**Êtes-vous un étudiant de l'EPFL à la recherche d'un projet de semestre?**

Travaillez avec nous sur des projets en science des données et en visualisation, et déployez votre projet sous forme d'application sur GraphSearch.

Publication# A Numerical Model For The Simulation Of Shallow Laser Surface Melting

Alexandre Caboussat, Julien Hess, Alexandre Masserey, Marco Picasso

*INT CENTER NUMERICAL METHODS ENGINEERING, *2019

Article de conférence

Article de conférence

Résumé

We present a multi-physics model for the approximation of the coupled system formed by the temperature-dependent Navier-Stokes equations with free surfaces. The main application is the industrial process of shallow laser surface melting (SLSM), for laser polishing of metal surfaces. We consider incompressible flow equations with solidification, and we model the laser source through physically-consistent boundary conditions. We incorporate Marangoni effects in the surface tension model to drive internal motion in the liquid metal. The numerical method relies on an operator splitting strategy and a two-grid approach. A proof of concept of the numerical model is achieved through a static laser melting process.

Official source

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Concepts associés

Chargement

Publications associées

Chargement

Publications associées (4)

Chargement

Chargement

Chargement

Concepts associés (11)

Analyse numérique

L’analyse numérique est une discipline à l'interface des mathématiques et de l'informatique. Elle s’intéresse tant aux fondements qu’à la mise en pratique des méthodes permettant de résoudre, par des

Free surface

In physics, a free surface is the surface of a fluid that is subject to zero parallel shear stress,
such as the interface between two homogeneous fluids.
An example of two such homogeneous fluids wo

Équations de Navier-Stokes

thumb|Léonard de Vinci : écoulement dans une fontaine
En mécanique des fluides, les équations de Navier-Stokes sont des équations aux dérivées partielles non linéaires qui décrivent le mouvement des f

The research work reported in the present dissertation is aimed at the analysis of complex physical phenomena involving instabilities and nonlinearities occurring in fluids through state-of-the-art numerical modeling. Solutions of intricate fluid physics problems are devised in two particularly arduous situations: fluid domains with moving boundaries and the high-Reynolds-number regime dominated by nonlinear convective effects. Shear-driven flows of incompressible Newtonian fluids enclosed in cavities of varying geometries are thoroughly investigated in the two following frameworks: transition with a free surface and confined turbulence. The physical system we consider is made of an incompressible Newtonian fluid filling a bounded, or partially bounded cavity. A series of shear-driven flows are easily generated by setting in motion some part of the container boundary. These driven-cavity flows are not only technologically important, they are of great scientific interest because they display almost all physical fluid phenomena that can possibly occur in incompressible flows, and this in the simplest geometrical settings. Thus corner eddies, secondary flows, longitudinal vortices, complex three-dimensional patterns, chaotic particle motions, nonuniqueness, transition, and turbulence all occur naturally and can be studied in the same geometry. This facilitates the comparison of results from experiments, analysis, and computation over the whole range of Reynolds numbers. The flows under consideration are part of a larger class of confined flows driven by linear or angular momentum gradients. This dissertation reports a detailed study of a novel numerical method developed for the simulation of an unsteady free-surface flow in three-space-dimensions. This method relies on a moving-grid technique to solve the Navier-Stokes equations expressed in the arbitrary Lagrangian-Eulerian (ALE) kinematics and discretized by the spectral element method. A comprehensive analysis of the continuous and discretized formulations of the general problem in the ALE frame, with nonlinear, non-homogeneous and unsteady boundary conditions is presented. In this dissertation, we first consider in the internal turbulent flow of a fluid enclosed in a bounded cubical cavity driven by the constant translation of its lid. The solution of this flow relied on large-eddy simulations, which served to improve our physical understanding of this complex flow dynamics. Subsequently, a novel subgrid model based on approximate deconvolution methods coupled with a dynamic mixed scale model was devised. The large-eddy simulation of the lid-driven cubical cavity flow based on this novel subgrid model has shown improvements over traditional subgrid-viscosity type of models. Finally a new interpretation of approximate deconvolution models when used with implicit filtering as a way to approximate the projective grid filter was given. This led to the introduction of the grid filter models. Through the use of a newly-developed method of numerical simulation, in this dissertation we solve unsteady flows with a flat and moving free-surface in the transitional regime. These flows are the incompressible flow of a viscous fluid enclosed in a cylindrical container with an open top surface and driven by the steady rotation of the bottom wall. New flow states are investigated based on the fully three-dimensional solution of the Navier-Stokes equations for these free-surface cylindrical swirling flows, without resorting to any symmetry properties unlike all other results available in the literature. To our knowledge, this study delivers the most general available results for this free-surface problem due to its original mathematical treatment. This second part of the dissertation is a basic research task directed at increasing our understanding of the influence of the presence of a free surface on the intricate transitional flow dynamics of shear-driven flows.

