# Luc PasturENSTA Paris - Institut polytechnique de Paris · Fluid Mechanics department

Luc Pastur

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125

Publications

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Introduction

**Skills and Expertise**

## Publications

Publications (125)

The turbulent wake behind a flat-back Ahmed body is investigated using stacked stereo-scopic particle image velocimetry (SSPIV). The wake is disturbed by a steady jet from the center of the base and the effects are quantified for key blowing rates. The unactuated wake exhibits bi-stable dynamics in the horizontal plane which are completely subdued...

Data-driven reduced-order modeling opens new avenues of understanding, predicting, controlling, and optimizing system behavior. Simple systems may have state spaces in which sparse human-interpretable dynamical systems can be identified. This approach has been pioneered by S. Brunton et al. (2016, PNAS) with Sparse Identification of Nonlinear Dynam...

We study the dynamics of a fixed wing at stall in a wind tunnel by measuring the aerodynamic forces. We report experimental evidence of a critical Reynolds number from which low-frequency oscillations in the force are replaced by random bistable dynamics. In this new regime, the flow explores each state intermittently with long residence times. Thi...

We are carrying out the experimental study of the emptying of a hermetically sealed cylindrical tank in a rotating frame. We determine the optimal rotational velocity for the tank, which minimizes the emptying time. Moreover, there exists a critical rotation velocity at which the emptying time exceeds that of the nonrotating case, depending on the...

We investigate experimentally the unsteady draining flow from a rotating tank. The fluid in the tank is first set in solid rotation, before the draining hole is opened. We show that the draining may be drastically reduced by the rotation, as the vortex circulation increases together with the surface deformation. We demonstrate that the usual Torric...

Base blowing is applied through a small, centrally located square aperture at the base of a flat-backed Ahmed body. In addition to the expected drag reduction effect at low momentum injection (i.e., base bleeding effect), a major result is the complete suppression of the steady asymmetry of the wake. Both the maximum drag reduction and the minimum...

We propose a self-supervised cluster-based hierarchical reduced-order modelling methodology to model and analyse the complex dynamics arising from a sequence of bifurcations for a two-dimensional incompressible flow of the fluidic pinball. The hierarchy is guided by a triple decomposition separating a slowly varying base flow, dominant shedding and...

The dynamics of the wake behind a flat-back Ahmed body are modified using a large-scale fluidic oscillator, aiming at drag reduction and the reflectional symmetry breaking (RSB) mode suppression. In the present experiment, the sweeping jet (SWJ) actuator is integrated into the base of the bluff body such that its nozzle width corresponds to about 2...

Paper currently in review for publication in Physics of Fluids.

We propose a self-supervised cluster-based hierarchical reduced-order modelling methodology to model and analyse the complex dynamics arising from a sequence of bifurcations for a two-dimensional incompressible flow of the unforced fluidic pinball. The hierarchy is guided by a triple decomposition separating a slowly varying base flow, dominant she...

Generically, a local bifurcation only affects a single solution branch. However, branches that are quite different may nonetheless share certain eigenvectors and eigenvalues, leading to coincident bifurcations. For the fluidic pinball, two supercritical pitchfork bifurcations, of the equilibrium and the periodic solutions, occur at nearly the same...

This paper addresses the case of a cylinder array in axial flow at Reynolds numbers from 60000 to 110000. A comprehensive experimental and numerical study of the steady fluid forces arising from a geometrical perturbation in the array arrangement is carried out and compared with a semi-empirical model from the literature. The test rig consists of a...

Inspired by the study of Rao et al. (2019), the aerodynamics of a simplified frigate is investigated experimentally. The natural wake flow dynamics is shown to be bi-stable at zero yaw angles, at both the rear of the ship superstructure and the stern. The bi-stable dynamics is strongly weakened at the stern when the ship is lifted off the ground in...

In a perspective of active flow control of the bistable wake of a square-back Ahmed body, we show that the steady blowing through a perimetric slit at the rear of the body is not equivalent to a material rear perimetric cavity, the latter being able to suppress the bistable dynamics and symmetrize the wake flow, while the former cannot achieve any...

Suction applied at the base of a square-back Ahmed body is shown to create a global effect on the wake, reducing the recirculating bubble length and increasing the base drag. Weak suction causes a small shortening of the bubble and intensifies the steady reflectional symmetry breaking (RSB) mode present in the horizontal direction. Stronger suction...

