Programme JDFP 2021

Homogeneous Rayleigh-Bénard convection on logarithmic lattices

Amaury Barral
CEA

We present a new Fourier space framework ("logarithmic lattices") to tackle numerical simulations on a huge scale of wavenumbers. We apply it to the Homogeneous Rayleigh-Bénard equation and re-investigate some interesting scaling laws.

Etude de la dynamique de décrochage : application au profil NACA0012

Amaury BELLIER-GANIERE Afaf KARROUK Luc PASTUR Laurent ZIMMER
EM2C - CNRS - CentraleSupelec - Université Paris Saclay ENSTA Paris - IPP

Etude expérimentale du décrochage par analyse PIV autour d'une NACA0012 et mise en évidence d'un régime bistable

Droplet detachment and short circuits in liquid metal batteries

S. Bénard [1], N. Weber [2], G. M. Horstmann [2], S. Landgraf [2] and T. Weier [2]
[1] Université Paris-Saclay, CNRS, LISN, 91400 Orsay, France [2] Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr. 400, 01328 Dresden, Germany.

A liquid metal battery is a cell composed of three superposed layers: two layers of liquid metal (positive and negative electrodes) separated by a liquid electrolyte. The bottom electrode is composed of an alloy between both metals. Eventually, in the top layer, the liquid metal is contained in a foam. The different densities of these fluids ensure a stable stratification. In order to avoid short circuits, the metal electrodes should not enter in contact. Using numerical simulations, we study in which cases interface deformation and droplet formation in the cell could lead to a detachment of a droplet or even to a short circuit.

Robust certification by Optimal Uncertainty Quantification

Luc Bonnet Eric Savin Houman Owhadi Tim Sullivan
ONERA/MSSMat ONERA Caltech University of Warwick

The expected performance of a system generally differs from its operational performance due to the variability of some parameters. Optimal Uncertainty Quantification is a powerful mathematical tool that can be used to rigorously bound the probability of exceeding a given performance threshold for uncertain operational conditions or system characteristics. An application of this framework to an aerodynamic case will be shown.

Apprentissage automatique et méthode de gradient pour le contrôle en boucle fermée de l'écoulement en cavité ouverte

Guy Cornejo Maceda (1), Eliott Varon (1), François Lusseyran (1) and Bernd R. Noack (2)
(1) Universite Paris-Saclay, CNRS, LISN, 91400 Orsay, France (2) Center of Turbulence Control, HIT, Shenzen, China

Nous présentons le contrôle expérimental de l'écoulement de cavité à l'aide d'une nouvelle méthode de contrôle combinant apprentissage automatique et méthode de gradient (gradient-based machine learning control, gMLC). gMLC permet l'apprentissage de lois de contrôle directement depuis l'expérience, sans modèle a priori, dans un espace de recherche de dimension infini, a priori non-convexe et présentant plusieurs minima. Dans le cas de la cavité, gMLC apprend une loi en boucle fermée minimisant l'amplitude des oscillations de la couche de mélange en aval de l'écoulement. Nous avons notamment établi la nécessité de la boucle fermée pour le contrôle de la cavité et étudié la robustesse de la solution en la testant à un différent régime.

Observation expérimentale quantitative de la turbulence faible d'ondes d'inertie

Pierre-Philippe Cortet (1), Eduardo Monsalve (1), Maxime Brunet (1), Basile Gallet (2)
(1) Université Paris-Saclay, CNRS, FAST (2) Université Paris-Saclay, CNRS, CEA, Service de Physique de l’État Condensé

