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International audience; A new approach to determine proper mean and fluctuating inlet boundary conditions is proposed. It is based on data driven techniques, i.e., machine learning approach, and its goal is to use any known information about the downstream flow to reconstruct the unknown or incomplete inlet boundary conditions for a numerical simulation. The European Research Community On Flow, Turbulence And Combustion (ERCOFTAC) test case of the swirling flow inside a conical diffuser is investigated. Despite its relatively simple geometry, it constitutes a very challenging test case for numerical simulations due to incomplete experimental data and to the delicate balance between core flow recirculation and boundary layer separation. Simulations are performed using both Reynolds averaged Navier–Stokes (RANS) and large-eddy simulations (LES) turbulence methods. The mean velocity and turbulence kinetic energy profiles obtained with the machine learning approach in RANS are found to be in very good agreement with the experimental measurements and the numerical predictions are greatly improved as compared to the previous results using basic inlet boundary conditions. They are indeed comparable to the best previous RANS using empirical ad hoc inlet conditions to accurately simulate the downstream flow. In LES, in addition to the mean velocity profiles, the machine learning approach also allows us to properly reconstruct the fluctuating part of the turbulent field. In particular, the methodology allows us to circumvent the lack of turbulent correlations associated with classical inlet synthetic turbulence.

Hydraulic machines are designed to operate in flow conditions close to the best efficiency point. However, to respond to the increasing demand for flexibility mainly due to the integration of renewable energy in the electric grid, the operating range of Francis turbines has to be extended towards smaller discharge levels without restriction. When Francis turbines are operated typically between 30% and 60% of the rated output power, the flow field is characterized by the appearance of inter-blade vortices in the runner. In these off-design operating conditions and due to these phenomena, dynamic stresses level can increase, and potentially lead to fatigue damage of the mechanical structure of the machine. The objective of this paper is to present investigations on the dynamic behaviour of the inter-blade vortices and their impact on the runner by using numerical simulations. Computations were performed with different turbulence modelling approaches to assess their relevance and reliability: Reynolds-Averaged Navier-Stokes (RANS) and Large-Eddy Simulation (LES). Computations aimed to better understand the emergence condition of the inter-blade vortices. The analysis showed that vortices can be generated due to poor inlet adaptation at part load, however other vortices can also be due to a local backflow in the runner. The competition between these both phenomena leads to various topologies of the inter-blade vortices. The numerical results were compared to experimental visualizations performed on scaled model as well as to previous numerical studies results. The impact of these inter-blade vortices on the runner were also investigated by considering the pressure fluctuations induced on the blades. The dynamic loading on the blade has to be known in order to evaluate the lifetime of the runner by mechanical analysis. Different operating conditions have been simulated to understand how the pressure fluctuations depend on the operating conditions. The localization of the pressure fluctuations and their consequences on the frequency signature of the torque fluctuations have been analyzed. This article is presenting a part of the work presented at the 29th IAHR Symposium on Hydraulic Machinery and Systems, Kyoto, 2018 [1], and presents another vortex topology and a comparison of LES results of several operating conditions.

Hydraulic machines are designed to operate in flow conditions close to the best efficiency point. However, to respond to the increasing demand for flexibility mainly due to the integration of renewable energy in the electric grid, the operating range of Francis turbines has to be extended towards smaller discharge levels without restriction. When Francis turbines are operated typically between 30% and 60% of the rated output power, the flow field is characterized by the appearance of inter-blade vortices in the runner. In these off-design operating conditions and due to these phenomena, dynamic stresses level can increase, and potentially lead to fatigue damage of the mechanical structure of the machine. The objective of this paper is to present investigations on the dynamic behaviour of the inter-blade vortices and their impact on the runner by using numerical simulations. Computations were performed with different turbulence modelling approaches to assess their relevance and reliability: Reynolds-Averaged Navier-Stokes (RANS) and Large-Eddy Simulation (LES). Computations aimed to better understand the emergence condition of the inter-blade vortices. The analysis showed that vortices can be generated due to poor inlet adaptation at part load, however other vortices can also be due to a local backflow in the runner. The competition between these both phenomena leads to various topologies of the inter-blade vortices. The numerical results were compared to experimental visualizations performed on scaled model as well as to previous numerical studies results. The impact of these inter-blade vortices on the runner were also investigated by considering the pressure fluctuations induced on the blades. The dynamic loading on the blade has to be known in order to evaluate the lifetime of the runner by mechanical analysis. A previous experimental study [S. Bouajila et al., IOP Conf. Ser.: Earth Environ. Sci., 2016] has shown that the appearance of the inter-blade vortices can be correlated with a large-band frequency signature in the pressure fluctuations measured on the blades. The numerical simulations presented in this paper focused on the prediction of this frequency signature as well as on the analysis of its origin.