In this work, we are interested in the transient dynamics of a fluid configuration consisting of three fixed cylinders whose axes distribute over an equilateral triangle in transverse flow << fluidic pinball >>. As the Reynolds number is increased on the route to chaos, its transient dynamics tell us about the contribution of the elementary degrees...

Reduced-order modelling and system identification can help us figure out the elementary degrees of freedom and the underlying mechanisms from the high-dimensional and nonlinear dynamics of fluid flow. Machine learning has brought new opportunities to these two processes and is revolutionising traditional methods. We show a framework to obtain a spa...

The fluidic pinball is a geometrically simple flow configuration with three rotating cylinders on the vertex of an equilateral triangle. Yet, it remains physically rich enough to host a range of interacting frequencies and to allow testing of control laws within minutes on a laptop. The system has multiple inputs (the three cylinders can independen...

The fluidic pinball has been recently proposed as an attractive and effective flow configuration for exploring machine learning fluid flow control. In this contribution, we focus on the route to chaos in this system without actuation, as the Reynolds number is smoothly increased. It was found to be of the Newhouse-Ruelle-Takens kind, with a seconda...

The goal of the paperJoly, Aurélien is to investigate experimentally and numerically theBadel, Pierre Taylor-Lighthill-Païdoussis (TLP) model of fluid forces in axial flow,De Buretel de Chassey, Nicolas in the case of a flexible cylinder confined in a cylinder array.Cadot, Olivier This model assumes that the local fluid forces depend only on the lo...

The paper reports on the bi-stable turbulent wake dynamics of a three-dimensional bluff body. It is shown that the occurrence of the switching between the two wake states decreases as the turbulent intensity of the incoming flow is made larger by an additional upstream grid. A detailed analysis of the jumps statistics indicates that the turbulent f...

We propose an aerodynamic force model associated with a Galerkin model for the unforced fluidic pinball, the two-dimensional flow around three equal cylinders with one radius distance to each other. The starting point is a Galerkin model of a bluff-body flow. The force on this body is derived as a constant-linear-quadratic function of the mode ampl...

This study reveals that injecting a light fluid of density ρ_{b} in the recirculating bubble of a bluff body at Re≈6.4×10^{4} has a greater drag reduction potential than blowing fluid of a density greater than or equal to that of the free stream ρ. It is found that the maximum drag reduction scales as (ρ_{b}/ρ)^{-1/6}. This power law combines the a...

The use of rear cavities at the base of a square-back Ahmed body has been experimentally evaluated as a passive control device under cross-wind conditions with yaw angles β≤10°, by means of pressure, force and velocity measurements. A comparative study has been performed at a Reynolds number Re=105, considering the reference square-back body (i.e....

The dynamics of an oscillating shear layer when confined is enriched by retarded actions whose physical modeling is not trivial. We present a nonlinear delayed saturation feedback model, which allows us to correctly reproduce the complex shear layer spectra observed experimentally in open cavity flows in the incompressible limit. The model describe...

Low-order model for successive bifurcations of the fluidic pinball - Volume 884 - Nan Deng, Bernd R. Noack, Marek Morzyński, Luc R. Pastur

Wake modes of a three-dimensional blunt-based body near a wall are investigated at a Reynolds number Re=$10^5$. The targeted modes are the static symmetry-breaking mode and two antisymmetric periodic modes. The static mode orientation is aligned with the horizontal major $y$-axis of the base and randomly switches between a positive P and a negative...

The wake of a square-back 3D bluff body is dominated by a stochastic switching between two reflectional symmetry breaking wake flows [1]. The two mirror wakes are associated with an increased drag. We, therefore, attempt to symmetrize the wake using a Sweeping Jet (SWJ) actuator located at the top of the bluff body base. Arrays of SWJs have been su...

In a perspective of active flow control of the bistable wake of a square‐back Ahmed body, we show that the steady blowing through a perimetric slit at the rear of the body is not equivalent to a material rear perimetric cavity, the latter being able to suppress the bistable dynamics and symmetrize the wake flow, while the former cannot achieve any...

The aim of our work is to advance a self‐learning, model‐free control method to tame complex nonlinear flows—building on the pioneering work of Dracopoulous [1]. The cornerstone is the formulation of the control problem as a function optimization problem. The control law is derived by solving a nonsmooth optimization problem thanks to an artificial...

In order to better understand the mechanisms of fretting wear damage of guide cards in some Pressurized Water Reactor (PWR) Nuclear Power Plant (NPP), an experimental investigation is undertaken at the Magaly facility in Le Creusot. The test rig consists of a complete Rod Cluster with eleven Guide Cards, submitted to axial flow inside a water tunne...

