Programme JDFP 2019

Non-modal linear stability analysis of ablation flows relative to inertial confinement fusion

Grégoire Varillon (1,2), Jean-Marie Clarisse (1), Arnaud Couairon (2)
(1) CEA, DAM, DIF, F-91297 Arpajon (2) CPHT, Ecole polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau

The hydrodynamic stability of ablation flows is a key issue in laser-driven inertial confinement fusion (ICF) where a sufficiently symmetric implosion of a spherical pellet is expected to achieve thermonuclear burn. Inherently unsteady, these flows are compressible, strongly accelerated and highly nonuniform with a steep heat front, owing to the strong nonlinearity of the heat transport. Here we investigate non-modal effects in planar radiative ablation waves by using self-similar ablation solutions to the Euler equations with nonlinear heat conduction without further approximation as model base flows. Solutions to perturbed Euler equations were found to behave as progressive waves in some regions of the flow. In these regions, we use a toy-model to compute the numerical abscissa and optimal growth initial condition of the time evolution operator for short wavelength perturbations. The existence of transient growth is assessed with the time integration of the full system. Computed optimal responses are physically analysed in terms of diffusion and propagation, with the help of a decomposition into linear hyperbolic waves and emphasize the role of acoustic waves in transient growth mechanisms.

Reduced-order modeling of blood flow across macroscopic through mesoscopic circulation scales

ADJOUA Passi Olivier ; LUCOR Didier
Sorbonne-Universités ISCD & LIMSI-CNRS ; LIMSI-CNRS

One-dimensional reduced-order models (ROM) are commonly used to simulate convection-dominated blood flow for which pulse waves propagate in large elastic arteries. They rely on a fluid-structure interaction modeling framework that is much simplified when assumptions of Newtonian properties, linear elasticity and homogeneous geometry are made for the blood fluid, the vessel walls mechanical response and the circulation network, respectively. In this case, these models numerically predict averaged hemodynamic quantities such as flow rates, cross-sectional areas or blood pressures with satisfactory accuracy. Moreover, their low computational cost enables the dynamic simulations of moderately large networks of arteries. In this presentation, we will show how we rely on this inherited framework to enrich the ROM and extend its capability toward microcirculation at mesoscopic scales both in terms of modeling and computational efficiency. These new developments require among others, the generation of a realistic multi-scale vascular network with an adaptation of the description of the blood rheology and the wall structural model within the arterioles and capillaries.

Reduced order model for coupled natural convection and radiation in Rayleigh-Bénard cubical cavities

Laurent Soucasse, Bérengère Podvin, Philippe Rivière, Anouar Soufiani
EM2C / LIMSI

Reduced-order modeling of the fluidic Pinball

Nan DENG Luc PASTUR Bernd NOACK Marek MORZYNSKI
IMSIA, ENSTA ParisTech, LIMSI-CNRS, Université Paris-Saclay IMSIA, ENSTA ParisTech LIMSI-CNRS, Harbin Institute of Technology (China), Tecnische Universität Berlin Poznan University of Technology (Poland)

In this work, we show a way for designing least-order mean-field models compatible with the Navier-Stokes equations for an incompressible flow undergoing two successive supercritical Hopf and pitchfork bifurcations, which are generic bifurcations commonly encountered in fluid mechanics. Our approach is illustrated on the fluidic pinball, a two-dimensional wake flow around a cluster of three equidistantly spaced cylinders. The five elementary degrees of freedom of the flow could be identified, on which a dynamical system could be designed, which repoduces remarkably well the main features of the original flow. This 5-dimensional reduced-order model is also the least-order Galerkin model compatible with the quadratic non-linearities of the Navier-Stokes equations.

An accurate sharp interface method for two-phase compressible flows at low-Mach regime

Ziqiang Zou, Edouard Audit, Nicolas Grenier, Christian Tenaud
Maison de la Simulation & LIMSI

An accurate numerical approach is presented for computing two-phase flows at low-Mach regime. The ordinary methods treat the flows at low-Mach regime as incompressible. Approaches with assumption of incompressibility are rather robust and efficient, but some compressible effects can occur in this kind of flow and may impact the behavior of fluid. In order to develop an accurate model, both the liquid and gas of the are considered compressible and described by a precise compressible solver. The interface between two-phase is caputred by the Level-Set method and considered to be sharp. The Riemann problem at interface is resolved by a Ghost-Fluid method based algorithm.