International audience; Nous présentons des Simulations des Grandes Échelles d'écoulements turbulents compressibles tridimensionnels se développant dans des conduits courbes de section rectangulaire. Ces écoulements sont caractérisés par la présence de flux secondaires intenses et de structures turbulentes responsables des transferts de masse et thermique. Le but est ici d'évaluer l'influence du rapport d'aspect de la section sur ce type d'écoulements. Les résultats montrent que ce paramètre modifie l'intensité et la localisation des tourbillons et donc indirectement le transfert de chaleur lorsqu'un chauffage est appliqué sur la paroi convexe.

The influence of the coherent structures on grid/subgrid-scale (GS/SGS) interactions in free shear layers is analysed through the application of a top-hat filter to several plane jet direct numerical simulations (DNS). The Reynolds number based on the plane jet inlet slot width is Reh = 3000. The study deals with energy containing (Kelvin–Helmholtz) and inertial range (streamwise) vortices, from the far field of the turbulent plane jet. The most intense kinetic energy exchanges between GS and SGS occur near these structures and not randomly in the space. The GS kinetic energy is dominated by GS advection and GS pressure/velocity interactions which appear located next to the Kelvin–Helmholtz rollers. Surprisingly, GS/SGS transfer is not very well correlated with the coherent vortices and GS/SGS diffusion plays an important role in the local dynamics of both GS and SGS kinetic energy. The so-called ‘local equilibrium assumption’ holds globally but not locally as most viscous dissipation of SGS kinetic energy takes place within the vortex cores whereas forward and backward GS/SGS transfer occurs at quite different locations. Finally, it was shown that SGS kinetic energy advection may be locally large as compared to the other terms of the SGS kinetic energy transport equation.

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.

A new subgrid-scale model called the spectral-dynamic model is proposed. It consists of a refinement of spectral eddy-viscosity models taking into account nondeveloped turbulence in the subgrid-scales. The proposed correction, which is derived from eddy-damped quasi-normal Markovian statistical theory, is based on an adjustment of the turbulent eddy-viscosity coefficient to the deviation of the spectral slope (at small scales) with respect to the standard Kolmogorov law. The spectral-dynamic model is applied to large eddy simulation (LES) of rotating and nonrotating turbulent plane channel flows. It is shown that the proposed refinement allows for clear improvement of the statistical predictions due to a correct prediction of the near-wall behavior. Cases of rotating and nonrotating low (DNS) and high Reynolds (LES) numbers are then compared. It is shown that the principal structural features of the rotating turbulent channel flow are reproduced by the LES, such as the presence of the near-zero mean absolute vorticity region, the modification of the anisotropic character of the flow (with respect to the nonrotating case), the enhancement of flow organization, and the inhibition of the high- and low-speed streaks near the anticyclonic wall. Only a moderate Reynolds number dependence is exhibited, resulting in a more unstable character of the longitudinal large-scale roll cells at high Reynolds number, and a slight increase of the laminarization tendency on the cyclonic side of the channel.

Baroclinic instabilities of jet flows are investigated by means of numerical simulations of the nonhydrostatic Boussinesq equations on the f plane. Frontal small scales are accurately described thanks to precise numerical methods (mixed spectral–high-order finite differences). First, direct numerical simulations are used to carry out linear instability studies. The authors show the existence for a critical value of Ro/F = 1.5, under which baroclinic instability dominates (Ro and F are the Rossby and the Froude numbers). Cyclogenesis events are then explored for various degrees of baroclinicity of the basic state with emphasis on the preferential amplification of cyclonic vorticity. The asymmetry of the vorticity field is quantified, and deterministic and statistical analyses of the various terms involved in the vorticity equation show simply how vertical stretching mechanisms are responsible for this asymmetry. The late stage of the instability following cutoff of the primary wave occlusion is th...

