Philippe Gondret

Instabilities in the flow between co- and counter-rotating disks

The flow between two rotating disks (radius to heigh ratio of 20.9), enclosed by a rotating cylinder, is investigated experimentally in the cases of both co- and counter-rotation. This flow gives rise to a large gallery of instability patterns. A regime diagram of these patterns is presented in the ( Re b , Re t )-plane, where Re b,t is the Reynolds number associated with each disk. The co-rotation case and the weak counter-rotation case are very similar to the rotor–stator case, both for the basic flow and the instability patterns: the basic flow consists of two boundary layers near each disk and the instability patterns are the axisymmetric vortices and the positive spirals described in the rotor–stator experiments of Gauthier, Gondret & Rabaud (1999), Schouveiler, Le Gal & Chauve (2001), and the numerical study of Serre, Crespo del Arco & Bontoux (2001). The counter-rotation case with higher rotation ratio is more complex: above a given rotation ratio, the recirculation flow becomes organized into a two-cell structure with the appearance of a stagnation circle on the slower disk. A new kind of instability pattern is observed, called negative spirals. Measurements of the main characteristics of this pattern are presented, including growth times, critical modes and phase velocities.

Local rheological measurements in the granular flow around an intruder.

The rheological properties of granular matter within a two-dimensional flow around a moving disk is investigated experimentally. Using a combination of photoelastic and standard tessellation techniques, the strain and stress tensors are estimated at the grain scale in the time-averaged flow field around a large disk pulled at constant velocity in an assembly of smaller disks. On the one hand, one observes inhomogeneous shear rate and strongly localized shear stress and pressure fields. On the other hand, a significant dilation rate, which has the same magnitude as the shear strain rate, is reported. Significant deviations are observed with local rheology that justify the need of searching for a nonlocal rheology.

Clustering and flow around a sphere moving into a grain cloud

Abstract.A bidimensional simulation of a sphere moving at constant velocity into a cloud of smaller spherical grains far from any boundaries and without gravity is presented with a non-smooth contact dynamics method. A dense granular “cluster” zone builds progressively around the moving sphere until a stationary regime appears with a constant upstream cluster size. The key point is that the upstream cluster size increases with the initial solid fraction

Crater jet morphology

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Poster: Erosion of a granular bed by an oscillating foil

but the cluster packing fraction takes an about constant value independent of

Drag force in a cold or hot granular medium

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A Two Phase Numerical Model For The Water Injection Dredging (WID) Technology: An Unified Formulation For Continuum Mechanic

. Although the upstream cluster size around the moving sphere diverges when

Patterns between Two Rotating Disks

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Competitive dynamics of two erosion patterns around a cylinder

approaches a critical value, the drag force exerted by the grains on the sphere does not. The detailed analysis of the local strain rate and local stress fields made in the non-parallel granular flow inside the cluster allows us to extract the local invariants of the two tensors: dilation rate, shear rate, pressure and shear stress. Despite different spatial variations of these invariants, the local friction coefficient μ appears to depend only on the local inertial number I as well as the local solid fraction, which means that a local rheology does exist in the present non-parallel flow. The key point is that the spatial variations of I inside the cluster do not depend on the sphere velocity and explore only a small range around the value one.Graphical abstract

Dense flow around a sphere moving into a cloud of grains

We present a detailed analysis of the morphology of craters induced by a round gas jet impinging vertically onto horizontal non-cohesive granular bed. The virtual origin of the jet from a self-similar model is taken into account both in the size scaling of the craters and in the inertial Shields number that governs the erosive processes. Two intrinsic types of craters with different morphologies are found and characterized in detail from shallow parabolic craters (type I) to deep conical craters (type II) whereas a flat central part arises from a finite bed thickness and leads to truncated morphologies. The transitions between the different crater morphologies are also analyzed in detail. The local Shields number based on the local velocity at the evolving bed surface is shown to depend on the local crater shape at the impinging point of the jet.