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Particle Image Velocimetry (PIV) is the most commonly used optical technique for measuring 2D velocity fields. However, improving the spatial resolution of instantaneous velocity fields and having access to the velocity field in real time remains a challenge. Optical Flow veolcimetry makes it possible to meet these challenges. In this study, we show that it is possible to access dense velocity fields (1 vector per pixel) in real-time using an appropriate seeding concentration adapted to optical flow algorithms and no longer to cross-correlation PIV algorithms. The influence of concentration on the quality of velocity fields is demonstrated using synthetic images generated for a Rankine vortex. We thus demonstrate that it is possible to precisely measure small vortices using optical flow provided that the seeding is suitable. The notion of "Active Pixels" is also introduced in order to define a seeding optimization criterion adapted to experimental measurements. This criterion is finally successfully applied to the flow downstream of a cylinder leading to a spatial resolution down to one vector per pixel.

Emulsion droplets trapped in an ultrasonic levitator behave in two ways that solid spheres do not: (1) Individual droplets spin rapidly about an axis parallel to the trapping plane, and (2) coaxially spinning droplets form long chains aligned with their common axis of rotation. Acoustically-organized chains interact hydrodynamically, either to merge into longer chains or to form three-dimensional bundles of chains. Solid spheres, by contrast, form close-packed planar crystals drawn together by the sound-mediated secondary Bjerknes interaction. We demonstrate the chain-to-crystal transition with a model system in which fluid emulsion droplets can be photopolymerized into solid spheres without significantly changing other material properties. The behavior of this experimental system is quantitatively consistent with an acoustohydrodynamic model for spinning spheres in an acoustic levitator. This study therefore introduces acoustically-driven spinning as a mechanism for guiding self-organization of acoustically levitated matter., Comment: 10 pages, 4 figures

We theoretically investigate how the acoustic radiation force and torque arise on a small spheroidal particle immersed in a nonviscous fluid inside an ideal cylindrical chamber. The ideal chamber comprises a hard top and bottom (rigid boundary condition), and a soft or hard lateral wall. By assuming the particle is much smaller than the acoustic wavelength, we present analytical expressions of the radiation force and torque caused by an acoustic wave of arbitrary shape. Unlike previous results, these expressions are given relative to a fixed laboratory frame. Our model is showcased for analyzing the behavior of an elongated metallic microspheroid (with a 10 : 1 aspect ratio) in a half-wavelength acoustofluidic chamber with a few millimeters diameter. The results show the radiation torque aligns the microspheroid along the nodal plane, and the radiation force causes a translational motion with a speed of up to one body length per second. At last, we discuss the implications of this study to propelled nanorods by ultrasound., Comment: 11 pages, 3 figures

In this study we focus on the control of the dynamics of 3D turbulent wake downstream a square-back Ahmed body ($Re_H=3.9\times10^5$). The peculiar dynamics of such a wake are first characterized through the trajectories of the pressure barycenter over the rear part of the model as well as the recirculation barycenter in the wake. In particular it is shown that these dynamics allow the definition of three different states: the two so-called reflectional symmetry-breaking (RSB) modes and the transient symmetric (TS) mode. It was shown recently that the time-fluctuations of the pressure barycenter could be characterized as a weak chaotic system with a well-defined attractor. We show that the dynamics of the bimodal wake can then be forced into a stable asymmetric or symmetric state in open loop control, using tangential continuous or pulsed blowing in three different regions along the upper edge of the rear part of the model. Finally, a simple closed-loop opposition control, based on real-time identification of the wake barycenter in the PIV fields, is used to force the chaotic dynamics of the wake into a regular oscillatory motion at a well-controlled frequency. Depending on the actuation parameters, the wake dynamics can also be switched from bimodal to a new multimodal behavior. We show that this new mode also exhibits a peculiar dynamics with an up-down instead of left-right chaotic oscillations. Interestingly, the recirculation area (size of the recirculation bubble) is much more reduced for the closed-loop experiments when the jets are pulsed rather than continuous. For the pulsed jets, the reduction is also increased when the proper frequency is chosen., Comment: Pre-print version of the article published in Experiments in Fluids (2019) 60: 124. Updated version of the previous arXiv submission. 22 pages, 22 figures

