Optimal transient growth and very large-scale structures in turbulent boundary layers

International audienceThe optimal energy growth of perturbations sustained by a zero pressure gradient turbulent boundary is computed using the eddy viscosity associated with the turbulent mean flow. it is found that even if all the considered turbulent mean profiles are linearly stable, they support transient energy growths. The most amplified perturbations are streamwise uniform and correspond to streamwise streaks originated by streamwise vortices. For sufficiently large Reynolds numbers two distinct peaks of the optimal growth exist, respectively scaling in inner and outer units. The optimal structures associated with the peak scaling in inner units correspond well with the most probable streaks and vortices observed in the buffer layer, and their moderate energy growth is independent of the Reynolds number. The energy growth associated with the peak scaling in outer units is larger than that of the inner peak and scales linearly with an effective turbulent Reynolds number Formed with the maximum eddy viscosity and a modified Rotta Clauser length based on the momentum thickness. The corresponding optimal perturbations consist of very large scale structures with a spanwise wavelength of the order of 8 delta. The associated optimal streaks scale in outer variables in the outer region and in wall units in the inner region of the boundary layer, in which they are proportional to the mean flow velocity, These outer streaks protrude far into the near wall region, having still 50% of their maximum amplitude at y(1) = 20. The amplification of very large scale structures appears to be a robust feature of the turbulent boundary layer: optimal perturbations with spanwise wavelengths ranging from 4 delta to 15 delta can all reach 80% of the overall optimal peak growth

Sensitivity of 2-D turbulent flow past a D-shaped cylinder using global stability

International audienceWe use adjoint-based gradients to analyze the sensitivity of turbulent wake past a D-shaped cylinder at Re = 13000. We assess the ability of a much smaller control cylinder in altering the shedding frequency, as predicted by the eigenfrequency of the most unstable global mode to the mean flow. This allows performing beforehand identification of the sensitive regions, i.e., without computing the actually controlled states. Our results obtained in the frame of 2-D, unsteady Reynolds-averaged Navier-Stokes compare favorably with experimental data reported by Parezanović and Cadot [J. Fluid Mech.693, 115 (2012)] and suggest that the control cylinder acts primarily through a local modification of the mean flow profiles

Stries optimales et réduction des instationnarités dans un sillage tridimensionnel

On calcule la distribution optimale azimutale périodique d'aspiration et de soufflage radiaux à la paroi latérale d'un corps épais axisymétrique à culot droit qui maximise la croissance d'énergie dans le sillage en utilisant la méthode utilisée récemment par Del Guercio, Cossu & Pujals (J. Fluid Mech. 2014) qui s'affranchit de la nécessité d'un code adjoint. L'aspiration et le soufflage optimaux entraînent la formation de tourbillons quasi-longitudinaux qui induisent l'amplification de stries longitudinales dans le sillage par effet lift-up (à l'exception du mode m=0 qui amplifie les perturbations axisymétriques). On remarque que la forme azimutale de la distribution optimale est très similaire pour tous les modes m > 1 considérés. Lorsqu'elles sont forcées à amplitude finie, les stries longitudinales ont un effet stabilisant sur le lâcher tourbillonnaire instationnaire dans le sillage, à l'exception du mode m=1 qui est déstabilisant. On montre que les modes m > 1, forcés avec un flux de masse nul, peuvent considérablement réduire l'amplitude de la force de portance instationnaire exercée sur le corps. Lorsqu'elles sont associées avec un soufflage au culot de faible amplitude, ces perturbations peuvent complètement supprimer l'instationnarité du sillage

A note on optimal transient growth in turbulent channel flows

International audienceWe compute the optimal transient growth of perturbations sustained by a turbulent channel flow following the same approach recently used by del Álamo and Jiménez [J. Fluid Mech.559, 205 (2006)]. Contrary to this previous analysis, we use generalized Orr-Sommerfeld and Squire operators consistent with previous investigations of mean flows with variable viscosity. The optimal perturbations are streamwise vortices evolving into streamwise streaks. In accordance with del Álamo and Jiménez, it is found that for very elongated structures and for sufficiently large Reynolds numbers, the optimal energy growth presents a primary peak in the spanwise wavelength, scaling in outer units, and a secondary peak scaling in inner units and corresponding to λ+z≈100. Contrary to the previous results, however, it is found that the maximum energy growth associated with the primary peak increases with the Reynolds number. This growth, in a first approximation, scales linearly with an effective Reynolds number based on the centerline velocity, the channel half width and the maximum eddyviscosity associated. The optimal streaks associated with the primary peak have an optimal spacing of λz=4h and scale in outer units in the outer region and in wall units in the near wall region, where they still have up to 50% of their maximum amplitude near y+=10. © 2009 American Institute of Physics

A note on optimal transient growth in turbulent channel flows

A measuring principle for qualitative and quantitative analyses of three-dimensional unsteady flows is presented. The principle is based on colour coding of the flow volume under consideration. Coloured light sheets are generated and used to illuminate the flow volume. Consecutive light sheets of different colours are scanned over the volume within a small interval of time. Thus, the volume is sliced and colour-coded quasi-instantaneously. With this technique, the 3D position of a particle in the volume can be identified by a 2D image and an associated colour. Since most optical flow measuring systems are based on tracers, colour coding allows the application of 2D image recorders to register 3D flow information. The paper discusses the state-of-the-art of this principle for three-dimensional flow analyses and gives information about applicability and limitations

Perturbations optimales dans les écoulements de paroi turbulents et application au contrôle de décollement

PALAISEAU-Polytechnique (914772301) / SudocSudocFranceF

Forcing large-scale coherent streaks in a zero-pressure-gradient turbulent boundary layer

International audienceLarge-scale coherent streaks are artificially forced in a well-developed turbulent boundary layer at [image omitted] using an array of cylindrical roughness elements. Measures of the velocity field with particle image velocimetry reveal the presence of well-reproducible, streamwise-oriented, steady coherent streaks. We show that the amplitude of these coherent streaks transiently grows in space. The position of the maximum amplitude is proportional to the spanwise wavelength of the streaks and the most amplified spanwise wavelength is of very large scale z approximate to 60. These results are in good agreement with the recent predictions based on the optimal transient growth analysis of turbulent mean flows