The separating and reattaching flows and the wake of a finite rectangular plate are studied by means of direct numerical simulation data. The large amount of information provided by the numerical approach is exploited here to address the multi-scale features of the flow and to assess the self-sustaining mechanisms that form the basis of the main unsteadinesses of the flows. We first analyse the statistically dominant flow structures by means of three-dimensional spatial correlation functions. The developed flow is found to be statistically dominated by quasi-streamwise vortices and streamwise velocity streaks as a result of flow motions induced by hairpin-like structures. On the other hand, the reverse flow within the separated region is found to be characterized by spanwise vortices. We then study the spectral properties of the flow. Given the strongly inhomogeneous nature of the flow, the spectral analysis has been conducted along two selected streamtraces of the mean velocity field. This approach allows us to study the spectral evolution of the flow along its paths. Two well-separated characteristic scales are identified in the near-wall reverse flow and in the leading-edge shear layer. The first is recognized to represent trains of small-scale structures triggering the leading-edge shear layer, whereas the second is found to be related to a very large-scale phenomenon that embraces the entire flow field. A picture of the self-sustaining mechanisms of the flow is then derived. It is shown that very-large-scale fluctuations of the pressure field alternate between promoting and suppressing the reverse flow within the separation region. Driven by these large-scale dynamics, packages of small-scale motions trigger the leading-edge shear layers, which in turn created them, alternating in the top and bottom sides of the rectangular plate with a relatively long period of inversion, thus closing the self-sustaining cycle.
Direct numerical simulation data of the separating and reattaching flow around a blunt bluff body are used for the assessment of the combined role played by the numerical resolution and subgrid turbulence closure in large eddy simulation. The ability of the large-scale resolved field to capture the main flow features is first analyzed. The behavior of the intensity of the resolved fluctuations as a function of the filter lengths reveals a higher sensitivity of the resolved flow on a reduction of resolution in the streamwise direction rather than in the spanwise one. On the other hand, the analysis of the subgrid stresses shows the presence of two challenging phenomena, a reversal of flow of energy from the fluctuating to the mean field in the leading-edge shear layer and a backward energy transfer from small to large scale within the main recirculating bubble. These two phenomena challenge for subgrid closures that should be able to reproduce a flow of energy from the space of small unknown subgrid scales to drive the resolved mean and fluctuating motion. In particular, it is found that the formalism of subgrid viscosity models allows us to capture neither the negative turbulence production of the leading-edge shear layer nor the backward energy transfer within the main flow recirculation. On the other hand, the subgrid similarity models are able to capture both these two phenomena but, from a quantitative point of view, the intensity of the reproduced stresses is very weak. In conclusion, the need of subgrid closures based on a mixed modeling approach for the solution of the flow is envisaged.
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