With the aid of a direct numerical simulation of an incompressible plane turbulent channel at ${h}^{+}=162$, we have determined the probability distribution functions (PDF's) of pressure and of the various velocity components from the wall to the channel center. The pressure turns out to be symmetric with exponential tails at the wall as well as at ${y}^{+}=2.5$. At ${y}^{+}=12$, where the streamwise streaks intensity is maximum, the pressure has become asymmetric. This character intensifies with the distance away from the wall and the distribution obtained in the channel center resembles those determined in isotropic turbulence and free-shear flows. Very close to the wall ${(y}^{+}=2.5)$, the PDF of ${u}^{\ensuremath{'}}$ is highly skewed, with exponential and sub-Gaussian distributions at high and low values, respectively. This indicates that the high-speed streaks are very intermittent at the wall. The reverse occurs close to the channel center, where intense negative ${u}^{\ensuremath{'}}$ prevail. Then we show that the most probable orientation of the fluctuating vorticity vector is perpendicular to the wall in the region $5l{y}^{+}l30$ (which is basically in the low- and high-speed regions), while it is $45\ifmmode^\circ\else\textdegree\fi{}$ with respect to the wall above.

We investigate, by means of direct numerical simulations, the three-dimensional (3-D) dynamics of coherent vortices in a rotating channel. We focus here on the structure of the instantaneous (absolute and relative) vorticity field. Both transitional and turbulent regimes are considered. Strong rotation is shown to suppress the transition towards turbulence (leading to two-dimensional [2-D1 flow). Conversely, moderate rotation yields strong longitudinal vortices on the anticyclonic side of the channel, which trigger early transition (earlier than without rotation). In that regime, the complete transition to fully developed turbulence is compared for two values of Rossby number: |Ro(i)|=2 and |Ro(i)|=6. In the early stage of the transition, perturbations are more strongly amplified at |Ro(i)|=2. The saturation is, however, reached earlier in that case, and a more energetic turbulent state is achieved at |Ro(i)|=6. In the fully developed turbulent case, nonrotating and moderately rotating channels are compared. Relaminarization occurs on the cyclonic wall, while turbulence is observed on the anticyclonic wall. The vortex topology is shown to be strongly affected by the rotation. The enhancement of the anticyclonic perturbations level is associated with hairpin vortices which are much more inclined (up to 10° to the wall) than in the nonrotating case (45°). These extend until the channel center and are associated with a characteristic region of zero absolute mean vorticity. Stretching mechanisms of absolute vortex lines are carefully examined.

It is well established that at low Rossby and Froude numbers modes possessing potential vorticity behave differently from gavity-inertial wave modes. Wave energy cascades relatively more efficiently downscale to the dissipation, resulting in a geostrophic adjustment. For this reason, it has been suggested that wave energy be subjected to relatively stronger dissipation via “divergence damping.” This study reports separate measurements of the effective eddy damping acting on wave and rotational modes in simulations of nonhydrostatic Boussinesq flow. The method employs an arbitrary cutoff wavenumber, kc, within the simulation’s range of resolved scales, in order to calculate explicitly the effect of the smaller-scale motion on wavenumbers below kc. It is found that the rotational-mode eddy viscosity resembles that found in studies of 2D turbulence, with a significant negative range, while it is positive at all wavenumbers for the wave modes.

The paper presents large-eddy simulation (LES) formalism, along with the various subgrid-scale models developed since Smagorinsky’s model. We show how Kraichnan’s spectral eddy viscosity may be implemented in physical space, yielding the structure-function model. Recent developments of this model that allow the eddy viscosity to be inhibited in transitional regions are discussed. We present a dynamic procedure, where a double filtering allows one to dynamically determine the subgrid-scale model constants. The importance of backscatter effects is discussed. Alternatives to the eddy-viscosity assumption, such as scale- similarity models, are considered. Pseudo-direct simulations in which numerical diffusion replaces subgrid transfers are mentioned. Various applications of LES to incompressible and compressible turbulent flows are given, with an emphasis on the generation of coherent vortices

Developed turbulent flows contain coherent vortices of various sizes, which play a major role in heat and mass transfer processes. We present here results of direct and large-eddy simulations LES focusing on the role played by these coherent vortices. We describe in detail the formalism of large-eddy simulations of turbulence, with a family of models developed on the basis of Kraichnan's eddy-viscosity. We see, for example, how longitudinal hairpin vortices are taken into account within these LES. We discuss vortex structure identification. Various results are presented concerning large-scale intermittency of a passive temperature and the role played by a stable-stratification to reduce this intermittency. We show numerical simulations of separated flows (backstep flow) with and without stratification, demonstrating the ability for LES to deal with complex geometries. Finally, the influence of solid-body rotation on free-shear flows is investigated, showing drastic modification of the flow topology.

