradient (ZPG) turbulent boundary layer (TBL) and an adverse-pressure-gradient (APG)-TBL were taken in the Laboratoire de MA©canique des Fluides de Lille (LMFL) High Reynolds number Boundary Layer Wind Tunnel. The ZPG-TBL has a momentum-thickness based Reynolds number R e I´ 2 = I´ 2 U e ∕ I½ = 7 , 750 (where I´ 2 is the momentum thickness and U e is the edge velocity), while the APG-TBL has a R e I´ 2 = 16 , 240 and a Clauser’s pressure gradient parameter I² = I´ 1 P x ∕ I„ w = 2 . 27 (where I´ 1 is the displacement thickness, P x is the pressure gradient in streamwise direction and I„ w is the wall shear stress). The 2C fluctuating flow field of each TBL was decomposed using proper orthogonal decomposition (POD) to investigate the large-scale motions (LSMs). The LSMs are found to be energized in the outer-layer, becoming stronger in the presence of the adverse-pressure-gradient. Profiles of the conditionally averaged Reynolds stresses show that high-momentum LSMs contribute more to the Reynolds stresses than low-momentum LSMs from the wall to the end of the log-layer while the opposite is found in the wake region. The cross-over point between the profiles of the conditionally averaged Reynolds stresses from the high- and low-momentum LSMs always has a higher value than the corresponding Reynolds stress from the unconditional ensemble average at the same wall-normal location. This difference is up to 80% in the Reynolds streamwise and shear stresses and up to 15% in the Reynolds wall-normal stresses. Furthermore, the cross-over point in the APG-TBL is found to be further from the wall than in the ZPG-TBL. The conditional Reynolds streamwise and shear stresses without the LSMs are reduced by up to 42% in the ZPG-TBL and by up to 50% in the APG-TBL, while having a minimal effect on the conditional Reynolds wall-normal stress without the LSMs in both the ZPG- and APG-TBL.

In this paper, the turbulence fields generated by a group of modified fractal grids, referred to as the rectangular fractal grids (RFGs), are documented and discussed. The experiments were carried out using hot-wire anemometry in three facilities at Imperial College London and the Laboratory of Fluid Mechanics in Lille, France. Due to the large Reynolds number of the resulting turbulence, several data processing methods for turbulence properties are carefully evaluated. Two spectral models were adopted, respectively, to correct the large and small wave-number ranges of the measured spectrum. After the technical discussion, the measurement results are presented in terms of one-point statistics, length scales, homogeneity, isotropy, and dissipation. The main conclusions are twofold. First, the location of maximum turbulence intensity xpeak is shown to be independent of the inlet Reynolds number but dependent on the ratio between the lengths of the largest grid bars in the transverse and vertical directions. This is crucial to the production of prescribed features of turbulent flows in laboratory. Second, these RFG-generated turbulent flows are shown to be quasihomogeneous in the decay region for x/xpeak>1.5, but the isotropy is poorer than that of the previous studied fractal square grid-generated turbulence. In the beginning of the decay region, a decreasing pattern of the integral length scale Lu and Taylor microscale λ was observed, yet the ratio Lu/λ remained roughly constant along the centerline, so Cε∼Re−1λ, complying with the nonequilibrium scaling relation reported in previous studies for various turbulent flows.

High-spatial-resolution (HSR) two-component, two-dimensional particle-image-velocimetry (2C-2D PIV) measurements of a zero-pressure-gradient (ZPG) turbulent boundary layer (TBL) and an adverse-pressure-gradient (APG)-TBL were taken in the LMFL High Reynolds number Boundary Layer Wind Tunnel. The ZPG-TBL has a momentum-thickness based Reynolds number $Re_{\delta_2} = \delta_2 U_e/\nu = 7,750$ while the APG-TBL has a $Re_{\delta_2} = 16,240$ and a Clauser's pressure gradient parameter $\beta = \delta_1 P_x/\tau_w = 2.27$ After analysing the single-exposed PIV image data using a multigrid/multipass digital PIV (Soria, 1996) with in-house software, proper orthogonal decomposition (POD) was performed on the data to separate flow-fields into large- and small-scale motions (LSMs and SSMs), with the LSMs further categorized into high- and low-momentum events. Profiles of the conditionally averaged Reynolds stresses show that the high-momentum events contribute more to the Reynolds stresses than the low-momentum between wall to the end of the log-layer and the opposite is the case in the wake region. The cross-over point of the profiles of the Reynolds stresses from the high- and low-momentum LSMs always has a higher value than the corresponding Reynolds stress from the original ensemble at the same wall-normal location. Furthermore, the cross-over point in the APG-TBL moves further from the wall than in the ZPG-TBL. By removing the velocity fields with LSMs, the estimate of the Reynolds streamwise stress and Reynolds shear stress from the remaining velocity fields is reduced by up to $42 \%$ in the ZPG-TBL. The reduction effect is observed to be even larger (up to $50\%$) in the APG-TBL. However, the removal of these LSMs has a minimal effect on the Reynolds wall-normal stress in both the ZPG- and APG-TBL., Comment: This paper is under consideration for publication in Experimental Thermal and Fluid Sciences

