A CONSERVATIVE SAINT-VENANT TYPE MODEL TO DESCRIBE THE DYNAMICS OF THIN PARTIALLY WETTING FILMS WITH REGULARIZED FORCES AT THE CONTACT LINE

This paper deals with the numerical simulation of thin liquid films flowing on partially wetting solid substrates. A 2D Saint-Venant like model is proposed. Its originality lies in the conservative formulation of the capillary forces and in the model used for the disjoining pressure that accounts for the contact line capillary forces. A finite volume scheme is proposed for the resolution of the system and various numerical examples are presented and discussed. In particular, when the mesh resolution is fine enough, the model is proved to be able to predict correctly the spreading of a film with the exact contact angle in the vicinity of the contact line. When the mesh size is larger than the film thickness (which could be the case for many industrial applications), it is of course no longer possible to recover the contact angle. However, the model is proved to correctly predict the spreading of the film. This important feature is related to the thermodynamic consistency of the model in the sense that the latter ensures by construction the decrease of the film total free energy in the absence of external driving forces

Numerical simulation and modeling of ice shedding: Process initiation

In aeronautics, the issue of ice shedding prediction is of prime importance in the assessment of electro-thermal ice protection systems. In this paper, an ice shedding mechanism based on pressure redistribution in the water film formed at the ice/airfoil interface is proposed. This pressure distribution induces a stress concentration that leads to crack propagation in the ice. To determine whether this mechanism is relevant or not, two numerical experiments are performed. The results of these numerical experiments and the influence of a few material parameters are discussed, as well as their limitations and possible consequences arising from some of the hypotheses. The numerical modeling is based on recent works on damage/fracture mechanics which provide a general framework for fracture mechanics computation. The effects of numerical parameters and mesh size are discussed. A mixed mode test case based on experimental data is also performed. This test case had not been attempted before on this particular numerical method, which therefore serves as further validation

A conservative saint-venant type model to describe the dynamics of thin partially wetting films with regularized forces at the contact line

This paper deals with the numerical simulation of thin liquid films flowing on partially wetting solid substrates. A 2D Saint-Venant like model is proposed. Its originality lies in the conservative formulation of the capillary forces and in the model used for the disjoining pressure that accounts for the contact line capillary forces. A finite volume scheme is proposed for the resolution of the system and various numerical examples are presented and discussed. In particular, when the mesh resolution is fine enough, the model is proved to be able to predict correctly the spreading of a film with the exact contact angle in the vicinity of the contact line. When the mesh size is larger than the film thickness (which could be the case for many industrial applications), it is of course no longer possible to recover the contact angle. However, the model is proved to correctly predict the spreading of the film. This important feature is related to the thermodynamic consistency of the model in the sense that the latter ensures by construction the decrease of the film total free energy in the absence of external driving forces

A shallow water type model to describe the dynamic of thin partially wetting films

Liquid films moving onto a solid substrate are present in a lot of natural and industrial processes and have been the object of a lot of research studies for several decades. In the context of deicing, when a thermal protection system is activated, the supercooled water droplets impacting an aircraft surface don't freeze instantaneously and can coalesce and form a thin liquid film as a result of aerodynamic forces. Experimental studies show that this liquid film isn't always stable and can split into rivulets that may refreeze on unprotected surfaces. The modeling of rivulet flows and thus the accurate prediction of wet and dry surfaces is still an unsolved problem. The objective of this work is to model the motion and the instabilities of partially wetting thin liquid films to derive models for the formation of wet and dry surfaces. This has a direct influence on the estimation of the wall heat and mass fluxes such as evaporation or exchanges with the boundary layer. For thin films, capillary forces generally play an important role and could strongly influence both the motion of the contact line and the development of longitudinal (surface waves) and transversal instabilities (dewetting and rivulets formation). To predict such flows, shallow water models are generally preferred to the full Navier-Stokes equations. The derivation of such models is based on closure assumptions on the normal film velocity profile which can be justified either by asymptotic analysis or by empirical arguments. The main idea of the work consists in reformulating the shallow water equations by introducing a ""disjoining pressure"" to model the effects of a partial wetting. This new term appears like a regularization of the discontinuous forces at the contact line. Emphasis is put on the numerical treatment of the capillary forces, especially those acting in the vicinity of the contact line, since they can strongly influence the development of instabilities. Based on the work of Noble & Vila, we use an augmented conservative system that consists in reducing the order of the shallow water system by adding one evolution equation. This model is suited for numerical purposes since the surface tension term only involves second order derivatives instead of third order derivatives in the classical shallow water systems with two equations. A conservative formulation of the system and the associated energy are derived. One-dimensional numerical simulations using a first order implicit finite volume scheme have been performed. Droplet's stationnary shape, spreading length and time on an horizontal substrate is well recovered for all contact angle. Moreover, based on a linear stability analysis, unstable dewetting regimes of an infinite film of uniform thickness are identified and simulated. The add of a dynamic contact angle, the hysteresis effects and the 3D extension of the method are also in progress

