Minisymposium: Interactions Fluides-Structures et problèmes d'interfaces
Lundi, 17 juin
Salle George V
Added Mass in a Bubbly Flow: Void fraction and Wall Influence
Béguin, Cédric, Étienne Pelletier and Stéphane Étienne
BWC / AECL / NSERC Chair of Fluid-Structure Interaction, Department of Mechanical Engineering, École Polytechnique de Montréal

Most of the added mass closure relations for two-phase modeling are numerically obtained from simulations involving single bubble or precise networks of bubbles. Their applicability to systems with high void fraction is therefore questionable. In this presentation, we will present a semi-analytical model using solid harmonics to resolve the potential flow around a cloud of bubbles and around a bubble in the vicinity of an infinite wall. We will show that our model proposes some relations for added mass with regards to the void fraction and wall proximity. We will also compare our model to previously published relations and unify some discrepancies between them.

Study of Self-Sustained Pitch-Heave Oscillations of an Elastically-Mounted Airfoil
Veilleux, Jean-Christophe and Guy Dumas
Laboratoire de Mécanique des Fluides Numérique, Département de génie mécanique, Université Laval

Airfoil flutter is the result of a net positive exchange of energy from the fluid to the structure. In the present study, a rigid symmetric airfoil is elastically maintained in an upstream flow and is totally free to pitch and heave independently. Over a wide range of stiffness and damping in both pitch and heave degrees of freedom, it is found that dynamic stall flutter occurs. It involves oscillations of various amplitudes and different phases between both motions with various levels of energy extraction from the flow. In addition to the structural characteristics of the airfoil support, the airfoil mass and moment of inertia as well as the pitching axis location provide enough adjustable parameters to control the airfoil’s dynamics and eventually optimize its application as a wind or hydro-kinetic turbine.

The present work focuses on a parametric study of an elastically mounted NACA0012 airfoil. It aims at providing physical insights onto the motion control available through key parameters of the setup. In this study, we use the open source CFD code OpenFOAM, which implements a finite-volume solver, to carry out unsteady Reynolds averaged Navier-Stokes (URANS) simulations. The proposed fluid-structure coupling strategy as well as some of the validation tests carried out with the present FSI solver will be presented together with the main results of this ongoing research.

Velocity-Pressure enrichments for the Taylor-Hood elements for solving moving interface two-phase flows
Fahsi, Adil and Azzeddine Soulaimani
École de technologie supérieure, Montréal, Canada

Multi-phase flows exist in nature and in technological systems. Numerical modeling of multi-phase flows faces several intrinsic difficulties, mainly due to the changes in the topology of the interface as it evolves with time, the jumps in fluid density and viscosity across the interface, and the multi-scales of time and space in the physical phenomena that may occur. Various numerical methods have been used to overcome these difficulties; for instance, interface-tracking and interface-capturing methods have been developed to describe the interface evolution. In standard finite element methods with level-set techniques, the approximation of the unknown interface is not always aligned with the grid. Standard polynomial finite element spaces have very poor approximation quality when used for discretization. For instance, in laminar flows with a high viscosity jump across the interface, the velocity profile has a kink that cannot be numerically captured if the interface is located inside the elements. With gravitational two-phase flows, it is the pressure that has a kink. Numerical discretization errors in the flow variables induce spurious currents that may be reduced by using very fine meshes. The eXtended Finite Element Method (XFEM) introduced initially by Belytschko and Black addresses these difficulties by potentially making the mesh independent of the interface geometry. In this talk, we address the issue of the choice of the enrichment functions for the velocity and for the pressure and investigate a solution algorithm. We consider flows dominated by gravity and by the jumps in the fluid properties (viscosity and density). We advocate the use of the Taylor-Hood element so that the impact of the enrichments can then be systematically investigated without any consideration of either the stabilization technique or the iterative solver. The velocity is either un-enriched or enriched by the modified-abs function ( P2-P1 Ridge function). The pressure is enriched by the modified-abs function, the discontinuous sign function or the discontinuous abs function. The latter function is proposed in this paper; it consists of the classical abs enrichment function in the cut elements and a zero-value in the blending elements. Therefore, it conserves the partition of unity property. Several numerical examples will be presented showing the stability and the accuracy of the enrichments.

Fluidelastic instability of tube array in two-phase cross-flow : a porous media approach
Tixier, Eliott, Cédric Béguin, Stéphane Étienne, Dominique Pelletier and Alexander Hay
École Polytechnique de Montréal

Heat exchangers are massive structures of tube bundles subject to cross-flow which induces potentially high amplitude vibrations. The most damaging mechanism is the fluidelastic instability (FEI). Beyond a critical velocity of the fluid, the fluidelastic forces have a destabilizing effect leading to the FEI.

The aim of this study is to simulate such an instability in an array of thousands of tubes. Direct solving of the Navier-Stokes equations is too costly for the current computational power. A more reasonable approach consists in averaging the fluid and solid equations on a control volume introducing a porosity function. The averaging process introduces new unknowns. As a consequence, new closure relations modeling the fluid-structure interactions need to be defined.