Sylvain Laizet

Short note: Straightforward high-order numerical dissipation via the viscous term for direct and large eddy simulation

In this short note, we show how to use a highly accurate finite-difference scheme to compute second derivatives in the Navier-Stokes equations while ensuring targeted numerical dissipation. This approach, essentially non conservative, is shown to be close to an upwind method and is straightforward to implement with a negligible computational extra cost. The benefit offered by the resulting discrete operator is illustrated for the direct computation of sound in aeroacoustics and in the more general context of large-eddy simulation through connections with hyperviscosity and spectral vanishing viscosity.

Direct numerical simulation of a mixing layer downstream a thick splitter plate

In this numerical study, the flow obtained behind a trailing edge separating two streams of different velocities is studied by means of direct numerical simulation. The main originality of this work is that the splitter plate itself is included in the computational domain using an immersed boundary method. The influence of the trailing-edge shape is considered through the analysis of the destabilizing mechanisms and their resulting effect on the spatial development of the flow. The streamwise evolution of the different flows is found to be very different for each of the configurations considered, both in terms of mean quantities and flow dynamics. Present results suggest that the wake component, which dominates the flow close to the trailing edge, is still influential further downstream, as already observed in pure wake flows but only conjectured in mixing layer. A detailed analysis of the vortex dynamics is proposed using instantaneous visualizations, statistical/stability analysis considerations, and pr...

MULTISCALE GENERATION OF TURBULENCE

This paper presents a brief but general introduction to the physics and engineering of fractals, followed by a brief introduction to fluid turbulence generated by multiscale flow actuation. Numerical computations of such turbulent flows are now beginning to be possible because of the immersed boundary method (IBM) and terascale parallel high performance computing capabilities. The first-ever direct numerical simulation (DNS) results of turbulence generated by fractal grids are detailed and compared with recent wind tunnel measurements.

Interscale energy transfer in decaying turbulence and vorticity–strain-rate dynamics in grid-generated turbulence

For decaying homogeneous turbulence, we present two assumptions about the energy spectrum and one on the dissipation rate coefficient Cϵ which, in a high inlet/initial Reynolds number limit, imply that a wide range of wavenumbers exists where the interscale energy flux is dependent on inlet/initial Reynolds number, is negative (kinetic energy is on average transferred from small to high wavenumbers) and is independent of wavenumber but not necessarily of viscosity. Our assumptions about the energy spectrum are not unusual, one concerns the finite nature of the energy and the other its time dependence, and our assumption about Cϵ is inspired by recent wind tunnel and water channel measurements of turbulence generated by fractal and regular grids. We then present a direct numerical simulation of fractal-generated turbulence where the second-order structure function in time exhibits a well-defined 2/3 power law over more than a decade at a position close to the grid where the local Reynolds number Reλ is only about 30 and where there is neither average production of enstrophy nor of strain rate. The Q–R and Qs–Rs diagrams do not have their usual appearance at this position but develop it gradually as the flow progresses downstream and the wide 2/3 power law of the second-order structure function is eroded. It is believed that this is the first time that the spatial development of Q, R, Qs and Rs statistics is obtained for a spatially developing turbulent flow.

The spatial origin of −5/3 spectra in grid-generated turbulence

A combined wind tunnel and computational study of grid-generated turbulence along the centreline shows that the close to −5/3 power law signature of energy spectra in the frequency domain originates relatively close to the grid not only where the velocity derivative statistics become quite suddenly isotropic but also where the turbulent fluctuating velocities are very intermittent and non-Gaussian. As the inlet flow velocity increases, these power laws are increasingly well defined and increasingly close to −5/3 over an increasing range of frequencies. However, this range continuously decreases with streamwise distance from the grid even though the local Reynolds number first increases and then decreases along the same streamwise extent. The intermittency at the point of origin of the close to −5/3 power spectra consists of alternations between intense vortex tube clusters with shallow broad-band spectra and quiescent regions where the velocity fluctuations are smooth with steep energy spectra.