The fluidic pinball is a geometrically simple wake flow configuration with three rotating cylinders on the vertex of an equilateral triangle. Yet, it remains physically rich enough to host a range of interacting frequencies and to allow testing of control laws within minutes on a laptop. The system has multiple inputs (the three cylinders can indep...

We propose the first least-order Galerkin model of an incompressible flow undergoing two successive supercritical bifurcations of Hopf and pitchfork type. A key enabler is a mean-field consideration exploiting the symmetry of the base flow and the asymmetry of the fluctuation. These symmetries generalize mean-field theory, e.g. no assumption of slo...

The fluidic pinball has been recently proposed as an attractive and effective flow configuration for exploring machine learning fluid flow control. In this contribution, we focus on the route to chaos in this system without actuation, as the Reynolds number is smoothly increased. It was found to be of the Newhouse-Ruelle-Takens kind, with a seconda...

The transition to unsteadiness of a three-dimensional open cavity flow is investigated using the joint application of direct numerical simulations and fully three-dimensional linear stability analyses, providing a clear understanding of the first two bifurcations occurring in the flow. The first bifurcation is characterized by the emergence of Tayl...

We analyze the temporal dynamics associated with axisymmetric coherent structures in a turbulent jet. It has long been established that turbulent jets comprise large-scale coherent structures, now more commonly referred to as “wave packets” [Jordan and Colonius, Annu. Rev. Fluid Mech. 45, 173 (2013)]. These structures exhibit a marked spatiotempora...

The flow through two facing, identical cavities (double-cavity) is characterized experimentally, as the inflow velocity and the distance between the cavities is varied. Standard 2D2C particle image velocimetry measurements in the spanwise mid-plane provide information on the instantaneous and mean velocity flow fields. Laser Doppler velocimetry mea...

The transport of passive tracers inside a two-dimensional differentially heated cavity is investigated numerically in the oscillatory regime, both in the vicinity and far from the corresponding Hopf bifurcation. Differential transport at low Rayleigh number is essentially linked to the exchange of fluid between two symmetric homoclinic tangles. A h...

This paper reports results obtained with two-dimensional numerical simulations of viscous incompressible flow in a symmetric channel with a sudden expansion and contraction, creating two facing cavities; a so-called double cavity. Based on time series recorded at discrete probe points inside the double cavity, different flow regimes are identified...

This study deals with the experimental investigation of the onset of instability in an open cavity flow, in the incompressible limit. Far below the development of self-sustained oscillations, the first instability is three-dimensional on the inner recirculating flow. We address the case of a cavity of a large span-wise aspect ratio in which the sid...

A large eddy simulation of flow over a forward-facing plate is performed and the resulting database analyzed with respect to sound radiation. Aeroacoustic analysis motivates an initial data compression comprising eduction of the zeroth-order spanwise Fourier mode. The space–time structure of this component of the flow is then analyzed using POD and...

We present an experimental parametric study of spanwise centrifugal instabilities in an open cavity flow. We show that the mode selected at threshold depends on the cavity streamwise aspect ratio. For small aspect ratio, a steady mode is enhanced, while travelling waves are observed for large aspect ratio. The bifurcation is found to be supercritic...

The complete cascade of bifurcations from steady to chaotic convection, as the Rayleigh number is varied, is considered numerically inside an air-filled differentially heated cavity. The system is assumed to be two-dimensional and is invariant under a generalized reflection about the center of the cavity. In the neighborhood of several codimension-...

The turbulent wake of a square-back body exhibits a strong bimodal behavior. The wake randomly undergoes symmetry-breaking reversals between two mirror asymmetric steady modes [reflectional symmetry-breaking (RSB) modes]. The characteristic time for reversals is about 2 or 3 orders of magnitude larger than the natural time for vortex shedding. Stud...

Detection of coherent structures is of crucial importance for understanding the dynamics of a fluid flow. In this regard, the recently introduced Dynamic Mode Decomposition (DMD) has raised an increasing interest in the community. It allows to efficiently determine the dominant spatial modes, and their associated growth rate and frequency in time,...

We present an alternative perspective on nonharmonic mode coexistence, commonly found in the shear layer spectrum of open-cavity flows. Modes obtained by a local linear stability analysis of perturbations to a two-dimensional, incompressible, and inviscid sheared flow over a cavity of finite length and depth were conditioned by a so-called coincide...

This paper focuses on the closed-loop control of an incompressible flow past an open cavity. We propose a delayed feedback controller to suppress the self-sustained oscillations of the shear layer. The control law shows robustness to changes in flow conditions. An extension of the Eigensystem Realization Algorithm (ERA) to closed-loop identificatio...

