Pierre Comte

Large-eddy simulation of a compressible flow in a three-dimensional open cavity at high Reynolds number

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

Large-eddy simulation of a compressible flow past a deep cavity

7\,{\times}\,10^6

The mixing layer and its coherence examined from the point of view of two-dimensional turbulence

. 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.

Filtered subgrid-scale models

Large-eddy simulations of the flow over a deep cavity are performed. The computations reproduce identically all the parameters of the experiment by Forestier and co-workers [J. Fluid Mech. (to be published)], including the high Reynolds number ReL=8.6×105. Spectra show an accurate prediction of the peak levels of the fundamental frequency and its first harmonics. Results are also analyzed both in terms of Reynolds and phase averages, the procedure used to compute phase averages being identical to the one used during the experiment. Agreement with the experimental data is found to be excellent. The expansion rate of the shear layer is accurately described, and the temporal physics of the flow, including the dynamics of the coherent structures, is fully recovered. By comparison with an auxiliary computation wherein the wind-tunnel upper wall is not taken into account, the cavity is found to oscillate in a flow-acoustic resonance mode. New values for the γ constant of Rossiter’s model are then proposed for a...

Large- and small-scale stirring of vorticity and a passive scalar in a 3-D temporal mixing layer

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.

Favre filtering and macro-temperature in large-eddy simulations of compressible turbulence

Filtered subgrid-scale models are derived, which are less sensitive to the low-frequency modes than their original counterparts. They are obtained thanks to the definition of a high-pass discrete test filter. After presenting the theoretical derivation of these models, some a posteriori tests on the incompressible channel flow case are presented.

From Two-Point Closures of Isotropic Turbulence to LES of Shear Flows

We investigate, with the aid of a three‐dimensional direct‐numerical simulation at high resolution, the origin and topology of the longitudinal vortex filaments which appear in the temporally growing mixing layer. The basic velocity field is a hyperbolic‐tangent profile U tanh(2y/δi), with a Reynolds number of Uδi/ν =100. The calculation uses pseudospectral methods, and is carried out at a resolution of 1283 grid points in a cubic box of size L containing four fundamental most‐amplified wavelengths (L=4λa). The initial velocity field is the basic velocity, upon which is superposed a three‐dimensional Gaussian perturbation of wide spectrum, peaking at ka=1/2πλa, with kinetic energy equal to 10−4U2, modulated by a Gaussian exp[−(y/δi)2] in the transverse direction. A passive‐scalar transport equation is solved as well, with the same initial profile as the basic velocity profile. Isosurfaces of the passive scalar and three vorticity components are visualized, permitting the 3‐D vortex structure of the flows ...

Generation of coherent structures in free shear layers

Abstract We show how Favre density-weighted filtering, used with a macro-temperature, simplifies considerably the formalism of large-eddy simulations in compressible turbulence. The method gives good results for a plane channel at Mach 0.3, and a transonic flow above a rectangular cavity. In both cases, the shedding of Λ -shaped coherent vortices is very well characterized thanks to positive iso-surfaces of Q , the velocity-gradient tensor second invariant.

Local optimization of the convergence rates of implicit time advancements for LES of complex flows

We first recall the EDQNM two-point closure approach of three-dimensional isotropic turbulence. It allows in particular prediction of the infrared kinetic-energy dynamics (with ak4 backscatter) and the associated time-decay law of kinetic-energy, useful in particular for one-point closure modelling. Afterwards, we show how the spectral eddy viscosity concept may be used for large-eddy simulations: we introduce the plateau-peak model and the spectral-dynamic models. They are applied to decaying isotropic turbulence, and allow recovery of the EDQNM infrared energy dynamics. Anew infrared k2 law for the pressure spectrum, predicted by the closure, is also well verified.Assuming that subgrid scales are not too far from isotropy, the spectral-dynamic model is applied to the channel flow at h+= 390, with statistics in very good agreement with DNS, while reducing considerably the computational time. We study with the aid of DNS and LES the case of the channel rotating about an axis of spanwise direction. The calculations allow to recover the universal linear behaviour of the mean velocity profile, with a local Rossby number equal to −1.We present also LES (using the Grenoble Filtered Structure-Function Model), of a turbulent boundary layer passing over a cavity. Finally, we make some remarks on the future of LES for industrial applications.

Direct and Large-Eddy Simulations of Transition of a Supersonic Boundary Layer

Direct numerical simulations are performed for the turbulent mixing layer and the turbulent plane wake. Coherent structures are qualitatively analyzed by means of graphic visualizations. In all cases, transition to turbulence is triggered by random noise superimposed onto a unidirectional basic flow. In the case of three-dimensional incompressible mixing layers, two regimes are found according to whether this noise is more two-dimensional or more three-dimensional. In the case of three-dimensional incompressible plane wakes, we first observe the formation of two staggered mixing-layers of opposite signs. Each of them features spanwise primary vortices connected together by streamwise secondary vortices. The interaction between the two layers then intensifies, until a Karman street forms. At this moment, closed vortex loops bridging primary vortices of unlike signs are observed. Two-dimensional compressible mixing-layer simulations verify that compressibility effects inhibit the spreading of mixing layers. Eddy-shocklets are found when the convective Mach number reaches 0.8. A two-dimensional simulation of a spatially-growing plane wake is also presented.