Le modèle des peaux entropiques en turbulence développée

A geometry called entropic skins has been recently proposed to describe and interpret the phenomenon of intermittency in fully developed turbulence. It is shown that the entropic skins model represents the geometrical counterpart of the She–Lévêque's model but with a different interpretation for the main parameters. The comparison with the multifractal approach shows that this is a new geometrical framework of intermittency.     

Instabilité non linéaire dans un milieu en expansionNonlinear instability in a expanding medium

We consider nonlinear acoustical phenomena, explosive instabilities and a formation of localized structures in nonstationary environment. An example of such a medium is our Universe in expansion considered as a fluid submissive to a gravitational self-concorded force field and governed by the classical hydrodynamics equations. We show that the taking into account of the nonlinear effects allow us to understand the causes of the appearance of the specific nonlinear instability, which is calling explosive instability. This type of instability is more fast, $～\ln [{(t_0?t)}^{\mathrm{?1}}]$ for density fluctuation, that the habitual instability (exponential, $～{\mathrm{e}}^{\gamma t}$): at the end of a finite time, all spatial inhomogeneity of the initials conditions lead to a formation of singularities in the fields. This phenomena will be appear if certains conditions for the initials amplitudes and wavelengths of the fluctuations are observed. To cite this article: F. Henon, V. Pavlov, C. R. Mecanique 334 (2006).     

A stability condition for turbulence model： From EMMS model to EMMS-based turbulence model

The closure problem of turbulence is still a challenging issue in turbulence modeling. In this work, a stability condition is used to close turbulence. Specifically, we regard single-phase flow as a mixture of turbulent and non-turbulent fluids, separating the structure of turbulence. Subsequently, according to the picture of the turbulent eddy cascade, the energy contained in turbulent flow is decomposed into different parts and then quantified. A turbulence stability condition, similar to the principle of the energy-minimization multi-scale （EMMS） model for gas-solid systems, is formulated to close the dynamic constraint equa- tions of turbulence, allowing the inhomogeneous structural parameters of turbulence to be optimized. We name this model as the ＂EMMS-based turbulence model＂, and use it to construct the corresponding turbulent viscosity coefficient. To validate the EMMS-based turbulence model, it is used to simulate two classical benchmark problems, lid-driven cavity flow and turbulent flow with forced convection in an empty room, The numerical results show that the EMMS-hased turbulence model improves the accuracy of turbulence modeling due to it considers the principle of compromise in competition between viscosity and inertia.     

Déformation cumulée tensorielle dans le référentiel en rotation logarithmiqueCumulated tensorial strain measure in the logarithmic rotating frame.

The time integration of strain rate tensor $\stackrel{?}{\mathit{D}}$ is a central problem in large transformations even if it is often an underlying one. The cumulated tensorial strains, obtained by the time integration of strain rate tensor $\stackrel{?}{\mathit{D}}$, allow the tackling of this problem from a geometrical point of view, and independently of material behaviour considerations. The time integration here takes place in the local objective frame defined by the logarithmic spin proposed by Lehmann et al. and Xiao et al. The numerical results obtained in a closed deformation path are presented here. The advantages and drawbacks of this novel integration for the development of behaviour laws are described. To cite this article: V. Mora et al., C. R. Mecanique 332 (2004).     

Active control of multiscale features in wall-bounded turbulence

This study experimentally investigates the impact of a single piezoelectric(PZT)actuator on a turbulent boundary layer from a statistical viewpoint.The working conditions of the actuator include a range of frequencies and amplitudes.The streamwise velocity signals in the turbulent boundary layer flow are measured downstream of the actuator using a hot-wire anemometer.The mean velocity profiles and other basic parameters are reported.Spectra results obtained by discrete wavelet decomposition indicate that the PZT vibration primarily influences the near-wall region.The turbulent intensities at different scales suggest that the actuator redistributes the near-wall turbulent energy.The skewness and flatness distributions show that the actuator effectively alters the sweep events and reduces intermittency at smaller scales.Moreover,under the impact of the PZT actuator,the symmetry of vibration scales’velocity signals is promoted and the structural composition appears in an orderly manner.Probability distribution function results indicate that perturbation causes the fluctuations in vibration scales and smaller scales with high intensity and low intermittency.Based on the flatness factor,the bursting process is also detected.The vibrations reduce the relative intensities of the burst events,indicating that the streamwise vortices in the buffer layer experience direct interference due to the PZT control.     