Two- and three-dimensional Direct Numerical Simulation of particle-laden gravity currents

In this numerical study, we are interested in the prediction of a mono-disperse dilute suspension particle-laden flow in the typical lock-exchange configuration. The main originality of this work is that the deposition of particles is taken into account for high Reynolds numbers up to 10000, similar to the experimental ones. Unprecedented two- and three-dimensional Direct Numerical Simulations (DNS) are undertaken with the objective to investigate the main features of the flow such as the temporal evolution of the front location, the sedimentation rate, the resulting streamwise deposit profiles, the wall shear velocity as well as the complete energy budget calculated without any approximations for the first time. It is found that the Reynolds number can influence the development of the current front. Comparisons between the 2D and 3D simulations for various Reynolds numbers allow us to assess which quantities of interest for the geoscientist could be evaluated quickly with a 2D simulation. We find that a 2D simulation is not able to predict accurately the previously enumerated features obtained in a 3D simulation, with maybe the exception of the sedimentation rate for which a qualitative agreement can be found.

Vortex line density in counterflowing He II with laminar and turbulent normal fluid velocity profiles

Superfluid helium is an intimate mixture of a viscous normal fluid, with continuous vorticity, and an inviscid superfluid, where vorticity is constrained to thin, stable topological defects. One mechanism to generate turbulence in this system is through the application of a heat flux, so-called thermal counterflow. Of particular interest is how turbulence in the superfluid responds to both a laminar and turbulent normal fluid in the presence of walls. We model superfluid vortex lines as reconnecting space curves with fixed circulation, and consider both laminar (Poiseuille) and turbulent normal fluid flows in a channel configuration. Using high resolution numerical simulations we show that turbulence in the normal fluid sustains a notably higher vortex line density than a laminar flow with the same mean flow rate. We examine Vinens relation, L=γvns, between the steady state vortex line density L and the counterflow velocity vns. Our results support the hypothesis that transition to turbulence in the norm...

A DNS study of jet control with microjets using an immersed boundary method

In this work, a microjet arrangement to control a turbulent jet is studied by means of direct numerical simulation. A customised numerical strategy was developed to investigate the interactions between the microjets and the turbulent jet. This approach is based on an improved immersed boundary method in order to reproduce realistically the control device while being compatible with the accuracy and the parallel strategy of the in-house code Incompact3d. The 16 converging microjets, so-called fluidevrons, lead to an increase of the turbulent kinetic energy in the near-nozzle region through an excitation at small scale caused by the interaction between the fluidevrons and the main jet. As a consequence, very intense unstable ejections are produced from the centre of the jet toward its surrounding. Further downstream, the turbulent kinetic energy levels are lower with a lengthening of the potential core compared to a natural jet, in agreement with experimental results.

The interaction between strain-rate and rotation in shear flow turbulence from inertial range to dissipative length scales

Direct numerical simulation data from the self similar region of a planar mixing layer is filtered at four different length scales, from the Taylor microscale to the dissipative scales, and is used to examine the scale dependence of the strain-rotation interaction in shear flow turbulence. The interaction is examined by exploring the alignment between the extensive strain-rate eigenvector and the vorticity vector. Results show that the mechanism for enstrophy amplification (propensity of which increases when the two vectors are parallel) is scale dependent with the probability of the two vectors being parallel higher for larger length scales. However, the mechanism for enstrophy attenuation, i.e., the probability of the two vectors being perpendicular to each other, appears to be scale independent.

Numerical dissipation vs. subgrid-scale modelling for large eddy simulation

This study presents an alternative way to perform large eddy simulation based on a targeted numerical dissipation introduced by the discretization of the viscous term. It is shown that this regularisation technique is equivalent to the use of spectral vanishing viscosity. The flexibility of the method ensures high-order accuracy while controlling the level and spectral features of this purely numerical viscosity. A Pao-like spectral closure based on physical arguments is used to scale this numerical viscosity a priori. It is shown that this way of approaching large eddy simulation is more efficient and accurate than the use of the very popular Smagorinsky model in standard as well as in dynamic version. The main strength of being able to correctly calibrate numerical dissipation is the possibility to regularise the solution at the mesh scale. Thanks to this property, it is shown that the solution can be seen as numerically converged. Conversely, the two versions of the Smagorinsky model are found unable to ensure regularisation while showing a strong sensitivity to numerical errors. The originality of the present approach is that it can be viewed as implicit large eddy simulation, in the sense that the numerical error is the source of artificial dissipation, but also as explicit subgrid-scale modelling, because of the equivalence with spectral viscosity prescribed on a physical basis.