The dynamics of a 3D bimodal turbulent wake downstream a square-back Ahmed body are experimentally studied in a wind-tunnel through high-frequency wall pressure probes mapping the rear of the model and a horizontal 2D velocity field. The barycenters of the pressure distribution over the rear part of the model and the intensity recirculation are found highly correlated. Both described the most energetic large-scale structures dynamics, confirming the relation between the large-scale recirculation bubble and its wall pressure foot-print. Focusing on the pressure, its barycenter trajectory has a stochastic behavior but its low frequencies dynamics exhibit the same characteristics as a weak strange chaotic attractor system, with two well defined attractors. The low frequencies dynamics associated to the large-scale structures are then analyzed. The largest Lyapunov exponent is first estimated, leading to a low positive value characteristic of strange attractors and weak chaotic systems. Afterwards, analyzing the autocorrelation function of the time-series, we compute the correlation dimension, larger than two. The signal is finally transformed and analyzed as a telegraph signal showing that its dynamics correspond to a quasi-random telegraph signal. This is the first demonstration that the low frequencies dynamics of a turbulent 3D wake are not a purely stochastic process but rather a weak chaotic process exhibiting strange attractors. From the flow-control point of view, it also opens the path to more simple closed-loop flow control strategies aiming at the stabilization of the wake and the control of the dynamics of the wake barycenter., Comment: This second version presents a more detailed study of the wake dynamics, adding sections and references, leading to a slightly revised conclusion. 10 pages, 17 figures

Turbulent shear flows have triggered fundamental research in nonlinear dynamics, like transition scenarios, pattern formation and dynamical modeling. In particular, the control of nonlinear dynamics is subject of research since decades. In this publication, actuated turbulent shear flows serve as test-bed for a nonlinear feedback control strategy which can optimize an arbitrary cost function in an automatic self-learning manner. This is facilitated by genetic programming providing an analytically treatable control law. Unlike control based on PID laws or neural networks, no structure of the control law needs to be specified in advance. The strategy is first applied to low-dimensional dynamical systems featuring aspects of turbulence and for which linear control methods fail. This includes stabilizing an unstable fixed point of a nonlinearly coupled oscillator model and maximizing mixing, i.e.\ the Lyapunov exponent, for forced Lorenz equations. For the first time, we demonstrate the applicability of genetic programming control to four shear flow experiments with strong nonlinearities and intrinsically noisy measurements. These experiments comprise mixing enhancement in a turbulent shear layer, the reduction of the recirculation zone behind a backward facing step, and the optimized reattachment of separating boundary layers. Genetic programming control has outperformed tested optimized state-of-the-art control and has even found novel actuation mechanisms., Comment: 49 pages, many figures, submitted to Phys Rev E

Every volumetric velocimetry measurements based on tracer (particles, bubbles, etc.) detection can be strongly influenced by the optical screening phenomenon. It has to be taken into account when the the statistical properties associated to the performances of the particle detection and tracking algorithms are significantly affected. It leads to a maximum concentration of particles in the images thus limiting the final spatial resolution of the instantaneous three-dimensional three-components (3D3C) velocity fields. A volumetric velocimetry system based on Defocused Digital Particle Image Velocimetry is used to show that above a critical visual concentration of particles in the images, the concentration and accuracy of the final instantaneous raw velocity vector field drop. The critical concentration depends on physical parameters as well as on the processing algorithms. Three distinct regimes are identified. In the first regime, the concentration is well adapted to volumetric velocimetry, the largest concentration being optimal to maximize the number of valid velocity vectors. In the second regime, the performances of the detection and tracking algorithms are no longer optimal. Finally, the third regime is strongly influenced by optical screening. A rigorous methodology is proposed to optimize volumetric measurements taking into account the system specifications (pixel size, focal length, system magnification, etc.). An optimal particle concentration of 0.045 particles/pixel (ppp) is found. A relationship between the imaged concentration and the optimal final spatial resolution for fully interpolated instantaneous velocity field is obtained. The present study can be used as a guideline to achieve the measurement of instantaneous three-dimensional velocity fields with a good spatial resolution. It is finally successfully applied to a complex 3D flow test case: a jet in crossflow., Comment: 35 pages, 19 figures, postprint version of an already published article

