Numerical simulation of a compressible mixing layer past an axisymmetric trailing edge is carried out for a Reynolds number based on the diameter of the trailing edge approximately equal to 2.9 × 106. The free-stream Mach number at separation is equal to 2.46, which corresponds to experiments and leads to high levels of compressibility. The present work focuses on the evolution of the turbulence field through extra strain rates and on the unsteady features of the annular shear layer. Both time-averaged and instantaneous data are used to obtain further insight into the dynamics of the flow. An investigation of the time-averaged flow field reveals an important shear-layer growth rate in its initial stage and a strong anisotropy of the turbulent field. The convection velocity of the vortices is found to be somewhat higher than the estimated isentropic value. This corroborates findings on the domination of the supersonic mode in planar supersonic/subsonic mixing layers. The development of the shear layer leads to a rapid decrease of the anisotropy until the onset of streamline realignment with the axis. Due to the increase of the axisymmetric constraints, an adverse pressure gradient originates from the change in streamline curvature. This recompression is found to slow down the eddy convection. The foot shock pattern features several convected shocks emanating from the upper side of the vortices, which merge into a recompression shock in the free stream. Then, the flow accelerates and the compressibility levels quickly drop in the turbulent developing wake. Some evidence of the existence of large-scale structures in the near wake is found through the domination of the azimuthal mode m = 1 for a Strouhal number based on trailing-edge diameter equal to 0.26.

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The response of a granular bed to a punctual, vertically flowing water jet underneath it is studied experimentally, theoretically, and numerically. Experiments show that three regimes depending on the flow rate Q appear to outline the bed's behavior. For sufficiently small Q , the bed remains motionless and acts as a rigid porous medium [regime (i)]. It then becomes deformed when Q is sufficiently increased [regime (ii)]. Finally, the bed "explodes" and a locally fluidized bed limited to a domain above the water jet is observed as Q is increased further [regime (iii)]. This fluidization creates a "chimney" in the bed, roughly cylindrical in shape, inside which the grains are in motion. The flow motion in regime (i) is theoretically modeled as a Darcy flow inside an unbounded granular bed while a numerical model accounting for the boundaries is performed. Results from the theory and computations are compared to experimental data and the effects of the boundaries, the bed's thickness, and the size of the jet on the flow motion inside the bed are underlined. The onset for fluidization [regime (iii)] is explained by assuming a stick-slip behavior of the chimney. Despite the simplistic model, the comparison with experimental data show very good agreement for bony sand granules and relatively good agreement for spherical glass beads.

We report on experiments of drop impacting a hydrophobic micro-grid, of typical spacing a few tens of µm. Above a threshold in impact speed, liquid emerges to the other side, forming microdroplets of size about that of the grid holes. We propose a method to produce either a mono-disperse spray or a single tiny droplet of volume as small as a few picoliters corresponding to a volume division of the liquid drop by a factor of up to 10 5 . We also discuss the discrepancy of the measured thresholds with that predicted by a balance between inertia and capillarity. PACS numbers: 47.55.db; 47.56.+r For discrete microfluidics, it is often desired to produce smaller and smaller quantities of liquid in a controlled fashion. Usual methods are the generation of secondary droplets by drop impact [1,2], the breakup-up of shear-flow-mediated ligaments [3], the appliance of intense electric fields to conductive liquids [4,5] or a high-frequency sound wave generated by a piezoelectric at the outlet of a nozzle [6]. Here, we propose an alternative method: the impact of drops on a hydrophobic grid of micron-sized holes (diameter d). Figure 1 shows three sequences of such impacts: a few tens of µs after the drop impacted the grid, the liquid previously lying at the base of the drop is grated over and turned into small -quite monodisperse -droplets with different spatial distribution. We show that, despite the violent character of impact leading to complex flows, the emerging volume depends on the impact speed in a reproducible way. Understanding the basic mechanisms of how the liquid passes through, or is retained by, the grid has multiple applications in processes such as aerosols or filters. Generally, this simple geometry helps to understand how liquid is captured by surface tension forces, during its contact on a porous solid of more complex shape.Previous studies on the impact of drops onto holes were carried out by Lorenceau and Quéré [7]. They used single-hole sieve of size ranging from 100 µm to 1.7 mm, smaller than the capillary length l c = σ/ρg. The authors proposed that the threshold for protruding liquid results in a balance between initial liquid inertia and capillarity. Hence, the natural control parameter of the experiment is the Weber number: We = ρU 2 d/(2σ), built with the impact velocity U , the typical size of the hole d, the surface tension σ and density ρ of the liquid. Due to the lowviscosity liquid we used (water), the Reynolds number is between 10 and 200: retention forces opposing liquid entry are mostly due to capillarity [7]. However, we evidence that the impact on a network of holes leads to collective effects which contrasts from the single hole * Electronic address: philippe.brunet@univ-lille1.fr case. In short, the threshold for droplet detachment below the grid is much smaller than for a single hole. Also, the distribution of emerging droplets can show peculiar shapes, either single- (Fig. 1-(a)) or doublepeaked ( Fig. 1-(c)), suggesting a non-trivial pressure profile produced by the impact itse...