After presenting the general features of turbulent flows and coherent vortices, we discuss the major progress brought by Computational Fluid Dynamics (CFD) to the understanding of coherent vortices in turbulence. Afterwards, we present some simple vortex dynamics arguments allowing us to understand qualitatively the formation of coherent vortices during the transition to turbulence in shear flows. Of particular interest are the following elementary vortex interactions: roll up of a vortex sheet, pairing, dipole, even longitudinal hairpin, and odd longitudinal hairpin. Then direct numerical or large-eddy simulations of free-shear flows (mixing layers, backstep, jets, wakes), isotropic turbulence, and spatially-developing boundary-layers on a flat plate are presented. Following the editor’s request, these simulations focus mainly on the work done in France in Grenoble, which is however discussed within a broader numerical and experimental context. We show for instance that helical pairings may occur in plane mixing layers. The paper also presents in details the formalism of large-eddy simulations (LES) of turbulence, with the various models developed since Smagorinsky. We see for instance how longitudinal hairpin vortices are taken into account within these LES. Effects of compressibility upon turbulence are also considered: we study in particular mixing layers (where it is shown that helical pairing is inhibited above a certain convective Mach number), strongly heated boundary layers at low Mach number, and supersonic compression ramps within the frame of the HERMES European space-shuttle reentry project. Finally, we look at the influence of solid-body rotation on incompressible turbulence. In the case of a free-shear layer, we study shear/Coriolis linear instability, which, in anticyclonic conditions and at moderate rotation rates, yields a purely longitudinal mode. Numerical simulations show how this mode evolves non-linearly into concentrated longitudinal hairpin vortices of absolute vorticity. We also consider the case of initially isotropic turbulence subject to rotation.

International audience; The swirling turbulent flow in a hydroturbine draft tube is computed with a nonintrusive uncertainty quantification (UQ) method coupled to Reynolds-Averaged Navier- Stokes (RANS) modelling in order to take into account in the numerical prediction the physical uncertainties existing on the inlet flow conditions. The proposed approach yields not only mean velocity fields to be compared with measured profiles, as is customary in Computational Fluid Dynamics (CFD) practice, but also variance of these quantities from which error bars can be deduced on the computed profiles, thus making more significant the comparison between experiment and computation.

International audience; The axis location of a Francis turbine guide vane is optimized on the basis of 2D interblade channel flow simulations using upstream boundary conditions that include the experimentally observed flow rate and incidence circumferential variations. These variations are treated as uncertainties and propagated through RANS and LES flow simulations using a non-intrusive polynomial chaos based uncertainty quantification. The computed mean value and variance of the guide vane torque are then used to design a robust optimal location for the guide vane axis.

International audience; In this work, modeling of the near-wall region in turbulent flows is addressed. A new wall-layer model is proposed with the goal to perform high-Reynolds number large-eddy simulations of wall bounded flows in the presence of a streamwise pressure gradient. The model applies both in the viscous sublayer and in the inertial region, without any parameter to switch from one region to the other. An analytical expression for the velocity field as a function of the distance from the wall is derived from the simplified thin-boundary equations and by using a turbulent eddy coefficient with a damping function. This damping function relies on a modified van Driest formula to define the mixing-length taking into account the presence of a streamwise pressure gradient. The model is first validated by a priori comparisons with direct numerical simulation data of various flows with and without streamwise pressure gradient and with eventual flow separation. Large-eddy simulations are then performed using the present wall model as wall boundary condition. A plane channel flow and the flow over a periodic arrangement of hills are successively considered. The present model predictions are compared with those obtained using the wall models previously proposed by Spalding, Trans. ASME, J. Appl. Mech 28, 243 (2008) and Manhart et al., Theor. Comput. Fluid Dyn. 22, 243 (2008) . It is shown that the new wall model allows for a good prediction of the mean velocity profile both with and without streamwise pressure gradient. It is shown than, conversely to the previous models, the present model is able to predict flow separation even when a very coarse grid is used.

