Gilles Bouchet

Nonvertical ascension or fall of a free sphere in a Newtonian fluid

It is shown that the system represented by a free sphere ascending or falling in a Newtonian fluid under the action of gravity buoyancy undergoes a regular, symmetry breaking bifurcation making the trajectory deviate from the vertical direction. The instability threshold expressed in terms of the asymptotic Reynolds number lies below that of a fixed sphere wake. The instability is shown to saturate and reach a fixed point corresponding to a straight oblique ascension (fall).

Numerical simulation of the dynamics of freely falling discs

We present a comprehensive parametric study of the transition scenario of freely falling discs. The motion of the discs is investigated by a direct numerical simulation of the solid-fluid interaction. The discs are assumed to be homogeneous and infinitely thin. The problem is shown to depend on two independent parameters, the Galileo number expressing the ratio between effects of gravity and viscosity and the non-dimensionalized mass characterizing the inertia of the disc. The obtained results are in agreement with known experimental and numerical data and provide both detailed and comprehensive picture of the transition scenario in the two-parameter plane defined by the Galileo number and the non-dimensionalized mass.

The motion of solid spherical particles falling in a cellular flow field at low Stokes number

We present a jointed experimental and numerical study examining the influence of vortical structures on the settling of solid spherical particles under the action of gravity at low Stokes numbers. The two-dimensional model experiment uses electroconvection to generate a two-dimensional array of controlled vortices which mimics a simplified vortical flow. Particle image-velocimetry and tracking are used to examine the motion of the particles within this vortical flow. Particle motion is compared to the predictions of a numerical simulation inspired by the model equation developed by Maxey [“The motion of small spherical particles in a cellular flow field,” Phys. Fluids 30, 1915 (1987)].

Numerical investigation of the subcritical effects at the onset of three-dimensionality in the circular cylinder wake

The presented numerical simulations focus on the strong non-linear effects at the onset of three-dimensionality in the circular cylinder wake. The obtained numerical results shed light on the link between the linear theory and experimental observations. The latter are represented mainly by the Williamson’s Strouhal vs. Reynolds number experimental curve presenting a double discontinuity at the onset of three-dimensionality. In this paper, we show that the subcritical nature of the secondary bifurcation triggering the three-dimensionality considerably weakens the relevance of linear predictions. We first investigate the bi-stability interval of the subcritical bifurcation as a function of the spanwise periodicity of simulations. This allows us to define a non-linear marginal stability curve and to show that it predicts no preferred wavelength. The large spanwise scales and their effect on the simulated flow are then investigated in simulations with a spanwise periodicity of 31.4d and run for subcritical Re...

Unsteady behavior of a confined jet in a cavity at moderate Reynolds numbers

Self-sustained oscillations in the sinuous mode are observed when a jet impinges on a rigid surface. Confined jet instability is experimentally and numerically investigated here at moderate Reynolds numbers. When the Reynolds number is varied, the dynamic response of the jet is unusual in comparison with that of similar configurations (hole-tone, jet edge, etc). Modal transitions are clearly detected when the Reynolds number is varied. However, these transitions result in a reduction of the frequency, which means that the wavelength grows with Reynolds number. Moreover, the instability that sets in at low Reynolds number, as a subcritical Hopf bifurcation, disappears only 25% above the threshold. Then, the flow becomes steady again and symmetric. This atypical behavior is compared with our previous study on a submerged fountain (Bouchet et al 2002 Europhys. Lett. 59 826).

Transitional Dynamics of Freely Falling Discs

The transitional regimes of freely falling discs are investigated by direct numerical simulation of the fluid-solid interaction. The discs are assumed to be homogeneous and infinitely thin. The regimes depend on two independent parameters, the Galileo number expressing the ratio between effects of gravity and viscosity and the non-dimensionalized mass characterizing the inertia of the disc. The paper completes a recently published comprehensive parametric study in this two-parameter space by providing details on several most relevant transitional states. The dynamics of the trajectories and the effect of variable body inertia are illustrated.

Influence of Instabilities on the Trajectory of a Light Sphere

Recent numerical simulations of the wake of a fixed sphere have confirmed that hydrodynamic forces are likely to have a significant impact on the trajectory of a freely falling (or ascending) sphere. An ideally spherical body ceases to follow a straight vertical trajectory at the Reynolds number (based on its velocity U and diameter d) corresponding to the onset of the primary instability responsible for the breaking of axisymmetry in a fixed sphere wake, i.e. at Re = 212. This instability has been shown to generate a steady non axisymmetric flow with a symmetry plane containing the asymptotic flow velocity, the orientation of which is arbitrary, i.e. selected by any small perturbation at the instability onset. In this communication, we present further work focussed on the experimental investigation of the effect of instabilities on the trajectory of a free sphere. The axisymmetry breaking results in a lift and torque, the vector of lift lying in the symmetry plane and the torque being normal to this plane. This leads to the conclusion that a free-falling (ascending) sphere will be deviated from its vertical trajectory as soon as its Reynolds number reaches the threshold of 212. Moreover, the trajectory will be deflected in an arbitrarily selected vertical plane. An experimental setup has been implemented to investigate this effect. It consists of a 2.5 m high water tank with a .5 times .5 m cross section placed in an air-conditioned chamber allowing to control finely the asymptotic Reynolds number of small spheres (on the order of a mm in diameter) by varying the water temperature. Spheres of densities close to that of water, both lighter and heavier, are considered. The trajectories are investigated fully in three dimensions by processing of images of two cameras following the sphere movement. The preliminary results, presented here for polypropylene spheres lighter than water, confirm the numerically and theoretically predicted effect. After a short acceleration phase roughly in vertical direction the primary instability deflects the trajectories each time in a different vertical plane. The investigation of the fixed sphere wake showed the onset of a secondary Hopf-type instability at Re ≈ 275. The same type of instability develops clearly for free spheres. Unlike for the fixed sphere, the secondary instability is observed to dominate and to yield a wavy trajectory with a vertical mean direction.Copyright