We present a numerical model for the simulation of 3D mono-dispersed sediment dynamics in a Newtonian flow with free surfaces. The physical model is a macroscopic model for the transport of sediment based on a sediment concentration with a single momentum balance equation for the mixture (fluid and sediments).
The model proposed here couples the Navier-Stokes equations, with a
volume-of-fluid (VOF) approach for the tracking of the free surfaces between the liquid
and the air, plus a nonlinear advection equation for the sediments (for the transport, deposition, and resuspension of sediments).
The numerical algorithm relies on a splitting approach to decouple diffusion and advection phenomena such that we are left with a Stokes operator, an advection operator, and deposition/resuspension operators.
For the space discretization, a two-grid method couples a finite element discretization for the resolution of the Stokes problem, and a finer structured grid of small cells for the discretization of the advection operator and the sediment deposition/resuspension operator.
SLIC, redistribution, and decompression algorithms are used for post-processing to limit numerical diffusion and correct the numerical compression of the volume fraction of liquid.
The numerical model is validated through numerical experiments.
We validate and benchmark the model with deposition effects only for some specific experiments, in particular erosion experiments. Then, we validate and benchmark the model in which we introduce resuspension effects. After that, we discuss the limitations of the underlying physical models.
Finally, we consider a one-dimensional diffusion-convection equation and study an error indicator for the design of adaptive algorithms. First, we consider a finite element backward scheme, and then, a splitting scheme that separates the diffusion and the convection parts of the equation.

Mathematical and numerical aspects of free surface flows are investigated. On one hand, the mathematical analysis of some free surface flows is considered. A model problem in one space dimension is first investigated. The Burgers equation with diffusion has to be solved on a space interval with one free extremity. This extremity is unknown and moves in time. An ordinary differential equation for the position of the free extremity of the interval is added in order to close the mathematical problem. Local existence in time and uniqueness results are proved for the problem with given domain, then for the free surface problem. A priori and a posteriori error estimates are obtained for the semi-discretization in space. The stability and the convergence of an Eulerian time splitting scheme are investigated. The same methodology is then used to study free surface flows in two space dimensions. The incompressible unsteady Navier-Stokes equations with Neumann boundary conditions on the whole boundary are considered. The whole boundary is assumed to be the free surface. An additional equation is used to describe the moving domain. Local existence in time and uniqueness results are obtained. On the other hand, a model for free surface flows in two and three space dimensions is investigated. The liquid is assumed to be surrounded by a compressible gas. The incompressible unsteady Navier-Stokes equations are assumed to hold in the liquid region. A volume-of-fluid method is used to describe the motion of the liquid domain. The velocity in the gas is disregarded and the pressure is computed by the ideal gas law in each gas bubble trapped by the liquid. A numbering algorithm is presented to recognize the bubbles of gas. Gas pressure is applied as a normal force on the liquid-gas interface. Surface tension effects are also taken into account for the simulation of bubbles or droplets flows. A method for the computation of the curvature is presented. Convergence and accuracy of the approximation of the curvature are discussed. A time splitting scheme is used to decouple the various physical phenomena. Numerical simulations are made in the frame of mould filling to show that the influence of gas on the free surface cannot be neglected. Curvature-driven flows are also considered.