An automatic building extraction method : Application to 3D-city modeling

In this report, we present an automatic building extraction method from Digital Elevation Models (DEMs). The DEMs are generated using an algorithm based on a maximum-flow formulation using three-view images. First, the building footprints are extracted from the DEMs through an automatic method based on marked point processes : they are represented by an association of rectangles. Then, these rectangular building footprints are regularized by improving both the connection of the neighboring rectangles and the facade discontinuity detection. We obtain structured footprints. These footprints are used for the 3D-city modeling by considering a parametric approach based on a skeleton process which allows to model the rooftops

Contribution à l'élaboration de modèles et de méthodes numériques pour la mécanique des fluides et les problèmes de givrage

The works presented here in order to obtain the “Habilitation à Diriger des Recherches” (HDR), are dedicated to the activities I have been carrying out at ONERA since 2009 as a research engineer. They reflect the two steps in my career at ONERA. First of all at the DAAA department in Châtillon where my topic was optimization and gradient computation by an adjoint method. It was also the opportunity for me to experience high order numerical methods like isogeometric analysis. Then, at the DMPE department in Toulouse where I have been focusing on icing activities, following the emergence of new certification rules for supercooled large droplets (SLD) or ice crystal icing for instance. In a context supported by French industry and European funding, I have been involved in many research subjects related to icing, such as complex wall impacts (SLD, ice crystals), thin liquid film runback and ice protection systems. My contribution consists in the coding of the 2D icing suite IGLOO2D and the derivation of models integrated in the code, notably through the supervision of interns and PhD students.Les travaux présentés résument les activités de Pierre Trontin à l'ONERA depuis 2009 comme ingénieur de recherche. Ils reflètent les deux étapes de sa carrière à l'ONERA. Tout d'abord au département DAAA de Châtillon où il a travaillé sur l'optimisation et le calcul de gradients par une méthode adjointe. Il a également mis en œuvre des méthodes numériques d'ordre élevé comme l'analyse isogéométrique. Puis, au département DMPE de Toulouse où il s’est concentré sur les activités liées au givrage, suite à l'émergence de nouvelles règles de certification pour la prise en compte de la présence de grosses gouttes en surfusion (SLD) ou de cristaux de glace dans l’atmosphère. Dans le cadre de cette thématique soutenue par l'industrie française et l’Europe, il a été impliqué dans de nombreux sujets de recherche, comme la modélisation des impacts sur une paroi pour les SLD et les cristaux de glace, la caractérisation du ruissellement de films minces sur une paroi et les systèmes de protection contre le givre. Ses contributions s’inscrivent dans le développement de la suite logicielle IGLOO2D dédiée au givrage dans laquelle les modèles et les méthodes numériques sont intégrés, notamment à travers la supervision de stagiaires et de doctorants

Développement d'une approche de type LES pour la simulation d'écoulements diphasiques avec interface. Application à l'atomisation primaire.