Advection-driven transition to chaos in chemically active microparticles and droplets

Matvey Morozov and Sébastien Michelin
LadHyX, École Polytechnique

A single chemically active microparticle or droplet that is suspended in the bulk of a reagent solution may excite the flow in the surrounding fluid even in the absence of preexisting asymmetries, such as gravity or inhomogeneous interfacial properties. In the absence of imposed asymmetries, the flow may be due to a spontaneous symmetry-breaking enabled by advection. We present numerical simulations revealing that advection may also play a key role in selection of a nonlinear flow pattern excited by the particle or drop. Specifically, we demonstrate that weak advection is associated with the steady self-propulsion of the particle or drop, while strong advection induces the onset of a chaotic flow.

Spontaneous self-assembly in microroller suspensions

Blaise Delmotte, Michelle Driscoll, Aleksandar Donev, Paul Chaikin
LadHyX, CNRS-Ecole Polytechnique/Department of Physics, Northwestern University/ Courant Institute, New York University/ Center for Soft Matter Research, New York University.

When colloidal particles are rotating adjacent to a nearby floor, strong advective flows are generated around them, even quite far away. When a group of these microrollers is driven by an external field, the strong hydrodynamic coupling between particles leads to formation of new structures. Our experimental observation show that a suspension of microrollers undergoes a cascade of instabilities: an initially uniform front of microrollers evolves first into a shock-like structure, which then quickly becomes unstable, emitting fingers of a well-defined wavelength; then the fingertips pinch off to form compact motile structures translating at high speed. These colloidal creatures are self-sustained and form a stable state of the system. They are the result of spontaneous self-assembly driven by hydrodynamics. Combining experiments, large scale numerical simulations and continuum models, we will detail the mechanisms involved at each step and demonstrate that the whole process is primarily controlled by a geometric parameter: the height of the particles above the floor. Hydrodynamic interactions are predominant in the development of these colloidal creatures. Thanks to these hydrodynamic collective effects, microrollers offer a promising platform for particle transport, mixing and flow generation in confined environments.

Cessation and reversals of large-scale structures in square Rayleigh–Bénard cells

Andres Castillo-Castellanos (1,3), Anne Sergent (1,2), Bérengère Podvin (1), Maurice Rossi (3)
(1) LIMSI, CNRS, Université Paris-Saclay. (2) Sorbonne Université. (3) IJLRA Sorbonne Université

We consider direct numerical simulations of turbulent Rayleigh-Bénard convection inside two-dimensional square cells. Two types of flow regimes are observed intermittently: consecutive flow reversals (CR), and extended cessations (EC). For each regime, we combine proper orthogonal decomposition (POD) and statistical tools on long-term data to characterise the dynamics of large-scale structures. An additional simplification of the dynamics is proposed based on a K-means clustering of the POD phase-space. It reduces the problem to a network dynamics of finite number of clusters. This simplified analysis captures the main features of the CR and EC dynamics. Finally, we analyse within a range of Rayleigh numbers up to turbulent flow, the relation between dynamical regimes and the POD energetic contents as well as the residence time in each cluster.

Apprentissage automatique de lois de contrôle d'écoulement par intelligence artificielle.

Guy Y. Cornejo Maceda, Bernd R. Noack, François Lusseyran, Nan Deng, Luc Pastur, Marek Morzynski
LIMSI/CNRS - Université Paris-Sud TU Braunschweig TU Berlin HIT, Shenzen IMSIA-ENSTA University of Technology, Poznan