International audience; We study the three-dimensional structure of turbulent velocity fields around extreme events of local energy transfer in the dissipative range. Velocity fields are measured by tomographic particle velocimetry at the centre of a von Kármán flow with resolution reaching the Kolmogorov scale. The characterization is performed through both direct observation and an analysis of the velocity gradient tensor invariants at the extremes. The conditional average of local energy transfer on the second and third invariants seems to be the largest in the sheet zone, but the most extreme events of local energy transfer mostly correspond to the vortex stretching topology. The direct observation of the velocity fields allows for identification of three different structures: the screw and roll vortices, and the U-turn. They may correspond to a single structure seen at different times or in different frames of reference. The extreme events of local energy transfer come along with large velocity and vorticity norms, and the structure of the vorticity field around these events agrees with previous observations of numerical works at similar Reynolds numbers.

Uniform blowing in wall bounded shear flows is well known for its drag reducing effects and has long been investigated ever since. However, many contemporary and former research on this topic has c...

Uniform momentum zones (UMZs) for an adverse pressure gradient turbulent boundary layer (APG-TBL) are characterised in this paper.The database described by Cuvier et al.(2017), which was obtained using 2-component 2-dimensional (2C-2D) particle image velocimetry (PIV) at two free-stream velocities of 5 m/s and 9 m/s, is used for this study.The methodology described by Adrian et al.(2000) is used to identify and hence, statistically characterise the UMZs and UMZ interfaces in the APG-TBL. This study shows that the number of detected UMZs increases in the streamwise direction for both free-stream velocities.This increase is primarily thought to be due to the adverse pressure gradient (APG) since a comparison of the results between the two free-stream velocity APG-TBLs did not show any statistically significant difference with Re θ for the range of Reynolds number examined in this study.The thickness of the UMZs, δ w and the jump in streamwise velocity across the UMZ interface were found to increase in the wall-normal direction, whereas the width of the UMZ interface, Δ u , was found to decrease.The number of UMZs, N umz , identified appeared to influence the modal velocities/uniform velocities, geometrical properties of the UMZs and statistics of the flow.With increasing N umz , the modal velocities of the UMZs moved to higher values to accommodate new UMZs that developed closer to the wall and the thickness of each UMZ and Δ u across the UMZ interface decreased, whereas δ w increased. A slight difference in the magnitude of streamwise Reynolds stress and Reynolds shear stress was observed in the inner and outer regions, and a slight difference in the magnitude of turbulence production was also observed in the inner region between the velocity fields having a low or high number of UMZs indicating that the flow statistics are influenced by the number of UMZs present in the APG-TBL.

We present an estimation method combining Proper Orthogonal Decomposition (POD) and Linear Stochastic Estimation (LSE). The method is based on a direct mapping of the POD amplitudes from the measurement space to the state space. The method is tested in the turbulent boundary layer for a numerical simulation as well as for experimental data. The goal is to recover the full velocity field on a fine grid from coarse measurements of a single (longitudinal) velocity component. A significant fraction of the turbulent kinetic energy for each component is captured by the estimation. A scale-by-scale analysis shows that lower order modes corresponding to large scales are recovered accurately. Although exact reproduction is not possible at small scales, examination of the spatial and temporal content of the estimated field shows a good statistical agreement with the real field at all scales.

This paper reports on near-wall two-component–two-dimensional (2C–2D) particle image velocimetry (PIV) measurements of a turbulent pipe flow at shear Reynolds numbers up to $Re_{\unicode[STIX]{x1D70F}}=40\,000$ acquired in the CICLoPE facility of the University of Bologna. The 111.5 m long pipe of 900 mm diameter offers a well-established turbulent flow with viscous length scales ranging from $85~\unicode[STIX]{x03BC}\text{m}$ at $Re_{\unicode[STIX]{x1D70F}}=5000$ down to $11~\unicode[STIX]{x03BC}\text{m}$ at $Re_{\unicode[STIX]{x1D70F}}=40\,000$. These length scales can be resolved with a high-speed PIV camera at image magnification near unity. Statistically converged velocity profiles were determined using multiple sequences of up to 70 000 PIV recordings acquired at sampling rates of 100 Hz up to 10 kHz. Analysis of the velocity statistics shows a well-resolved inner peak of the streamwise velocity fluctuations that grows with increasing Reynolds number and an outer peak that develops and moves away from the inner peak with increasing Reynolds number.