Vortex dynamics of turbulence–coherent structure interaction

We study the interaction between a coherent structure (CS) and imposed external turbulence by employing direct numerical simulations (DNS) designed for unbounded flows with compact vorticity distribution. Flow evolution comprises (i) the reorganization of turbulence into finer-scale spiral filaments, (ii) the growth of wave-like perturbations within the vortex core, and (iii) the eventual arrest of production, leading to the decay of ambient turbulence. The filaments, preferentially aligned in the azimuthal direction, undergo two types of interactions: parallel filaments pair to form higher-circulation “threads”, and anti-parallel threads form dipoles that self-advect radially outwards. The consequent radial transport of angular momentum manifests as an overshoot of the mean circulation profile—a theoretically known consequence of faster-than-viscous vortex decay. It is found that while the resulting centrifugal instability can enhance turbulence production, vortex decay is arrested by the dampening of the instability due to the “turbulent mixing” caused by instability-generated threads. Ensemble-averaged turbulence statistics show strong fluctuations within the core; these are triggered by the external turbulence, and grow even as the turbulence decays. This surprising growth on a normal-mode-stable vortex results from algebraic amplification through “linear transient growth”. Transient growth is examined by initializing DNS with the “optimal” modes obtained from linear analysis. The simulations show that the growth of transient modes reproduces the prominent dynamics of CS-turbulence interaction: formation of thread-dipoles, growth of core fluctuations, and appearance of bending waves on the column’s core. At the larger Reynolds numbers prevailing in practical flows, transient growth may enable accelerated vortex decay through vortex column breakdown.     

Modélisation et simulation numérique du changement de phase liquide–vapeur en cavitéModeling and numerical simulation of liquid–vapor phase change in an enclosed cavity

A model for the simulation of boiling flow with phase change in a closed cavity is presented. A front-tracking method is used to deal with the liquid–vapor interface. The liquid phase is incompressible while the vapor phase is weakly compressible and obeys to the perfect gas law. This model can deal with large density ratio (${\rho }_l/{\rho }_v?1000$) flows while accounting for the saturation curve. Computations are performed on a 1D validation case, idealizing a pressure cooker. Results are compared with a low Mach number approximation. To cite this article: V. Daru et al., C. R. Mecanique 334 (2006).     

“Equilibrium”and“non-equilibrium”turbulence

We review the concept of ‘‘equilibrium' in turbulence. It generally means a property of the energy spectrum, it can also be understood in terms of a scalar property, the Taylor–Kolmogorov formula relating the dissipation rate to the total energy and integral length scale. The implications of equilibrium and strong departure from equilibrium for turbulence modeling are stressed.     

Vorticity dynamics after the shock–turbulence interaction

The interaction of a shock wave with quasi-vortical isotropic turbulence (IT) represents a basic problem for studying some of the phenomena associated with high speed flows, such as hypersonic flight, supersonic combustion and Inertial Confinement Fusion (ICF). In general, in practical applications, the shock width is much smaller than the turbulence scales and the upstream turbulent Mach number is modest. In this case, recent high resolution shock-resolved Direct Numerical Simulations (DNS) (Ryu and Livescu, J Fluid Mech 756:R1, 2014) show that the interaction can be described by the Linear Interaction Approximation (LIA). Using LIA to alleviate the need to resolve the shock, DNS post-shock data can be generated at much higher Reynolds numbers than previously possible. Here, such results with Taylor Reynolds number approximately 180 are used to investigate the changes in the vortical structure as a function of the shock Mach number, \(M_{s}\), up to \(M_{s}=10\). It is shown that, as \(M_{s}\) increases, the shock interaction induces a tendency towards a local axisymmetric state perpendicular to the shock front, which has a profound influence on the vortex-stretching mechanism and divergence of the Lamb vector and, ultimately, on the flow evolution away from the shock.     