Nous présentons la première observation expérimentale quantitative du régime de turbulence d’ondes de la turbulence en rotation. La spécificité de notre dispositif est d’injecter l’énergie dans une assemblée de nombreuses ondes d’inertie, statistiquement homogène et axisymétrique, et de prévenir l’émergence d’un mode géostrophique (tourbillons d’axe parallèle à la rotation) grâce à l’ajout de parois rugueuses en bas et en haut de l’écoulement. À mesure que l'amplitude de forçage augmente, nous observons l’émergence d’une cascade d’énergie vers les basses fréquences et les petites échelles où toute l’énergie est portée par des ondes. Nous montrons que les interactions triadiques résonantes au cœur de la théorie de la turbulence faible, qui essaie de décrire ce type de systèmes, se développent sur un large continuum de fréquences. Nous montrons finalement que les spectres spatiaux de l’énergie de notre écoulement turbulent suivent une loi de puissance, dont l'exposant et le préfacteur sont en accord quantitatif avec les prédictions de la théorie de la turbulence faible.

Avalanche granulaire au travers une forêt d’obstacles

Baptiste Darbois Texier, Yann Bertho, Philippe Gondret
Université Paris-Saclay, CNRS, FAST

Ce travail expérimental porte sur la dynamique d’une avalanche granulaire au travers d’une forêt d’obstacles constitués par des piliers cylindriques. Nous avons mesuré l’effet des ces obstacles sur la vitesse d’écoulement des grains en régime stationnaire et en particulier du rôle de la densité de piliers. Une modélisation de ce problème est proposée en se basant sur la rhéologie μ(I) pour décrire l’écoulement granulaire et en y intégrant les forces exercées par chaque pilier sur la couche de grains. Au final, ce travail permet de prédire sous quelles conditions une forêt d’obstacles diminue sensiblement l’énergie cinétique d’une avalanche.

Dynamique non linéaire de deux vortex hélicoïdaux

I. Delbende, M. Rossi & C. Selçuk
LIMSI/d'Alembert, Sorbonne Université

Les vortex hélicoïdaux coaxiaux comme ceux produits par les pales des rotors interagissent et donnent lieu à des dynamiques non triviales. Nous faisons ici une étude systématique de la dynamique non linéaire de deux vortex identiques en fonction de leur pas hélicoïdal commun. A l'aide de modèles simplifiés, il est possible de décrire les trajectoires relatives des vortex comme des orbites dans un espace des phases de dimension 2 structuré par des points elliptiques et hyperboliques. Ceci permet de déterminer les différents régimes dynamiques possibles en fonction du pas hélicoïdal : saute-mouton (connu), dépassements successifs et flottement (jamais observés).

Évaporation de liquides confinés dans des capillaires plats

Christophe Poulard
LPS

A model of interacting

Hugues Faller, Damien Geneste, Bérengère Dubrulle
CEA Saclay, Service physique de l'état condensé

We introduce a model of interacting singularities of Navier-Stokes, named pinçons. They follow a Hamiltonian dynamics, obtained by the condition that the velocity field around these singularities obeys locally Navier-Stokes equations. This model can be seen of a generalization of the vorton model of Novikov, that was derived for the Euler equations. When immersed in a regular field, the pinçons are further transported and sheared by the regular field, while applying a stress onto the regular field, that becomes dominant at a scale that is smaller than the Kolmogorov length.

Properties of sub-grid terms in a turbulent von Kármán flow.

D. Geneste∗ , H. Faller∗ , T. Chaabo† , Y. Ostovan† , V. Valori∗ , A. Cheminet∗ , C. Cuvier† , F. Daviaud∗, J-M. Foucaut† , J-P. Laval† and B. Dubrulle∗
∗ SPEC, CEA, Université Paris-Saclay, 91190 Gif sur Yvette, France †LML FRE3723, Univ. Lille, Centrale Lille, Villeneuve dAscq, France