On the basis of (i) particle image velocimetry data of a turbulent boundary layer with large field of view and good spatial resolution and (ii) a mathematical relation between the energy spectrum and specifically modeled flow structures, we show that the scalings of the streamwise energy spectrum E_{11}(k_{x}) in a wave-number range directly affected by the wall are determined by wall-attached eddies but are not given by the Townsend-Perry attached eddy model's prediction of these spectra, at least at the Reynolds numbers Re_{τ} considered here which are between 10^{3} and 10^{4}. Instead, we find E_{11}(k_{x})∼k_{x}^{-1-p} where p varies smoothly with distance to the wall from negative values in the buffer layer to positive values in the inertial layer. The exponent p characterizes the turbulence levels inside wall-attached streaky structures conditional on the length of these structures. A particular consequence is that the skin friction velocity is not sufficient to scale E_{11}(k_{x}) for wave numbers directly affected by the wall.

Understanding the turbulence organization near a wall is necessary to help improving turbulence models. From the experimental point of view, many researchers have worked on this subject since the fifties. Recently, Foucaut et al. (Exp. Fluids 50(4, Sp. Iss. SI):839–846, 2011) [16] have proposed a new idea to compute the 3D correlation tensor from two normal velocity fields when there are two homogeneous directions in the flow. The idea of the present contribution is to propose a specific SPIV experiment which allows the computation of the full 3D spatial correlation tensor in the near wall region of the TBL. This experiment composed of two Stereoscopic PIV planes normal to the wall which were simultaneously recorded was performed in the LML wind tunnel. The 3D correlation is then computed from the two velocity planes in order to give some information about the near wall turbulence organization. Conditioning the average by specific events allows us to improve the analysis of the organisation. It can evidence the link between the events.

We propose a novel closed-loop control strategy of turbulent flows using machine learning methods in a model-free manner. This strategy, called Machine Learning Control (MLC), allows – for the first time – to detect and exploit all enabling nonlinear actuation mechanisms in an un-supervised automatic manner. In this communication, we focus on MLC applications for in-time control of experimental shear flows and demonstrate how it outperforms state-of-the-art control. In particular, MLC is applied to three different experimental closed-loop control setups: (1) the TUCOROM mixing layer tunnel, (2) the Gortler PMMH water tunnel with a backward facing step, and (3) the LML Boundary Layer wind tunnel with a separating turbulent boundary layer. In all three cases, MLC finds a control which yields a significantly better performance with respect to the given cost functional as compared to the best previously tested open-loop actuation. We foresee numerous potential applications to most nonlinear multiple-input multiple-output (MIMO) flow control problems, particularly in experiments. In particular, the model-free architecture of MLC enables its application to a large class of complex nonlinear systems in all areas of science.

International audience; The flow over a ramp model is characterised in detail in the present study. In the selected configuration, a turbulent boundary layer developed on a flat plate is first accelerated in a curved contraction. It is then submitted to a mild adverse pressure gradient on a flat plate followed by a separation above a flap. Inlet boundary conditions and pressure distribution are provided to allow numerical simulations. The flow in the mild adverse pressure gradient region is characterised with hot-wire anemometry. In this region, the boundary layer thickness is of the order of 20 cm, the momentum Reynolds number is about 11,000 and the Clauser pressure gradient parameter β in the stabilised region is about 0.4. Particular emphasis is laid on the separation to provide quantitative information to evaluate turbulence models. This is achieved through a large streamwise two-dimensional two-component particle image velocimetry (2D2C PIV) plane which contains all the separation bubble and part of the flow upstream and downstream of it. The separation border is detected using the backflow coefficient, resulting in a separation length of about 3.49 Hs (with Hs the flap step height) and a maximum height of about 0.17 Hs. The Reynolds stresses and their main production terms are also determined. A region of high turbulence intensity develops above the separation border for all the measured components. The production of dominates the production of turbulent kinetic energy which implies a redistribution from to to explain the increase observed. The production term drives the production of in the first part of the flap which is not the case for zero pressure gradient boundary layers. Finally, a high similarity is observed between and as the production of the latter is dominated by . This flow appears as a challenging test case for Reynolds averaged Navier–Stokes (RANS) and large eddy simulation (LES) validation.