3 results
Large-eddy simulation of transition to turbulence in a boundary layer developing spatially over a flat plate
- FréDÉRic Ducros, Pierre Comte, Marcel Lesieur
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- Journal:
- Journal of Fluid Mechanics / Volume 326 / 10 November 1996
- Published online by Cambridge University Press:
- 26 April 2006, pp. 1-36
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It is well known that subgrid models such as Smagorinsky's cannot be used for the spatially growing simulation of the transition to turbulence of flat-plate boundary layers, unless large-amplitude perturbations are introduced at the upstream boundary: they are over-dissipative, and the flow simulated remains laminar. This is also the case for the structure-function model (SF) of Métais & Lesieur (1992). In the present paper we present a sequel to this model, the filtered-structure-function (FSF) model. It consists of removing the large-scale fluctuations of the field before computing its second-order structure function. Analytical arguments confirm the superiority of the FSF model over the SF model for large-eddy simulations of weakly unstable transitional flows. The FSF model is therefore used for the simulation of a quasi-incompressible (M∞ = 0.5) boundary layer developing spatially over an adiabatic flat plate, with a low level of upstream forcing. With the minimal resolution 650 × 32 × 20 grid points covering a range of streamwise Reynolds numbers Rex1 ε [3.4 × 105, 1.1 × 106], transition is obtained for 80 hours of time-processing on a CRAY 2 (whereas DNS of the whole transition takes about ten times longer). Statistics of the LES are found to be in acceptable agreement with experiments and empirical laws, in the laminar, transitional and turbulent parts of the domain. The dynamics of low-pressure and high-vorticity distributions is examined during transition, with particular emphasis on the neighbourhood of the critical layer (defined here as the height of the fluid travelling at a speed equal to the phase speed of the incoming Tollmien–Schlichting waves). Evidence is given that a subharmonic-type secondary instability grows, followed by a purely spanwise (i.e. time-independent) mode which yields peak-and-valley splitting and transition to turbulence. In the turbulent region, flow visualizations and local instantaneous profiles are provided. They confirm the presence of low- and high-speed streaks at the wall, weak hairpins stretched by the flow and bursting events. It is found that most of the vorticity is produced in the spanwise direction, at the wall, below the high-speed streaks. Isosurfaces of eddy viscosity confirm that the FSF model does not perturb transition much, and acts mostly in the vicinity of the hairpins.
The mixing layer and its coherence examined from the point of view of two-dimensional turbulence
- Marcel Lesieur, Chantal Staquet, Pascal Le Roy, Pierre Comte
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- Journal:
- Journal of Fluid Mechanics / Volume 192 / July 1988
- Published online by Cambridge University Press:
- 21 April 2006, pp. 511-534
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A two-dimensional numerical large-eddy simulation of a temporal mixing layer submitted to a white-noise perturbation is performed. It is shown that the first pairing of vortices having the same sign is responsible for the formation of a continuous spatial longitudinal energy spectrum of slope between k−4 and k−3. After two successive pairings this spectral range extends to more than 1 decade. The vorticity thickness, averaged over several calculations differing by the initial white-noise realization, is shown to grow linearly, and eventually saturates. This saturation is associated with the finite size of the computational domain.
We then examine the predictability of the mixing layer, considering the growth of decorrelation between pairs of flows differing slightly at the first roll-up. The inverse cascade of error through the kinetic energy spectrum is displayed. The error rate is shown to grow exponentially, and saturates together with the levelling-off of the vorticity thickness growth. Extrapolation of these results leads to the conclusion that, in an infinite domain, the two fields would become completely decorrelated. It turns out that the two-dimensional mixing layer is an example of flow that is unpredictable and possesses a broadband kinetic energy spectrum, though composed mainly of spatially coherent structures.
It is finally shown how this two-dimensional predictability analysis can be associated with the growth of a particular spanwise perturbation developing on a Kelvin-Helmholtz billow: this is done in the framework of a one-mode spectral truncation in the spanwise direction. Within this analogy, the loss of two-dimensional predictability would correspond to a return to three-dimensionality and a loss of coherence. We indicate also how a new coherent structure could then be recreated, using an eddy-viscosity assumption and the linear instability of the mean inflexional shear.
Large-eddy simulation of a compressible flow in a three-dimensional open cavity at high Reynolds number
- LIONEL LARCHEVÊQUE, PIERRE SAGAUT, THIÊN-HIÊP LÊ, PIERRE COMTE
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- Journal:
- Journal of Fluid Mechanics / Volume 516 / 10 October 2004
- Published online by Cambridge University Press:
- 24 September 2004, pp. 265-301
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Large-eddy simulations of a subsonic three-dimensional cavity flow with self-sustaining oscillations are carried out for a Reynolds number based on the length of the cavity equal to $7\,{\times}\,10^6$. Meticulous comparisons with available experimental data corresponding to the same configuration demonstrate a high level of accuracy. Special attention is paid to the mixing layer that develops over the cavity and two different zones are identified. The first one is dominated by Kelvin–Helmholtz instability, and the linear as well as quadratic energy transfers leading to the filling of velocity spectra are described. The Kelvin–Helmholtz instability also appears to be forced near the origin of the layer, and it is postulated that the small recirculation bubble located in this area is responsible for the forcing. Downstream of the first zone and up to the vicinity of the aft wall, the layer behaves very similarly to a free mixing layer by exhibiting a linear spreading. An influence of the recirculating flow inside the cavity upon the growth of the layer is nevertheless observed at downstream stations. Analysis of the pressure on the floor of the cavity reveals that the self-sustaining oscillation-related pressure modes (Rossiter modes) are independent of their spanwise location inside the cavity. On the contrary, Rossiter modes exhibit streamwise modulations and it is demonstrated that a very simple two-wave model is able to reproduce the spatial shape of the modes. Nonlinear interactions between Rossiter modes are encountered, as well as nonlinear interactions with low-frequency components. A joint time–frequency analysis shows a temporal modulation of the Rossiter mode levels at similar low frequencies, resulting in a special form of intermittency with competitive energy exchanges between modes.