Le contrôle d'écoulement est au coeur de nombreux défis en ingénierie tel que la réduction de la trainée pour les véhicules de transport terrestre ou aérien, l'augmentation de la portance en aéronautique, l'amélioration du mélange pour les réactions chimiques pour ne citer que quelques exemples. Le contrôle des écoulements par rétroaction s'appuyant sur la connaissance de l'état du système, ouvre la possiblité de contrôle robuste pour ces applications (Brunton & Noack, 2015 Appl. Mech. Rev. 67, 050801). Ce projet vise à la mise en place d'une stratégie de contrôle générale, sans modèle et auto-adaptaptive pour stabiliser/contrôler les systèmes non-linéaires et la turbulence dans des applications concrètes, aussi nommée "machine learning control" (MLC) (Duriez et al. 2016 Springer). Parmi les différentes techniques d'intelligence artificiel, nous explorons la programmation génétique. Elle est inspirée de la biologie et mime le processus de selection naturelle Darwinien pour faire émerger empiriquement une loi de contrôle efficace. Cette approche est appliquée à un système de mécanique des fluides, le pinball fluidique, présentant une dynamique riche et permettant un contrôle MIMO. Remerciement au projet ASTRID-ANR-17- FLOwCON, Contrôle d'écoulements turbulents en boucle fermée par apprentissage automatique

Stability, singularity and bifurcations of triadic resonant stability curves : algebraic/transient growth and vertically shear horizontal flow

Kevin Ha, Jean- Marc Chomaz, Sabine Ortiz
École Polytechnique

Triadic resonant instability plays a major role in the understanding of dissipation processes related to internal gravity waves. In a geophysical context, gravito-inertial waves are responsible for the mixing of layers in stratified fluids such as the atmosphere or the ocean. We revisit some key results on the triadic resonant curves with a special highlight on singularities due to changes of stability properties. Among the identified bifurcations, the most remarkable corresponds to a physical reality involving the well-known vertically shear mode, hence introducing the concept of algebraic growth. The fascinating idea of a double singularity when transitioning to the stratified case without rotation is one of the main consequences of the theory of bifurcations we want to emphasize through this presentation.

Numerical simulation of passive scalar transport by an incompressible flow, with adaptive multiresolution techniques on dual grids

Marc-Arthur N'Guessan, Laurent Series, Marc Massot, Christian Tenaud
CMAP, École Polytechnique / LIMSI, CNRS, Université Paris-Saclay

Relying on a building block developed by the authors in order to resolve the incompressible Navier-Stokes equation with high order implicit time stepping and dynamic mesh adaptation based on multiresolution analysis with collocated variables, the present contribution investigates the ability to extend such a strategy for scalar transport at relatively large Schmidt numbers using a finer level of refinement compared to the resolution of the hydrodynamic variables, while preserving space adaptation with error control. This building block is a key part of a strategy to construct a low-Mach number code based on a splitting strategy for combustion applications, where several spatial scales are into play. The computational efficiency and accuracy of the proposed strategy is assessed on a well-chosen three-vortex simulation.

On the Modeling of the Magnetic Body Force for Thermomagnetic Convection

R. Zanella, F. Bouillault, X. Mininger, C. Nore, J-L Guermond
Paris Saclay

The goal of this paper is to show that several force expressions modeling the action of a magnetic field on a ferrofluid, including the Kelvin and Helmholtz forces, generate the same velocity and temperature fields. This result is established theoretically. The equivalence of the forces is then illustrated by using a finite element code for simulating a thermomagnetic convection problem. We finally demonstrate the benefit of the magnetic body force for heat transfer in ferrofluids by reporting numerical results on a transformer cooling.

Attracteur d’ondes d’inertie en régime linéaire et non-linéaire

Maxime Brunet (1), Thierry Dauxois (2), Pierre-Philippe Cortet (1)
(1) Laboratoire FAST, Université Paris-Sud (2) Laboratoire de Physique, ENS de Lyon