On the instantaneous formation of cavitation in hydrodynamic lubricationSur la formation instantanée de la cavitation en lubrification hydrodynamique

We consider the Elrod–Adams model extending the classical lubrication Reynolds equation to the case of the possible presence of a cavitation region. We show that the behaviour of the pressure and saturation depends crucially on the behaviour of the separation $h(t,x,y)$ among the two surfaces. In particular, we exhibit some simple formulations for which we prove (rigorously) that a cavitation region is formed instantaneously (even for initially saturated flows). Some numerical experiences are also given. To cite this article: J.I. Díaz, S. Martin, C. R. Mecanique 334 (2006).     

Preface: symposium on turbulence structures and aerodynamic heat/force(STSAHF2018)——scientific significance of turbulence research

<正>Most fluid flows in nature and engineering applications are in the state of turbulence. Turbulent motions usually exhibit a wide range of spatial and temporal scales, such as the flow of natural gas and oil in pipelines, the wakes of cars and submarines, the boundary layer of an     

Near-wall turbulence closure modeling without “damping functions”

An elliptic relaxation model is proposed for the strongly inhomogeneous region near the wall in wall-bounded turbulent shear flow. This model enables the correct kinematic boundary condition to be imposed on the normal component of turbulent intensity. Hence, wall blocking is represented. Means for enforcing the correct boundary conditions on the other components of intensity and on the k — equations are discussed. The present model agrees quite well with direct numerical simulation (DNS) data. The virtue of the present approach is that arbitrary damping functions are not required.     

Stabilité de l'écoulement de Hartmann chauffé par le basStability of the Hartmann flow heated from below

A numerical study is conducted in order to determine the influence of a vertical magnetic field, the Reynolds number and a temperature stratification on the instabilities occurring in the Hartmann flow heated from below. For $\mathit{Pr}=0.001$ and $\mathit{Ha}?2.5$, the results show that the vertical magnetic field has a stabilizing effect on both transverse oscillatory travelling waves $(T)$ and longitudinal stationary rolls $(L)$. The temperature stratification is responsible of a destabilization of the transverse $(T)$ modes and the appearance of longitudinal $(L)$ modes non-existent for the isothermal Hartmann flow. Moreover, the extent of the domains of Re where the transverse modes $(T)$ prevail is found to narrow when Ha increases and to widen when Ra increases for a given value of Ha. On the other hand, for the $(L)$ modes, the extent of the domains of Re where they prevail increases when Ha grows. To cite this article: W. Fakhfakh et al., C. R. Mecanique 334 (2006).     

A continuum mechanical theory for turbulence: a generalized Navier–Stokes-<Emphasis Type="Italic">α</Emphasis> equation with boundary conditions

