Condition de non-glissement | EPFL Graph Search

En mécanique des fluides, il est traditionnel de considérer que la vitesse tangentielle à une surface solide est nulle, autrement dit que le fluide ne glisse pas sur la surface solide. Cette hypothèse constitue la condition de non-glissement. Pour décrire l'écoulement d'un fluide dans une situation donnée, il est nécessaire de préciser les conditions aux limites de l'écoulement. Lorsque la région occupée par le fluide est bordée par une surface solide, le fluide ne peut la traverser. Sa vitesse est donc forcément nulle dans la direction perpendiculaire à la surface. En revanche, elle n'est pas forcément nulle dans les directions tangentielles. En toute rigueur, il y a toujours un glissement, mais il n'est appréciable qu'à des échelles spatiales microscopiques. Dans certains cas, le glissement est notable. Pour décrire quantitativement le glissement, on utilise souvent la longueur de glissement : il s'agit de la distance au-delà de la surface solide à laquelle la vitesse tangentiel

Transitional cylindrical swirling flow in presence of a flat free surface

Roland Bouffanais, David Lo Jacono

This article is devoted to the study of an incompressible viscous flow of a fluid partly enclosed in a cylindrical container with an open top Surface and driven by the constant rotation of the bottom wall. Such type of flows belongs to a group of recirculating lid-driven cavity flows with geometrical axisymmetry and of the prescribed boundary conditions of Dirichlet type-no-slip on the cavity walls. The top Surface of the cylindrical cavity is left open with an imposed stress-free boundary condition, while a no-slip condition with a prescribed rotational velocity is imposed on the bottom wall. The Reynolds regime corresponds to transitional flows with some incursions in the fully laminar regime. The approach taken here revealed new flow states that were investigated based on a fully three-dimensional Solution of the Navier-Stokes equations for the free-surface cylindrical swirling flow, without resorting to any symmetry property unlike all other results available in the literature, Theses solutions are obtained through direct numerical simulations based on a Legendre spectral element method. (C) 2009 Elsevier Ltd. All rights reserved.

2009

Large Eddy Simulation of Particle Dynamics Inside a Differentially Heated Cavity

Christoph Bosshard

In nuclear safety, most severe accident scenarios lead to the presence of fission products in aerosol form in the closed containment atmosphere. It is important to understand the particle depletion process to estimate the risk of a release of radioactivity to the environment should a containment break occur. As a model for the containment, we use the three-dimensional differentially heated cavity (DHC) problem. DHC is a cubical box with a hot wall and a cold wall on vertical opposite sides. On the other walls of the cube we have adiabatic boundary conditions. For the velocity field the no-slip boundary condition is valid. The flow of the air in the cavity is described by the Boussinesq equations. Complex flow patterns develop and the flow characteristics depend on the non-dimensional Rayleigh and Prandtl numbers. The predominant flow type in the DHC is a turbulent natural convection flow. This work aims at reaching Rayleigh numbers and turbulent levels as high as possible given the available computational resources. The method used to simulate the turbulent flow is the large eddy simulation (LES) where the dynamics of the large eddies is resolved by the computational grid and the small eddies are modelled by the introduction of subgrid scale quantities using a filter function. Numerically, the LES equations are discretized by the spectral element method. Particle trajectories are computed using the Lagrangian particle tracking method, including the relevant forces (drag, gravity, thermophoresis). Four different particle sets with each set containing one million particles and diameters of 10 μm, 15 μm, 25 μm and 35 μm are simulated. The complexity and the size of the large three-dimensional problem requires the use of massively parallel supercomputers. Spectral element methods are naturally suitable for parallelisation by distributing the elements among the processors. For the Lagrangian particle tracking we use a method where equal numbers of particles are assigned to every processor. The flow field is broadcast and every particle processor tracks the assigned particles, a procedure which leads to a perfect load balancing. Simulation results for the flow field and particle sizes from 15 μm to 35 μm at a Rayleigh number of 109 are compared to previous results from a direct numerical simulation. First order statistics of the LES flow fields are in very good agreement with the direct numerical simulation while the agreement of second order moments is fair. Also the turbulent structures associated to the maximum of turbulent kinetic energy production are correctly reproduced. Particle statistics in the LES and the direct numerical simulation were similar and the settling rates practically identical. Contrary to previous particle simulations in LES, it was found that no model was necessary for the influence of the unresolved flow scales on the particle motions. This can be explained, because the important settling mechanism is through gravity and particle deposition at the walls by turbophoresis is negligible.

EPFL2012

Large Eddy Simulation of Particle Dynamics Inside a Differentially Heated Cavity

Christoph Bosshard

EPFL2012