Les fluides soumis à une rotation d’ensemble sont le support d’une classe d’ondes, appelées ondes d’inertie, fruit de l’action de rappel de la force de Coriolis. Dans les domaines fermés, dont les parois ne sont pas systématiquement verticales ou horizontales, peuvent se développer des modes ondulatoires appelés attracteurs d’ondes dans lesquels toute l’énergie à une fréquence donnée tend à se concentrer sur un cycle limite. Ces attracteurs apparaissent en conséquence des lois anormales de réflexion des ondes d’inertie dont la relation de dispersion contraint la direction de propagation. Nous présentons une étude expérimentale des régimes linéaires et non-linéaires d’un attracteur d’ondes dans une cavité trapézoïdale en rotation. Nous mettons en évidence que l’attracteur est sujet à une instabilité par résonance triadique qui alimente en énergie des ondes sous-harmoniques. Ce mécanisme non-linéaire a pour conséquence de réduire l’amplitude de l’attracteur et de faire croître sa longueur d’onde en accord avec des résultats récents dans des simulations numériques et des expériences en fluide stratifié. En variant le taux de rotation ainsi que l’amplitude et la longueur d’ondes du forçage, nous avons identifié les lois d’échelles suivies par l’amplitude et la longueur d’onde de l’attracteur dans les régimes linéaire et non-linéaire. Nous avons montré que le régime non-linéaire de l’attracteur peut être décrit quantitativement en remplaçant dans le modèle linéaire, aujourd’hui bien établi, la viscosité du fluide par une viscosité turbulente, prenant en compte de manière effective la dissipation que constitue l’instabilité triadique pour l’attracteur. Ce dernier résultat pourrait notamment être utile pour extrapoler la théorie des attracteurs aux situations géo et astrophysiques où de forts effets non-linéaires sont évidemment attendus et où la présence d’attracteurs a déjà été montré numériquement.

Rhéologie des sédiments de cavités souterraines. Application au phénomène de vermiculation.

Perrine Freydier*, Jérôme Martin*, Béatrice Guerrier*, Pierre-Yves Jeannin**, Frédéric Doumenc***
* FAST, UMR7608, CNRS/Univ. Paris-Sud ** ISSKA *** FAST, UMR7608, CNRS/Univ. Paris-Sud, Sorbonne Université

Nous étudions expérimentalement la formation de vermiculations. Les vermiculations sont des agrégats de particules naturelles (argiles, minéraux, matière organique, calcite ..) se formant parfois à la surface des parois des grottes. Ces agrégats, qui ont l’aspect d’une pâte cohésive, forment des motifs qui peuvent atteindre plusieurs centimètres de long, pour une épaisseur généralement inférieure à 1mm. Dans cette étude, nous cherchons à déterminer les propriétés rhéologiques de ce matériau. Nous verrons que la valence des ions en contact avec le matériau joue un rôle majeur dans son comportement rhéologique.

Buckling of a rod penetrating into granular media

A. Seguin & P. Gondret
Laboratoire FAST

Nous étudions expérimentalement la possibilité de flambement d'une tige mince en pénétration vertical dans un empilement granulaire. Lorsque son extrémité inférieure atteint une certaine profondeur, la tige peut commencer à se déformer, à condition que l'étreinte ne soit pas suffisante pour empêcher ce phénomène. La profondeur critique atteinte par la tige au moment du flambement évolue en fonction de la longueur de la tige L, soit en 1/L ou en 1/L^2. Ces deux régimes résultent des deux termes de force qui entrent en jeu pendant la pénétration de la tige : une force de pression au fond de la tige qui augmente linéairement avec la profondeur et une force de friction sur le côté de la tige qui augmente quadratiquement avec la profondeur. Enfin, nous dessinons un diagramme de phase de flambage/non-flambage dans un espace de paramètres donné par le rapport d'aspect de la tige et un rapport de rigidité entre la tige et l'empilement granulaire.

Effect of fluid nonlinearities on the flutter instability

Johann Moulin and Olivier Marquet
ONERA-DAAA

A flexible wing immersed in a fluid flow may undergo large amplitude oscillations when the flow velocity is increased above some threshold value. This is the classical flutter instability. The critical velocity is well predicted with linear stability analysis, but becomes an irrelevant stability criterion when the nonlinearities at stake induce a subcritical bifurcation. Using weakly non-linear and harmonic balance methods, we study numerically the effect of fluid nonlinearities on the flutter instability of a purely linear solid model consisting in a rigid plate mounted on two springs. We will show that increasing the Reynolds number promotes subcritical bifurcations and large-amplitude limit-cycle oscillations.