Incompressible flows can be described by Navier-Stokes equations. However, for most of application, it is far too costly to compute their solutions via Direct Numerical Simulation (DNS). It exists many ways to compute an approximate solution though. Approximate solutions are then computed by replacing some modes (small scales or fluctuations) by a suitable model. The most popular model adds an eddy-viscosity to the equation. Such a term is supposed to compensate the lack of energy flux. The goal of the present study is to investigate some properties of the subgrid tensors using a special property of experimental measurements. Indeed, in a perfect world, the flow recorded from any experiment follows Navier-Stokes equations. Unfortunately, every measurement technic has its own physical limit. The experimentalist does not access real data but only filtered ones whose filter depends on the experimental system. Most of the time this filter is unknown or even not accessible. In experiment, the resolution cannot be infinite and the experimental system applies a filter. Because of such a filter, there exists nevertheless a non zero sub-grid term in the vorticity equation. In this presentation, we will study the properties of such term using data from the same experiment using two different reconstructions technics. The first reconstruction is Tomographic Particle Image Velocimetry (TPIV) a volumetric reconstruction of the whole set of particles a spatial correlation between two consecutive frames gives the Eulerian velocity field. The second reconstruction is a Particle Tracking Velocimetry (PTV) a Lagrangian reconstruction of the path individually followed by each particle. An interpolation on a Eulerian grid of filtered tracks is computed to compare with the TPIV data. We also compared these datas with a DNS to which we applied a controlled filter. From our different experimental and numerical data, we study the impact on the sub-grid term for different filters controlled or uncontrolled. From visual and statistical studies, we try to understand the sub-grid scales properties and their relations with other quantities related to energy transfer.

Far Field of Turbulent Spots

Pavan KASHYAP(1), Yohann DUGUET(1), Matthew CHANTRY(2)
(1)LISN (2) University of Oxford

The far field of localized turbulent patches (spots) and the associated large-scale flow are investigated in various wall bounded shear flows. A computational study is performed in large periodic domains using the efficient parallel spectral code Channelflow 2.0. The large-scale flow generated by the localized spots is observed to be structured according to the symmetries of the laminar base flow. Simulations show that the velocity fluctuations decay algebraically away from the spot, with a decay exponent depending on the structure of the large-scale flow but independent of the Reynolds number.

Multi-scale interaction with flows of Kirigami structures

Tom Marzin, Emmanuel de Langre & Sophie Ramananarivo
LadHyX - école Polytechnique

We study the deformation of a kirigami- that is a sheet slit with a network of cuts in a water flow. When stretched, the kirigami significantly opens up and thus acts as a poro-elastic surface that lets fluid through. We characterize experimentally and theoretically the relation between the cuts geometry and the resulting shape transformation. We show that macroscopic morphing is dictated by interactions with fluid at the scale of individual pores, whose geometry changes in turn with the sheet elongation. Understanding those multi-scale couplings provides a novel way to control and program shape-shifting in flows through the reverse-engineering of cut motifs.

Three-dimensionality of the triadic resonance instability of a plane inertial wave

Daniel Odens Mora (1), Eduardo Monsalve (1), Maxime Brunet (1), Thierry Dauxois (2), Pierre-Philippe Cortet (1)
(1) Université Paris-Saclay, CNRS, FAST (2) Université de Lyon, ENS de Lyon, CNRS, Laboratoire de Physique

Given their importance for the weak turbulence theory which aims to describe the small-scale dynamics of the oceanic and atmospheric turbulence, the triadic resonant interactions of internal waves and especially their triadic resonance instability (TRI) have received considerable attention in the last two decades. Nevertheless, previous studies have overlooked a key component of the TRI that we reveal for inertial waves in rotating fluids: the instability produces secondary waves propagating in different vertical planes than the primary wave. In this work, we prove this result theoretically and experimentally. Our observations imply that ensembles of weakly nonlinear inertial waves will quickly reach a statistically axisymmetric state around the rotation axis, which is one of the key assumptions made in the derivation of the weak inertial-wave turbulence theory.

