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DIRECT NUMERICAL SIMULATION OF IMPULSIVELY STARTED, AND UNIFORMELY ACCELERATED, PLATES USING ADAPTIVE WAVELET AND FOURIER METHODS WITH PENALISATION

Kai Schneider
Laboratoire de Modélisation et Simulation Numérique en Mécanique, CNRS et Universités d'Aix-Marseille & CMI, Université de Provence, 39 rue Frédéric Joliot-Curie, 13453 Marseille, France

Mickael Paget-Goy
Ecole Supérieure de Mécanique de Marseille IMT - Technopole de Chateau-Gombert; Laboratoire de Modelisation et Simulation Numerique en Mecanique du CNRS IMT - Technopole de Chateau-Gombert 38 rue F. Joliot-Curie, 13541 Marseille Cedex 20, France

Giulio Pellegrino
ICT, Universitat Karlsruhe (TH) Kaiserstr. 12, 76128 Karlsruhe, Germany; Laboratoire de Modélisation et Simulation Numérique en Méecanique du CNRS IMT - Technopole de Chateau-Gombert 38 rue F. Joliot-Curie, 13541 Marseille Cedex 20, France

Alberto Verga
Institut de Recherche sur les Phénomènes Hors Equilibre Technopôle de Château-Gombert 49 rue F. Joliot-Curie, 13384 Marseille Cedex 13, France

Marie Farge
LMD-IPSL-CNRS Ecole Normale Superieure 24 rue Lhomond, 75231 Paris Cedex 5, France

Resumo

We present high resolution direct numerical simulation of 2D viscous incompressible flows past a flat plate. We study the shear layer instability of a flow past, either an impulsively started plate, or an uniformely accelerated plate, for Reynolds number Re = 9500. The numerical schemes are based on adaptive wavelet and Fourier pseudospectral methods with volume penalisation to take into account the plate with no-slip boundary conditions. The geometry of the plate is simply described by a mask function. We have chosen one tip of the plate to be rectangular while the other is a wedge with an angle of 30° degrees or a circluar shape. On both tips we observe the formation of thin shear layers which are rolling up into spirals and form two primary vortices. The selfsimilar scaling of the spirals corresponds with theoretical predictions of Saffman for the inviscid case [12]. At later times these vortices are advected downstream and the free shear layers undergo a secondary instability. We show that their formation and subsequent dynamics is highly sensitive to the shape of the tips. The numerical results agree well with observations from laboratory experiments. Finally we also check the influence of a small riblet being added on the back of the plate on the flow evolution.