Mélange et transport par des micro-nageurs

Mojtaba Jarrahi (LIMSI), Harold Auradou (FAST), Behnam Taidi (LGPM), Pedro ARANA AGUDELO (Paris Saclay)
LISMI, FAST, LGPM, Paris Saclay

Les micro-organismes vivent souvent dans un milieu aquatique et ceux qui sont nageurs, cherchent des nutriments grâce à leur motilité. Leur nage perturbe le milieu fluide. Dans cette étude expérimentale nous cherchons à caractériser la motilité d’une microalgue modèle, Chlamydomonas Reinhardtii, dans un milieu confiné et nous nous intéressons à la quantification et au contrôle du mélange engendré par celle-ci.

Solitons visqueux générés par le vent.

Marine Aulnette, Frédéric Moisy et Marc Rabaud.
Laboratoire FAST, UMR7608, CNRS, Université Paris-Sud

Lorsque le vent souffle à la surface d'un liquide, il est bien connu qu'il se forme, au-delà d'une vitesse seuil, une onde propagative quasi-monochromatique. Mais qu'advient-il lorsque le fluide est très visqueux, au point que ces ondes propagatives deviennent amorties de manière critique ? On constate expérimentalement que les ondes se déstabilisent, et l'énergie injectée par le vent se concentre alors dans des vagues isolées de grande amplitude. Ces "plis liquides", fortement non linéaires, conservent leur forme lors de leur propagation : nous les appelons solitons dissipatifs. Nous présentons ici une étude expérimentale de leur dynamique.

Weak formulation and scaling properties of energy fluxes in 3D numerical turbulent Rayleigh-Benard convection

Valentina Valori, Alessio Innocenti, Berengere Dubrulle, Sergio Chibbaro
Valentina Valori and Berengere Dubrulle: DRF/IRAMIS/SPEC, CNRS UMR 3680, CEA, Univ. Paris-Saclay, 91190 Gif sur Yvette, France. Sergio Chibbaro and Alessio Innocenti: Sorbonne Universite, CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France

Energy fluxes and their scalings were studied in an aspect ratio one cubical Rayleigh-Benard cell, in which a horizontal fluid layer is heated from below. Two different Rayleigh numbers were considered, Ra = 10^7 and Ra = 10^8, with Prandtl number equal to 1. Direct Numerical Simulations (DNS) were performed using the open-source code Basilisk (see http://www.basilisk.fr/). DNS data were analyzed using a local fluctuating form of the Karman-Howarth-Monin (KHM) equation, in the Boussinesq approximation [1], for a wide range of scales, from sub-Kolmogorov values, to the inertial range. Statistics of energy fluxes were computed by averaging over time and space on six horizontal slices, at mid height of the cell. Results showed the presence of Bolgiano scaling [2] for a small interval of scales in the inertial range. [1] Davide Faranda, Valerio Lembo, Manasa Iyer, Denis Kuzzay, Sergio Chibbaro, Francois Daviaud, and Berengere Dubrulle, Computation and characterization of local sub-filter-scale energy transfers in atmospheric flows. Journal of the Atmospheric Sciences, 2018. [2] Bolgiano, R. 1959. Turbulent spectra in a stably stratied atmosphere. J. Geophys. Res. 64 (12). 2226-2229.

Heat transport enhancement over a rough plate in turbulent Rayleigh-Bénard convection

Mebarek Belkadi (1), Anne Sergent (1,2), Bérengère Podvin (1)
(1) LIMSI, CNRS, Université Paris-Saclay, Orsay. (2) Sorbonne Université, Paris.

Direct numerical simulations of thermal convection over a regularly roughened plate are performed in a Rayleigh Bénard cell. The simulations are performed in a box-shaped cell of aspect ratio (depth over cell height) equal to 1/2 with water as working fluid. The Rayleigh number is ranged from 5x10^5 to 5x10^9 in order to bring three successive regimes out from a regime where roughness acts as an insulator to a regime where the heat transfer relative increase is larger than the relative surface increase induced by roughness addition. After validation against experimental and numerical data from literature, we investigate the different heat transport mechanisms at the roughness scale. Boundary layers and mean wind close to roughness elements are also examined.