The chaotic advection of passive tracers in a two-dimensional confined convection flow is addressed numerically near the onset of the oscillatory regime. We investigate here a differentially heated cavity with aspect ratio two and Prandtl number 0.71 for Rayleigh numbers around the first Hopf bifurcation. A scattering approach reveals different zon...

Open cavity flows are known to select and enhance locked-on modes or tones. High-energy self-sustained oscillations arise within the shear layer, impinging onto the trailing edge of the cavity. These self-sustained oscillations are subject to amplitude modulations (AMs) at multiple low frequencies. However, only a few studies have addressed the ide...

Shear-layer driven open cavity flows are known to exhibit strong self-sustained oscillations
of the shear-layer. Over some range of the control parameters, a competition
between two modes of oscillations of the shear layer can occur. We apply
both Proper Orthogonal Decomposition and Dynamic Mode Decomposition to experimental
two-dimensional two-com...

Accurate reference solutions are very important in stability analysis, where they must act as a reliable base-state. They are also quite useful for unsteady numerical simulations, where they play key roles as initial conditions and in the implementation of boundary conditions, such as buffer zones. Quite often they are approximate solutions for a s...

This work aims to reconstruct three-dimensional coherent structures associated with centrifugal instabilities by making use of the dynamics in a space-time volume (x, y, t) with the mono-chormatic spanwise-travelling wave assumption.

Side-band frequencies in an incompressible flow past a rectangular cavity are characterized through their space-time coherent structures. A parametric study over a range of dimensionless cavity length L/θo has been carried out in the incompressible regime. It yields the general evolution of self-sustained oscillations, for which primary characteris...

We propose an algorithm that combines Proper Orthogonal Decomposition with a spectral method to analyse and extract from time data series of velocity fields, reduced order models of flows. The flows considered in this study are assumed to be driven by non linear dynamical systems exhibiting a complex behavior within quasi-periodic orbits in the pha...

Les écoulements de cavité constituent une classe d’écoulements marqués par la présence d’une recirculation, qui impose une courbure pouvant donner naissance à une instabilité centrifuge [1]. Il existe différentes configurations d’écoulements de cavité, on distingue ici les écoulements de cavités ouvertes et les écoulements de cavités entraînées par...

Three-dimensional direct numerical simulations of an incompressible open
square cavity flow are conducted. Features of the permanent (non-linear) regime
together with the linear stability analysis of a two-dimensional steady base
flow are discussed. Spanwise boundary conditions are periodic and control
parameters set such that the shear layer is st...

This paper presents a haptic stimulus that enables the discrimination between linear and non-linear functions. These functions correspond to the evolution of divergency for two important states of dynamic systems: quasi-periodic and chaotic states respectively. The proposed approach combines a kinaesthetic feedback, to attract the user on explored...

We present an interaction design study of several non-overlapping direct-touch interaction widgets, postures, and bi-manual techniques to support the needs of scientists who are exploring a dataset. The final interaction design supports navigation/zoom, cutting plane interaction, a drilling exploration, the placement of seed particles in 3D space,...

The dynamic dimension of an impinging flow may be significantly reduced by its boundary conditions and self-sustained oscillations they induce. The spectral signature is associated with remarkable spatial coherent structures. Dynamic modes decomposition (DMD) makes it possible to directly extract the dynamical properties of a non-linearly saturated...

La dimension effective de la dynamique d’un écoulement impactant peut-être considérablement réduite par les conditions aux limites et les oscillations auto-induites qu’elles engendrent. Dans ce cas la signature spectrale de ces oscillations est associée à des structures spatiales remarquables que l’on souhaite identifier. La méthode de décompositio...

We present a method that seeks to combine the properties of optimal control with the robust character of closed-loop control.
The method relies on the availability of a reduced model of the system to be controlled, in order to express the control problem
in a low-dimensional space where the system-state-dependent optimal control law is subsequently...

An open cavity flow is strongly dependant on its geometry and Reynolds number, yielding to development of different types of instabilities. The shear layer between the external and the inner cavity flow is able to give rise to a Kelvin-Helmholtz-like instability, coupled with the shear flow impingement on the downstream cavity wall. The velocity gr...

We present a method which seeks to combine the efficiency of an optimal control command with the robustness of a closed-loop controller. While the performance of optimal control is excellent, it cannot account for perturbations to the system under control which make the resulting performance to drop. On the other hand, a closed-loop control makes u...