Lionel Le Penven

On the Approach to Isotropy of Homogeneous Turbulence: Effect of the Partition of Kinetic Energy Among the Velocity Components

It has long been admitted by folk wisdom rather than by analytical proof that in the absence of mean velocity gradients, homogeneous anisotropic turbulence evolves towards isotropy. The first experimental findings were due to UBEROI (19 57) for the velocity and vorticity components, and to MILLS and CORRSIN (19 59) for the velocity components, the temperature fluctuations and their associated skewness factors (signals and derivatives). Experimental confirmation was later given by COMTE-BELLOT and CORRSIN (19 66), TUCKER and REYNOLDS (1968), WARHAFT (1980), and GENCE and MATHIEU (1980) for velocity components. Numerical studies made in wave-number space supported also the same trend (SCHUMANN and PATTERSON, 1978).

Oscillatory jets and instabilities in a rotating cylinder

The viscous flow inside a closed rotating cylinder of gas subject to periodic axial compression is investigated numerically. The numerical method is based on a spectral Galerkin expansion of the velocity field, assuming axisymmetry of the flow. If the forcing amplitude is weak and the angular forcing frequency is less than twice the rotation rate, inertial waves emanate from the corners, forming conical oscillatory jets which undergo reflections at the walls. Their thickness is O(E1∕3), or O(E1∕4) for particular forcing frequencies, where E is the Ekman number. For larger forcing amplitudes, the conical pattern breaks down. When the forcing frequency is resonant with a low-order inertial mode, the flow can undergo two types of parametric instabilities: a mode-triad resonance, and a subharmonic instability. The combination of both these mechanisms provides a possible route to quasiperiodicity of the flow.

Compression of a turbulent vortex flow

Abstract Reynolds-averaged Navier–Stokes equations are used in conjunction with different turbulence models to simulate the evolution of a turbulent vortex flow submitted to a compression in a direction normal to its axis. A simplified configuration is considered idealizing important flow features observed in Internal Combustion engines (tumbling flows). Strong differences are observed between predictions of k – e and Reynolds stress models. Comparison to the experimental data obtained recently by Marc et al. (Marc, D., Boree, J., Bazile, R., Charnay, G., 1997. In: 11th Symposium on Turbulent Shear Flows. Grenoble, France; SAE paper 972834), indicates a better agreement for the latter. The possible existence of precession motion of the vortex core and a three-dimensional evolution for the mean flow are also discussed using direct numerical simulations of a simplified vortex (Taylor vortex).

Instability inside a rotating gas cylinder subject to axial periodic strain

We study numerically the instability of a confined rotating gas flow subject to periodic strain along the axis of rotation, under the low Mach number approximation. An axisymmetric time-stepping spectral Galerkin-type code is used to investigate the viscous basic flow and its stability. Parametric resonance can lead to instability of this flow via the growth of inertial modes coupled by the oscillating strain. The marginal stability curve compares well with earlier experimental and (asymptotic) analytical results in the case of the axisymmetric inertial mode (1,1,0). The resulting flow is dominated by a time-oscillating toroidal vortex and differs very little from the theoretical mode. Two different nonlinear regimes are found, one with saturation to a constant modal amplitude, the other with weak periodic modulation. We also show evidence of the presence of an azimuthal circulation, apparently responsible for the observed modulation.

In situ analysis and visualization of massively parallel computations

Massively parallel simulations generate increasing volumes of big data, whose exploitation requires increasingly large storage resources, efficient networking technologies and post-processing facilities. In the coming era of exascale supercomputing, there is an emerging need for new data analysis and visualization strategies. A promising solution consists of coupling analysis with simulation, so that both are performed simultaneously. This paper describes a client–server in situ analysis for massively parallel time-evolving computations. Its application to very large turbulent transition simulations using a spectral approximation is presented. It is shown to have a low impact on the computational time with a reasonable increase of resource usage, while enriching data exploration. Computational steering is performed with real-time adjustment of the simulation parameters, thereby getting closer to a numerical experiment process. This would not have been achieved with a classical work flow using off-line visualization.

On the Stability of Vortices in an Ideal Gas

Two distinct mechanisms of three-dimensional instability in compressible planar vortices in an ideal gas are presented. Both mechanisms have been obtained with the geometrical optics (WKB) stability theory which consists in studying the evolution of short-wavelength disturbances localized along the trajectories of the vortex. The first one corresponds to parametric resonances arising when a vortex is periodically compressed; the resulting instabilities are localized in the core of the vortex. On the contrary, in the second case, which corresponds to the generalization to compressible flows of the Rayleigh stability criterion for centrifugal instability, the growing perturbation surrounds the vortex at a given radius. In the latter case, the structure of the corresponding discrete eigenmodes may be described exactly, thus complementing and improving the WKB theory.

Stability of periodically compressed vortices at low Mach number

Stability analysis of circular and elliptical vortices periodically compressed axially in their plane reveals, at low Mach number, two distinct mechanisms of three-dimensional instability. The first one is a manifestation of the elliptical instability, modified by compression. The second one, which exists also in the circular case, is a resonance between the frequency of compression and the intrinsic rotation rate of the uncompressed vortex.

Destabilization of Inertial Waves in a Rotating Cylinder

This study is aimed at performing computations of a new hydrodynamic instability inside a closed rotating gas cylinder, one of whose ends is a piston undergoing small sinusoidal compression. The velocity field was calculated using a new Galerkin spectral approach, allowing a numerical treatment of the corner singularity. The algorithm was tested in several configurations already known in literature. Instability was observed for different values of the relevant dynamic parameters and the overall agreement with theoretical and experimental data is satisfactory.

Analysis of a turbulent compressed flow by a second-order model

This paper is concerned with the simulation of a turbulent flow submitted to a cyclic one-dimensional compression and expansion between two parallel flat pistons moving with opposite velocities in the direction of their perpendicular axis. The turbulence model used is the second-order model developed at a low Reynolds number by Craft and Launder. Numerical results show that the turbulent field may be considered as homogeneous in an extended part of the domain. The confinement effect appears mainly in the vicinity of the moving walls while the central region is especially influenced by the compression effect. The evolution of the heat flux, transferred from the fluid through the moving walls, tends to a zero limit cycle in the turbulent flow and to a non-zero limit cycle in the laminar flow. The disappearance of the turbulent energy is not predicted by the κ-e model

Numerical Simulation and Modelling of a Wall-bounded Compressed Turbulence

Direct numerical simulation is used to study the influence of a one-dimensional com-pression on a turbulent flow bounded by two parallel walls. Statistical analysis reveals that the linear (or rapid) part of the pressure-velocity correlation contributes significantly to transport turbulent energy in direction of the walls, and, thereby, increases the near¬wall dissipation. We derive a model for this energy flux based on an hypothesis of local homogeneity. This method is also applied to a wider class of strained and rotating flows.