We develop a continuum-mechanical formulation and generalization of the Navier–Stokes-α equation based on a recently developed framework for fluid-dynamical theories involving higher-order gradient dependencies. Our flow equation involves two length scales α and β. The first of these enters the theory through the specific free-energy α ²|D|², where D is the symmetric part of the gradient of the filtered velocity, and contributes a dispersive term to the flow equation. The remaining scale is associated with a dissipative hyperstress which depends linearly on the gradient of the filtered vorticity and which contributes a viscous term, with coefficient proportional to β ², to the flow equation. In contrast to Lagrangian averaging, our formulation delivers boundary conditions and a complete structure based on thermodynamics applied to an isothermal system. For a fixed surface without slip, the standard no-slip condition is augmented by a wall-eddy condition involving another length scale ℓ characteristic of eddies shed at the boundary and referred to as the wall-eddy length. As an application, we consider the classical problem of turbulent flow in a plane, rectangular channel of gap 2h with fixed, impermeable, slip-free walls and make comparisons with results obtained from direct numerical simulations. We find that α/β ~ Re ^0.470 and ℓ/h ~ Re ^−0.772, where Re is the Reynolds number. The first result, which arises as a consequence of identifying the specific free-energy with the specific turbulent kinetic energy, indicates that the choice β = α required to reduce our flow equation to the Navier–Stokes-α equation is likely to be problematic. The second result evinces the classical scaling relation η/L ~ Re ^−3/4 for the ratio of the Kolmogorov microscale η to the integral length scale L.      

Two-phase turbulence models for simulating dense gas–particle flows

The two-fluid model is widely adopted in simulations of dense gas–particle flows in engineering facilities. Present two-phase turbulence models for two-fluid modeling are isotropic. However, turbulence in actual gas–particle flows is not isotropic. Moreover, in these models the two-phase velocity correlation is closed using dimensional analysis, leading to discrepancies between the numerical results, theoretical analysis and experiments. To rectify this problem, some two-phase turbulence models were proposed by the authors and are applied to simulate dense gas–particle flows in downers, risers, and horizontal channels; Experimental results validate the simulation results. Among these models the USM-Θ and the two-scale USM models are shown to give a better account of both anisotropic particle turbulence and particle–particle collision using the transport equation model for the two-phase velocity correlation.     

Étude numérique du couplage de la convection naturelle avec le rayonnement de surfaces en cavité carrée remplie d'airNumerical study of natural convection-surface radiation coupling in air-filled square cavities

A numerical tool is developed for coupling natural convection in cavities with surface radiation and computations are performed for an air-filled square cavity whose four walls have the same emissivity. Compared to the adiabatic case without radiation, the top wall is cooled, the bottom wall is heated, air flow along the horizontal walls are reinforced and thermal stratification in cavity core is reduced. Detailed analysis shows that net radiative heat flux is linear with ΔT if $\mathrm{\Delta }T?T_0$, which is the case at low Rayleigh number, and that radiative Nusselt number is a linear function of the cavity height. Surface radiation induces an early transition to time-dependent flows: for $?=0.2$ and a cavity height of 0.335 m the critical Rayleigh number is equal to $9.3\times {10}^6$ and the corresponding Hopf bifurcation is supercritical. Furthermore, multiple periodic solutions are observed between $\mathit{Ra}=1.2\times {10}^7$ and $1.3\times {10}^7$. To cite this article: H. Wang et al., C. R. Mecanique 334 (2006).     

Experimental analysis of scaling laws in low Re λgrid-generated turbulence

An experimental investigation of scaling laws in turbulence generated by a biplane grid for low Reynolds numbers (Re ) is presented. The present study covers a wide range of flow field conditions (from Re 2.5 to Re 36) that have not been analyzed from this point of view. It is shown that following the Kolmogorov theory a scaling range can not be observed since the separation between the energy production scales and the dissipative scales is too short. On the other hand, an extended form of scaling, the Extended Self-Similarity (ESS), permits the identification of a range of scales characterized by the same scaling exponent much wider than the one previously examined. Thus the scaling laws for the first six moments of the velocity structure function are accurately calculated by means of the ESS and an anomalous scaling with respect to the Kolmogorov theory is observed for Re down to the order of 10. As a matter of fact the scaling exponents are in good agreement with the ones that were determined at higher Re by previous experimental and numerical investigations. For Re 6 a regularization of the scaling exponents is observed as an effect of the dissipation. We also present an analysis of the universality properties of the ESS form of scaling by means of the form function and an analysis of the sensitivity of the scaling range to the Re .