A pressure impulse theory for hemispherical liquid impact problems

Liquid impact problems for hemispherical fluid domain are considered. By using the concept of pressure impulse we show that the solution of the flow induced by the impact is reduced to the derivation of Laplace's equation in spherical coordinates with Dirichlet and Neumann boundary conditions. The structure of the flow at the impact moment is deduced from the spherical harmonics representation of the solution. In particular we show that the slip velocity has a logarithmic singularity at the contact line. The theoretical predictions are in very good agreement both qualitatively and quantitatively with the first time step of a numerical simulation with a Navier-Stokes solver named Gerris.Comment: 11 pages, 14 figures, Accepted for publication in European Journal of Mechanics - B/Fluid

Impact de goutte sur une surface solide

In this thesis we consider the problem of drop impact onto a solid surface. In order to study this phenomenon we consider a more general framework by using analogies with some other impact problems which are a priori very different. In the first part of the thesis we propose to revisit the inertia-dominated drop impact problem for short times at the light of the dual problem defined by the impact of a solid object onto a liquid bath. We deduce from this analogy a model based on potential flow theory. Then asymptotic analysis is used to determine the essential mechanisms of the problem at leading order. This approach reveal a self-similar structure both for the velocity field and the pressure field induced by the impact. The structure of the boundary layer is also studied. Theoretical predictions deduced from this model are compared with numerical solutions obtained with the Navier-Stokes multiphase flow solver Gerris. Then we study the impact for intermediates times which correspond to the period of the breakdown of the self-similar solution. The origin of the transition is determined by using new numerical experiments. In a third part we propose to study a particular case of long time evolution by revisiting the problem of drop impact onto a solid target matching its own size. We obtain analytical solutions for pressure and velocity fields at initial time by using pressure impulse theory and we propose few research directions for the study of the evolution of the liquid sheet induced by the impact. This thesis ends with a brief introduction to drop impact of Bingham fluids.Dans cette thèse nous nous intéressons au problème de l’impact d’une goutte sur une surface solide. Nous proposons pour cela de nous placer dans un cadre plus général en utilisant les analogies existantes avec d’autres problèmes d’impact. Dans la première partie de ce manuscrit nous proposons de revisiter le problème de l’impact de goutte pour les temps courts à la lumière de son problème dual à savoir l’impact d’un objet solide dans un bain liquide lorsque l’inertie est l’effet dominant. De cette analogie est déduit un modèle reposant sur la théorie des écoulements potentiels. L’analyse asymptotique nous permet de dégager à l’ordre dominant les mécanismes essentiels de ce problème puis nous mettons en évidence la structure autosimilaire des champs de pression et de vitesse induits par l’impact. La structure de la couche limite est également étudiée. Les prédictions théoriques issues de ce modèle sont comparées à des solutions numériques obtenues à l’aide d’un solveur des équations de Navier-Stokes. Nous étudions ensuite les temps intermédiaires de l’impact, correspondants au moment où la solution autosimilaire cesse d’être valide et nous déterminons les causes de cette transition. Dans la troisième partie nous étudions un cas particulier d’évolution aux temps longs en revisitant le problème de l’impact d’une goutte sur un disque de même taille. Nous obtenons les solutions analytiques pour les champs de pression et de vitesse à l’instant initial et nous proposons ensuite différentes directions de recherche pour l’étude de l’évolution de la nappe liquide induite par l’impact. Nous finissons ce manuscrit par une brève introduction aux impacts de goutte de fluides à seuil

EUREC⁴A

The science guiding the EUREC⁴A campaign and its measurements is presented. EUREC⁴A comprised roughly 5 weeks of measurements in the downstream winter trades of the North Atlantic – eastward and southeastward of Barbados. Through its ability to characterize processes operating across a wide range of scales, EUREC⁴A marked a turning point in our ability to observationally study factors influencing clouds in the trades, how they will respond to warming, and their link to other components of the earth system, such as upper-ocean processes or the life cycle of particulate matter. This characterization was made possible by thousands (2500) of sondes distributed to measure circulations on meso- (200 km) and larger (500 km) scales, roughly 400 h of flight time by four heavily instrumented research aircraft; four global-class research vessels; an advanced ground-based cloud observatory; scores of autonomous observing platforms operating in the upper ocean (nearly 10 000 profiles), lower atmosphere (continuous profiling), and along the air–sea interface; a network of water stable isotopologue measurements; targeted tasking of satellite remote sensing; and modeling with a new generation of weather and climate models. In addition to providing an outline of the novel measurements and their composition into a unified and coordinated campaign, the six distinct scientific facets that EUREC⁴A explored – from North Brazil Current rings to turbulence-induced clustering of cloud droplets and its influence on warm-rain formation – are presented along with an overview of EUREC⁴A's outreach activities, environmental impact, and guidelines for scientific practice. Track data for all platforms are standardized and accessible at https://doi.org/10.25326/165 (Stevens, 2021), and a film documenting the campaign is provided as a video supplement