Efficient mixing in liquid metal batteries by swirling electrovortex flows

C. Nore [1], W. Herreman [1], L. Cappanera [2] and J.-L. Guermond [3]
[1] Universite Paris-Saclay, CNRS, LISN, 91400 Orsay, France [2] Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA [3] Department of Mathematics, Texas A&M University 3368 TAMU, College Station, TX 77843-3368, USA

Using direct numerical simulations, we study the flow and composition of the bottom alloy layer of a discharging liquid metal battery (LMB). This layer is submitted to a uniform vertical magnetic field Bz and it is electrically connected from below to a thinner solid copper wire. The current is deviated towards the wire and creates a mainly azimuthal Lorentz-force always localized near the electrical contact. This force generates a swirling electrovortex flow that pumps the material downwards in a spiral motion prior to ejecting it radially. By studying the flow in various parameter regimes, we identify and explain a novel scaling law for the intensity of these swirling electrovortex flows. Using this scaling law and the model described in Herreman et al.,Phys. Rev. Fluids 5(7),(2020), we estimate the minimal intensity of the external magnetic field that is needed for the swirling electrovortex to enhance the mixing of the alloys in the bottom electrode of arbitrary liquid metal batteries. Mixing is very intense and three-dimensional. However axisymmetric simulations provide good estimates of the mixing capabilities of the swirling electrovortex flow. More details can be found in Herreman et al.,J. Fluid Mech. 915, A17 (2021).

Settling dynamics of particle clouds in still water

Till Zürner, David De Souza, Romain Monchaux
IMSIA, ENSTA Paris / CNRS / CEA / EDF / Institut Polytechnique de Paris, 828 Boulevard des Maréchaux, 91120 Palaiseau

The settling of heavy inertial particles in still water is investigated experimentally using simultaneous particle tracking and particle image velocimetry. The movement of the particles and their back-reaction on the fluid are characterised in terms of the particle inertia and loading (i.e., the amount of particles introduced into the experiment). It is found that the particles overall agree with the empirical Schiller-Naumann drag model but in detail show a complex interaction with the background flow that they themselves induce.

Subcritical transition to turbulence: the dimension of the edge

Y. Duguet (LISN), M. Beneitez, P. Schlatter, D.S. Henningson
LISN-CNRS, KTH

The edge state is an unstable regime at the verge between laminar and turbulent. In most cases it is chaotic. We compute the Kaplan-Yorke dimension of the associated dynamics using a new method and demonstrate that it remains small compared to that of the turbulent attractor.

Characterization of the amplitude modulation phenomenon of wind turbines noise

Lisa SICARD, David RAUS, Benjamin COTTE, Romain MONCHAUX
ENSTA Paris

Experimental study of dynamic stall noise

Rotation et explosion d'un ellipsoide en Faraday spherique

Antoine Mille, Jalel Chergui, Ali-higo Ebo-Adou, Nicolas Périnet, Laurette Tuckerman, Damir Juric, S. Shin,
ENS-Saclay, LISN-CNRS, C.E.R. Djibouti, Univ. Chile, PMMH-CNRS, Hongik Univ.

Nous étudions une goutte sphérique soumise à une force radiale oscillatoire, telle que sa forme oscille entre une forme prolate et oblate. Nous constatons que la goutte perd son axisymétrie, se met à tourner de plus en plus vite, et finit par exploser. Nous explorons les liens possibles entre ces phénomènes.

Multiple drops interacting on swelling fibres

Pierre Van de Velde, Camille Duprat, Suzie Protière
LadHyX, Ecole Polytechnique Institut Jean le Rond d'Alembert

Many real fibers such as cellulose, wood or polymer fibers may swell when interacting with a favorable solvent. We study the interaction between swelling fibers and drops of a favorable solvent. Generally, the curvature of a fiber prevents the total spreading of a drop even if the fluid is fully wetting the fiber. On a swelling fiber, a drop locally penetrates and swells the fiber thus moving further through the polymer network. If two drops are placed close enough to each other on the same fiber, they may interact via the swollen polymer network leading to different spontaneous movements. The drops may drift apart or in some cases attract each other or even coalesce in a counterintuitive manner. In this talk, by making use of our previous work on the absorption of a single drop on a fiber, we attempt to rationalize the dynamics of two or more interacting droplets on a fiber through controlled experiments and simple models.