We study experimentally a round Jet In CrossFlow (JICF) at low values of the jet to-crossflow velocity ratio R using instantaneous and time-averaged three-dimensions three-components (3D3C) velocimetry. The difference between instantaneous and time-averaged swirling structures of the JICF is emphasized. Through the analysis of spatial distribution of instantaneous transverse and longitudinal vortices the main transitions of the JICF are characterized for 0.15 < R < 2.2. A new transition at very low velocity ratio is found (R < 0.3). When R is large enough (R > 1.25), the classic JICF topology is recovered. In between, a deformation of the classical JICF topology is observed consisting in a progressive disappearance of the leading-edge vortices, a bending of the jet trajectory and thus a strengthened interaction with the boundary layer. toward the wall. Thanks to a state-of-the-art review on the JICF topology and using visualizations of the flow structures extracted from our experimental volumetric velocimetry measurements, this article provides a complete transition scenario of the JICF topology from the high velocity ratios to the lowest ones, and gives the topological transition threshold associated with each kind of vortex.

Many experimental and numerical studies report a large reduction of the recirculation bubble in Backward-Facing Step flows or airfoils in stall situation when excited at the natural shedding frequency $f_0$. Through a simple experiment using Dielectric Barrier Discharge actuator, we find a different result. For a given Reynolds number, the frequency of the perturbation is varied for a fixed duty-cycle dc = 27%. Through phase-averaging of Particle Image Velocimetry measurements, we show that the actuation creates a forced vortex which interacts with the natural shedding with a different phase velocity than the unforced one. The largest reduction of the recirculation bubble (-35%) is obtained in a very narrow frequency range around $0.73 f_0$ where early vortex pairing occurs between forced and unforced vortices. Phase averaging shows that in this case, the actuation clearly forces the vortex pairing in the shear layer. On the contrary, when the forcing frequency is higher, the shear layer behaves like an amplifier synchronized on the forced frequency, leading to a constant 10% reduction of the recirculation bubble.

The flow downstream a backward-facing step is controlled using a pulsed jet placed upstream of the step edge. Experimental velocity fields are computed and used to the recirculation area quantify. The effects of jet amplitude, frequency and duty cycle on this recirculation area are investigated for two Reynolds numbers (Re=2070 and Re=2900). The results of this experimental study demonstrate that upstream actuation can be as efficient as actuation at the step edge when exciting the shear layer at its natural frequency. Moreover it is shown that it is possible to minimize both jet amplitude and duty cycle and still achieve optimal efficiency. With minimal amplitude and a duty-cycle as low as 10\% the recirculation area is nearly canceled.

A novel, model free, approach to experimental closed-loop flow control is implemented on a separated flow. Feedback control laws are generated using genetic programming where they are optimized using replication, mutation and cross-over of best performing laws to produce a new generation of candidate control laws. This optimization process is applied automatically to a backward-facing step flow at Re=1350, controlled by a slotted jet, yielding an effective control law. Convergence criterion are suggested. The law is able to produce effective action even with major changes in the flow state, demonstrating its robustness. The underlying physical mechanisms leveraged by the law are analyzed and discussed. Contrary to traditional periodic forcing of the shear layer, this new control law plays on the physics of the recirculation area downstream the step. While both control actions are fundamentally different they still achieve the same level of effectiveness. Furthermore the new law is also potentially easier and cheaper to implement actuator wise.