EUREC⁴A

The science guiding the EUREC⁴A campaign and its measurements is presented. EUREC⁴A comprised roughly 5 weeks of measurements in the downstream winter trades of the North Atlantic – eastward and southeastward of Barbados. Through its ability to characterize processes operating across a wide range of scales, EUREC⁴A marked a turning point in our ability to observationally study factors influencing clouds in the trades, how they will respond to warming, and their link to other components of the earth system, such as upper-ocean processes or the life cycle of particulate matter. This characterization was made possible by thousands (2500) of sondes distributed to measure circulations on meso- (200 km) and larger (500 km) scales, roughly 400 h of flight time by four heavily instrumented research aircraft; four global-class research vessels; an advanced ground-based cloud observatory; scores of autonomous observing platforms operating in the upper ocean (nearly 10 000 profiles), lower atmosphere (continuous profiling), and along the air–sea interface; a network of water stable isotopologue measurements; targeted tasking of satellite remote sensing; and modeling with a new generation of weather and climate models. In addition to providing an outline of the novel measurements and their composition into a unified and coordinated campaign, the six distinct scientific facets that EUREC⁴A explored – from North Brazil Current rings to turbulence-induced clustering of cloud droplets and its influence on warm-rain formation – are presented along with an overview of EUREC⁴A's outreach activities, environmental impact, and guidelines for scientific practice. Track data for all platforms are standardized and accessible at https://doi.org/10.25326/165 (Stevens, 2021), and a film documenting the campaign is provided as a video supplement

Drop impact on a solid surface

Dans cette thèse nous nous intéressons au problème de l’impact d’une goutte sur une surface solide. Nous proposons pour cela de nous placer dans un cadre plus général en utilisant les analogies existantes avec d’autres problèmes d’impact. Dans la première partie de ce manuscrit nous proposons de revisiter le problème de l’impact de goutte pour les temps courts à la lumière de son problème dual à savoir l’impact d’un objet solide dans un bain liquide lorsque l’inertie est l’effet dominant. De cette analogie est déduit un modèle reposant sur la théorie des écoulements potentiels. L’analyse asymptotique nous permet de dégager à l’ordre dominant les mécanismes essentiels de ce problème puis nous mettons en évidence la structure autosimilaire des champs de pression et de vitesse induits par l’impact. La structure de la couche limite est également étudiée. Les prédictions théoriques issues de ce modèle sont comparées à des solutions numériques obtenues à l’aide d’un solveur des équations de Navier-Stokes. Nous étudions ensuite les temps intermédiaires de l’impact, correspondants au moment où la solution autosimilaire cesse d’être valide et nous déterminons les causes de cette transition. Dans la troisième partie nous étudions un cas particulier d’évolution aux temps longs en revisitant le problème de l’impact d’une goutte sur un disque de même taille. Nous obtenons les solutions analytiques pour les champs de pression et de vitesse à l’instant initial et nous proposons ensuite différentes directions de recherche pour l’étude de l’évolution de la nappe liquide induite par l’impact. Nous finissons ce manuscrit par une brève introduction aux impacts de goutte de fluides à seuil.In this thesis we consider the problem of drop impact onto a solid surface. In order to study this phenomenon we consider a more general framework by using analogies with some other impact problems which are a priori very different. In the first part of the thesis we propose to revisit the inertia-dominated drop impact problem for short times at the light of the dual problem defined by the impact of a solid object onto a liquid bath. We deduce from this analogy a model based on potential flow theory. Then asymptotic analysis is used to determine the essential mechanisms of the problem at leading order. This approach reveal a self-similar structure both for the velocity field and the pressure field induced by the impact. The structure of the boundary layer is also studied. Theoretical predictions deduced from this model are compared with numerical solutions obtained with the Navier-Stokes multiphase flow solver Gerris. Then we study the impact for intermediates times which correspond to the period of the breakdown of the self-similar solution. The origin of the transition is determined by using new numerical experiments. In a third part we propose to study a particular case of long time evolution by revisiting the problem of drop impact onto a solid target matching its own size. We obtain analytical solutions for pressure and velocity fields at initial time by using pressure impulse theory and we propose few research directions for the study of the evolution of the liquid sheet induced by the impact. This thesis ends with a brief introduction to drop impact of Bingham fluids

