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SUMMARYThis work describes a projection method for approximating incompressible viscous ows of nonuniform density. It is shown that unconditional stability in time is possible provided two projections are performed per time step. A ÿnite element implementation and a ÿnite volume one are described and compared. The performance of the two methods are tested on a Rayleigh-Taylor instability. We show that the considered problem has no inviscid smooth limit; hence conÿrming a conjecture by Birkho stating that the inviscid problem is not well-posed. Furthermore, we show that at even moderate Reynolds numbers, this problem is extremely sensitive to mesh reÿnement and to the numerical method adopted.

In this paper we propose a method to reconstruct the flow at a given time over a region of space using partial instantaneous measurements and full-space proper orthogonal decomposition (POD) statistical information. The procedure is tested for the flow past an open cavity. 3D and 2D POD analysis are used to characterize the physics of the flow. We show that the full 3D flow can be estimated from a 2D section at an instant in time provided that some 3D statistical information—i.e., the largest POD modes of the flow— is made available.

The flow induced by a disk rotating at the bottom of a cylindrical tank is characterised using numerical techniques – computation of steady solutions or time-averaged two-dimensional and three-dimensional direct simulations – as well as laser-Doppler velocimetry measurements. Axisymmetric steady solutions reveal the structure of the toroidal flow located at the periphery of the central solid body rotation region. When viewed in a meridional plane, this flow cell is found to be bordered by four layers, two at the solid boundaries, one at the free surface and one located at the edge of the central region, which possesses a sinuous shape. The cell intensity and geometry are determined for several fluid-layer aspect ratios; the flow is shown to depend very weakly on Froude number (associated with surface deformation) or on Reynolds number if sufficiently large. The paper then focuses on the high Reynolds number regime for which the flow has become unsteady and three-dimensional while the surface is still almost flat. Direct numerical simulations show that the averaged flow shares many similarities with the above steady axisymmetric solutions. Experimental measurements corroborate most of the numerical results and also allow for the spatio-temporal characterisation of the fluctuations, in particular the azimuthal structure and frequency spectrum. Mean azimuthal velocity profiles obtained in this transitional regime are eventually compared to existing theoretical models.

DARU-On wall pressure fluctuations and their coupling with vortex dynamicsin a separate d-reattache d turbulent flow over a blunt flat plate

This paper reports results obtained with two-dimensional numerical simulations of viscous incompressible flow in a symmetric channel with a sudden expansion and contraction, creating two facing cavities; a so-called double cavity. Based on time series recorded at discrete probe points inside the double cavity, different flow regimes are identified when the Reynolds number and the intercavity distance are varied. The transition from steady to chaotic flow behaviour can in general be summarized as follows: steady (fixed) point, period-1 limit cycle, intermediate regime (including quasi-periodicity) and torus breakdown leading to toroidal chaos. The analysis of the intracavity vorticity reveals a ‘carousel’ pattern, creating a feedback mechanism, that influences the shear-layer oscillations and makes it possible to identify in which regime the flow resides. A relation was found between the ratio of the shear-layer frequency peaks and the number of small intracavity structures observed in the flow field of a given regime. The properties of each regime are determined by the interplay of three characteristic time scales: the turnover time of the large intracavity vortex, the lifetime of the small intracavity vortex structures and the period of the dominant shear-layer oscillations.

We applied to an open flow a proper orthogonal decomposition (POD) technique, on two-dimensional (2D) snapshots of the instantaneous velocity field, to reveal the spatial coherent structures responsible for the self-sustained oscillations observed in the spectral distribution of time series. We applied the technique to 2D planes out of three-dimensional (3D) direct numerical simulations on an open cavity flow. The process can easily be implemented on usual personal computers, and might bring deep insights regarding the relation between spatial events and temporal signature in (both numerical or experimental) open flows.