Closed-loop control of an amplifier flow is experimentally investigated. A feed-forward algorithm is implemented to control the flow downstream a backward-facing step. Upstream and downstream data are extracted from real-time velocity fields to compute an ARMAX model used to effect actuation. This work, done at Reynolds number 430 investigates the practical feasibility of this approach which has shown great promise in a recent numerical study by Herv\'e et al (2012). The linear nature of the regime is checked, 2D upstream perturbations are introduced, and the degree to which the flow can be controlled is quantified. The resulting actuation is able to effectively reduce downstream energy levels and fluctuations. The limitations and difficulties of applying such an approach to an experiment are also emphasized.

We present new experimental results on the development of turbulent spots in channel flow. The internal structure of a turbulent spot is measured, with Time Resolved Stereoscopic Particle Image Velocimetry. We report the observation of travelling-wave-like structures at the trailing edge of the turbulent spot. Special attention is paid to the large-scale flow surrounding the spot. We show that this large-scale flow is an asymmetric quadrupole centred on the spot. We measure the time evolution of the turbulent fluctuations and the mean flow distortions and compare these with the predictions of a nonlinear reduced order model predicting the main features of subcritical transition to turbulence.

We present an experimental study of transition to turbulence in a plane Poiseuille flow. Using a well-controlled perturbation, we analyse the flow using extensive Particule Image Velocimetry and flow visualisation (using Laser Induced Fluorescence) measurements and use the deformation of the mean velocity profile as a criterion to characterize the state of the flow. From a large parametric study, four different states are defined depending on the values of the Reynolds number and the amplitude of the perturbation. We discuss the role of coherent structures, like hairpin vortices, in the transition. We find that the minimal amplitude of the perturbation triggering transition scales like Re^-1.

The vortex streets produced by a flapping foil of span-to-chord aspect ratio of 4:1 are studied in a hydrodynamic tunnel experiment. In particular, the mechanisms giving rise to the symmetry breaking of the reverse B\'enard-von K\'arm\'an vortex street that characterizes fish-like swimming and forward flapping flight are examined. Two-dimensional particle image velocimetry measurements in the mid-plane perpendicular to the span axis of the foil are used to characterize the different flow regimes. The deflection angle of the mean jet flow with respect to the horizontal observed in the average velocity field is used as a measure of the asymmetry of the vortex street. Time series of the vorticity field are used to calculate the advection velocity of the vortices with respect to the free-stream, defined as the phase velocity $U_{phase}$, as well as the circulation $\Gamma$ of each vortex and the spacing $\xi$ between consecutive vortices in the near wake. The observation that the symmetry breaking results from the formation of a dipolar structure from each couple of counter-rotating vortices shed on each flapping period serves as starting point to build a model for the symmetry breaking threshold. A symmetry breaking criterion based on the relation between the phase velocity of the vortex street and an idealized self-advection velocity of two consecutive counter-rotating vortices in the near wake is established. The predicted threshold for symmetry breaking accounts well for the deflected wake regimes observed in the present experiments and may be useful to explain other experimental and numerical observations of similar deflected propulsive vortex streets reported in the literature., Comment: 10 pages

We study experimentally the vortex streets produced by a flapping foil in a hydrodynamic tunnel, using 2D Particle Image Velocimetry (PIV). An analysis in terms of a flapping frequency-amplitude phase space allows to identify: 1) the transition from the well-known B\'enard-von K\'arm\'an (BvK) wake to the reverse BvK vortex street that characterizes propulsive wakes, and 2) the symmetry breaking of this reverse BvK pattern giving rise to an asymmetric wake. We also show that the transition from a BvK wake to a reverse BvK wake precedes the actual drag-thrust transition and we discuss the significance of the present results in the analysis of flapping systems in nature., Comment: Revised version includes minor changes in the discussion of the drag coefficient calculation. The 4 figures are unchanged