Solutal convection instability caused by dissolution

When a soluble solid body is suddenly put in contact with water, a convection flow can be generated. Once the fluid layer charged into solute is sufficiently dense, this layer becomes unstable under the action of the buoyancy forces. We perform here a linear stability analysis in order to predict the time of appearance of the convection flow, the onset time, and the associated wavelength. As the base state evolves with time due to the solute diffusion, the usual theoretical methods cannot be used. We show that the criterion of marginal instability with a “frozen base state” used for convection in porous media fails for providing the onset parameters in fluid convection. Here, using a modified criterion, i.e. the instability growth rate must be larger than the time evolution of the base state, we find the onset parameters in satisfying agreement with the previous experimental and numerical works. Our results complete our previous numerical work [J. Philippi et al. “Solutal convection induced by dissolution,” Phys. Rev. Fluids 4, 103801 (2019)] in order to determine the conditions for generating a convective flow under the action of dissolution.SCOPUS: ar.jDecretOANoAutActifinfo:eu-repo/semantics/publishe

Drop impact on a solid surface : short-time self-similarity

International audienceThe early stages of drop impact onto a solid surface are considered. Detailed numerical simulations and detailed asymptotic analysis of the process reveal a self-similar structure both for the velocity field and the pressure field. The latter is shown to exhibit a maximum not near the impact point, but rather at the contact line. The motion of the contact line is furthermore shown to exhibit a 'tank treading' motion. These observations are apprehended with the help of a variant of Wagner theory for liquid impact. This framework offers a simple analogy where the fluid motion within the impacting drop may be viewed as the flow induced by a flat rising expanding disk. The theoretical predictions are found to be in very close agreement both qualitatively and quantitatively with the numerical observations for about three decades in time. Interestingly the inviscid self-similar impact pressure and velocities are shown to depend solely on the self-similar variables (r/ √ t, z/ √ t). The structure of the boundary layer developing along the wet substrate is investigated as well. It is found to be in first approximation analogous to the boundary layer growing in the trail of a shockwave. Interestingly, the corresponding boundary layer structure only depends on the impact self-similar variables. This allows to construct a seamless uniform analytical approximation encompassing both impact and viscous effects. The depiction of the different dynamical fields enables to quantitatively predict observables of interest, such as the evolution of the integral viscous shearing force and of the net normal force

Solutal convection induced by dissolution

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Coalescence de bulles dans des fluides visqueux et génération de bulles satellites

International audienceDans le but d'assurer un brassage mécanique et d'accroître les transferts thermiques des dispositifs de bullage fonctionnant à débit constant sont introduits dans les fours d'élaboration des verres. Ces dispositifs créent des bulles de tailles centimètres qui montent sous forme de train de bulles. A faible débit, les bulles ainsi créées montent de façon régulière et sans grande interaction. Avec l'augmentation du débit, les bulles commencent à interagir provoquant des coalescences. Dès lors que des phénomènes de coalescence sont observés, un envahissement de petites bulles dans le volume du liquide est observé. Il est donc important de connaître les conditions d'apparition de ces bulles et d'en comprendre l'origine. Au delà des intérêts industriels, les mécanismes provoquant l'apparition de bulles lors de la coalescence de deux bulles de grandes tailles restent des questions ouvertes en mécanique des fluides

Linear stability analysis of nonisothermal glass fiber drawing

The draw resonance effect appears in fiber drawing processes when the draw ratio, defined as the ratio between the take-up and the inlet velocities, exceeds a critical value. In many cases, inertia, gravity, and surface tension cannot be neglected, and a model combining all these effects is necessary in order to correctly describe the physics of the phenomenon. Additionally, it is also known that cooling can have a highly stabilizing effect on the draw resonance instability. However, a detailed analysis encompassing the effect of inertia, gravity, surface tension, and temperature is still lacking. Due to a destabilizing effect induced by geometry in the heat equation, we first show that the maximum critical draw ratio for fiber drawing can be two orders of magnitude lower than the one for the film casting problem when the heat transfer coefficient is assumed constant. By introducing a scaling making the fiber aspect ratio an independent parameter, we next show that the high value of the critical draw ratio encountered in industrial applications could be rationalized only if we consider that the heat transfer coefficient is not constant but depends on both the velocity and the cross-section area of the fiber. Within this framework, we show how the practical stability window is affected by the five control parameters: the draw ratio, the fiber aspect ratio, the inlet temperature, the convective heat transfer coefficient, and the stiffness of the non-homogeneous ambient temperature. We finally discuss the influence of radiative heat transfer on the stability.SCOPUS: ar.jinfo:eu-repo/semantics/publishe