Whereas Large Eddy Simulation (L.E.S.) of single-phase flows is already widely used in the CFD world, even for industrial applications, L.E.S. of two-phase interfacial flows, i.e. two-phase flows where an interface separates liquid and gas phases, still remains a challenging task. The main issue is the development of subgrid scale models well suited for two-phase interfacial flows. The aim of this work is to generate a detailed D.N.S. database of incompressible two-phase interfacial flows in order to clearly understand interactions between small turbulent scales and the interface separating the two phases. The different subgrid scale terms derive from an a priori analysis of this D.N.S. database. To do this, different numerical techniques are firstly compared to find which methods are well adapted to deal with turbulent configurations where large interfacial deformations occur. Then, the interface/turbulence interaction is studied in the configuration where the interface is widely deformed and where both phases are resolved by D.N.S. The interaction between an initially plane interface and a freely decaying homogeneous isotropic turbulence (H.I.T.) is studied. The densities and viscosities are the same for both phases in order to focus on the effect of the surface tension coefficient. A parametric study based on the Weber number is performed. Finally, an a priori study is carried out where the different subgrid scale terms derive from the filtering of the D.N.S. database.Alors que la simulation aux grandes échelles (L.E.S.) des écoulements monophasiques est largement répandue même dans le monde industriel, ce n'est pas le cas pour la L.E.S. d'écoulements diphasiques avec interface (c'est-à-dire d'écoulements où les deux phases liquide et gazeuse sont séparées par une interface). La difficulté majeure réside dans le développement de modèles de sous-maille adaptés au caractère diphasique de l'écoulement. Le but de ce travail est de générer une base D.N.S. dans le cadre d'écoulements diphasiques turbulents avec interface pour comprendre les interactions entre les petites échelles turbulentes et l'interface. Les différents termes sous-maille proviendront d'une analyse a priori de cette base D.N.S. Pour mener à bien ce travail, différentes techniques numériques sont testées et comparées dans le cadre de configurations turbulentes où de grandes déformations interfaciales apparaissent. Puis, l'interaction interface/turbulence est étudiée dans le cadre où les deux phases, séparées par une interface largement déformée, sont résolues par une approche D.N.S. La configuration retenue est l'interaction entre une nappe initialement plane et une T.H.I. libre. Les rapports de densités et de viscosités sont fixés à 1 pour se concentrer sur l'effet du coefficient de tension de surface. Une étude paramétrique sur le nombre de Weber est menée. Finalement, un filtrage a priori de la base D.N.S. est réalisé et les termes sous-maille qui en découlent sont comparés les uns aux autres

Goal oriented mesh adaptation using total derivative of aerodynamic functions with respect to mesh coordinates

International audienceIn aeronautical CFD, engineers require accurate predictions of the forces and moments but they are less concerned with flow-field accuracy. Hence, the so-called "goal oriented" mesh adaptation strategies have been introduced to get satisfactory values of functional outputs at an acceptable cost, using local node displacement and insertion of new points rather than mesh refinement guided by uniform accuracy. Most often, such methods involve the adjoint vector of the functional of interest. Our purpose is precisely to present new goal oriented mesh adaptation strategies in the framework of finite-volume schemes and a discrete adjoint method. It is based on the total derivative of the goal with respect to (w.r.t.) mesh nodes. More precisely, a projection of the goal derivative, removing all components corresponding to geometrical changes in the solid walls or the support of the output, is used to adapt the meshes either by adding nodes or by displacing current mesh nodes. The methods are assessed in the case of 2D and 3D Euler flow computations

Goal oriented mesh adaptation using total derivative of aerodynamic functions with respect to mesh coordinates - With applications to Euler flows

International audienceIn aeronautical CFD, engineers require accurate predictions of the forces and moments but they are less concerned with the accuracy of the detailed flow-field. Hence, the so-called "goal oriented" mesh adaptation strategies have been introduced to get satisfactory values of functional outputs at an acceptable cost, using local node displacement and insertion of new points rather than mesh refinement guided by uniform accuracy. Most often, such methods involve the adjoint vector of the function of interest. Our purpose is precisely to present new goal oriented mesh adaptation strategies in the framework of finite-volume schemes and a discrete adjoint method. It is based on the total derivative of the goal with respect to (w.r.t.) mesh nodes. More precisely, a projection of the goal derivative, removing all components corresponding to geometrical changes in the solid walls or the support of the output, is used to adapt the meshes either by inserting new nodes or by displacing current mesh nodes. The methods are assessed in the case of 2D and 3D Euler flow computations