Retraction d'un film d'eau sur une couche de glace

Christophe Josserand, Thomas Seon et Virgile Thievenaz
LadHyX, CNRS & Ecole Polytechnique Institut D'Alembert, Sorbonne Université

Lors de l'impact d'une goutte sur un substrat froid, on obtient une situation où un film liquide mince est au-dessus d'une couche de glace (mince également) en croissance. A partir d'expériences, nous allons discuter la dynamique de ce film d'eau, jusqu`à la formation des structures de glaces finales.

Frequency prediction from exact or self-consistent meanflows

Yacine Bengana & Laurette Tuckerman

The amplitude and nonlinear frequency are needed to fully characterize time periodic fluid flows. Linear stability about the stationary Navier-Stokes equation fails to predict the nonlinear frequency. A different approach is the linearization about the mean flow. This approach gives frequencies very close to that of the nonlinear system and shows in most cases a nearly zero growth rate. In the thermosolutal convection, the frequencies obtained by the linearization about the mean field of the standing waves do not match the nonlinear frequencies and the growth rate is far from zero, on the other hand for the traveling waves this property is fully satisfied. We studied the validity of a self-consistent model in the case of the traveling waves. The self-consistent model consists of the mean field governing equation coupled with the linearized Navier-Stokes equation through the most unstable mode and the Reynolds stress term. This model calculates the mean field, the nonlinear frequency, and the amplitude without time integration. The self-consistent model is assumed to be valid for flows that satisfy the property of the mean field. We have shown that in this case, this model predicts the nonlinear frequency only very close to the threshold. We have improved significantly the predictions by considering higher orders in the Reynolds stress term.

Cycles hétéroclines dans l'écoulement de Taylor-Couette contra-rotative

Yacine Bengana et Laurette Tuckerman
PMMH-CNRS-ESPCI-PSL-Sorbonne

Lorsque les deux cylindres concentriques de l'écoulement de Taylor-Couette tournent dans des sens opposées, des spirales remplacent les tourbillons classiques. En outre, une superposition de deux régimes spirales mène à un autre état nommé rubans. Dans ce régime, nous avons découvert deux cycles héteroclines, un axisymétrique et l'autre non-axisymétrique, qui coexistent et sont en concurrence.

Falling liquid film sheared by a counter-current gas flow: effect of confinement and onset of flooding

Yiqin Li, Sophie Mergui, Gianluca Lavalle, Nicolas Grenier, Georg Dietze
FAST, LIMSI, Université Paris Sud

We present an experimental study of a falling water film sheared by a counter-current air flow in an inclined rectangular channel. The effect of the gas flow on γ2 solitary waves is analyzed. In particular, we focus on the effect of the confinement, when the channel gap is reduced to 5mm from 19mm. In addition, the so-called flooding phenomenon, when at least part of the liquid is carried upstream as the gas flow rate reaches a critical level, is studied.

Perturbations minimales qui déclenchent la dynamo dans les écoulements cisaillés

Wietze Herreman
LIMSI, U-Psud

Des écoulements cisaillés ne sont jamais des dynamos cinématiques, mais l'ajout de petites perturbations de vitesse peut tout changer. Utilisant des méthodes d’optimisation variationnelle, on trouve les plus petites perturbations d'écoulement qui peuvent déclencher la dynamo. La dynamo optimale peut être modélisée par un modèle type champ moyen et cela permet d’identifier les mécanismes qui sont en jeu. On remarque quelques similitudes avec le processus auto-entretenu (SSP) de la transition sous-critique à la turbulence.

Some advances in the simulation of two-phase flow-regime transitions with NEPTUNE_CFD

Mathieu GUINGO, Nicolas MERIGOUX, Jerome LAVIEVILLE, Stéphane MIMOUNI
EDF – R&D, Fluid Mechanics, Energy and Environment Dpt.

This presentation will focus on the numerical model implemented in the “NEPTUNE_CFD” solver (the plug-in of Code_Saturne dedicated to multiphase flows), which aims at simulating two-phase flows with various flow regimes (from dispersed bubbly to stratified flows).