This paper presents a statistical and topological study of a complex turbulent flow over a backward-facing step by means of direct and large-eddy simulations. Direct simulations are first performed for an isothermal two-dimensional case. In this case, shedding of coherent vortices in the mixing layer is demonstrated. Both direct and large-eddy simulations are then carried out in three dimensions. The subgrid-scale model used is the structure-function model proposed by Métais & Lesieur (1992). Lowstep computations corresponding to the geometry of Eaton & Johnston's (1980) laboratory experiment give turbulence statistics in better agreement with the experimental data than both Smagorinsky's method and K-ε modelling. Furthermore, calculations for a high step show that the eddy structure of the flow presents striking analogies with forced plane mixing layers: large billows are shed behind the step with intense longitudinal vortices strained between them.

We present the eddy-viscosity concept in Fourier space. For large-eddy simulations (LES) of isotropic turbulence, EDQNM eddy coefficients are compared with those obtained through a double filtering in spectral space. In real space, the spectral eddy-viscosity is equivalent to the combination of an eddy viscosity and a hyperviscosity. The spectral-dynamic model, which accounts for cutoff spectra not following Kolmogorov’s law, is applied with success to a temporal mixing layer and a plane channel.

We discuss the limits of turbulence direct-numerical simulations (DNS), and the need for large-eddy simulations (LES). We present spectral LES using subgrid models developed first in spectral space, then implemented in physical space. For a flow of constant density or weakly compressible, they are applied successively to inviscid isotropic turbulence, plane channels, and an obstacle with wall effect. The second part of the chapter is more geophysical and reproduces with permission granted by Cambridge University Press the chapter on “Geophysical fluid dynamics” from the book Large-eddy simulations of turbulence by Lesieur, Metais and Comte [2005] . We first make a survey of flows encountered in Geophysics, with relevant climatic issues. Then the effect of spanwise rotation upon a plane channel is investigated with DNS and LES. For “moderate” (in terms of initial Rossby number based on the vorticity at the wall) rotation rates, one confirms the complete modification of the mean velocity profile into a linear profile over a large part of the channel, with a corresponding zero absolute mean vorticity. At “high” rotation rates, the channel flow becomes two-dimensional. Analogies with mixing layers and wakes submitted to spanwise rotation are also discussed, showing a universal character of rotating free- and wall-bounded shear flows. Finally, the development of a baroclinic jet in the atmosphere is studied. DNS and LES allow to show the formation of big quasi two-dimensional cyclonic vortices, with an intense vertical stretching of cyclonic vorticity in braids forming along the thermal fronts on the floor and the lid of the computational domain. Only LES did show secondary instabilities on the cold fronts of the braids. We discuss analogies with storm formation.

Large-eddy simulation of a turbulent channel flow is performed with a spectral model which takes the slope of the spectra into account—as suggested in Metais & Lesieur (1992, J. Fluid Mech., 239, pp. 157–194.)—instead of assuming k −5/3 spectra as we have done so far. Considerable improvement of statistics at the wall are obtained. Transposition to the physical space is in progress. In the meantime, spatially-growing mixing layers and transitional compressible boundary layers are simulated thanks to the structure-function model and two improved versions of it which still assume Kolmogorov spectra, but are nevertheless capable of not acting during transition. It is in particular found that a high-Mach number (4.5) boundary layer over an adiabatic flat plate undergoes a first transient in the form of Kelvin-Helmholtz-like vortices developing in the outer part of the layer. This activity is suddenly overwhelmed by a transition scenario going on at the wall which is reminiscent of incompressible boundary layers.

Direct numerical simulations are performed to analyze the flow dynamics and the mixing properties of natural unforced and excited coaxial jets at moderate Reynolds number. First, the study of the natural coaxial jet, with species injected in the outer jet alone, allows us to understand the role of the coherent vortices on the mixing process during the transition stage. It is observed that the global flow behavior is controlled by the dynamics of the outer shear layer during the transition. The streamwise vortices are shown to play a significant role in the mixing process since they initiate intense ejections from the seeding regions. Spots of pure unmixed species from the outer jet are seen to persist far downstream. Two different types of inflow forcing are then considered based on the information provided by the natural coaxial jet: first, a purely axisymmetric excitation and second, combined axisymmetric and azimuthal excitations all of moderate amplitude. These excitations are applied to the outer shear layer with a frequency corresponding to the periodic passage of the outer vortical structures. The goal of these excitations is to trigger the vortices formation and to control their dynamics to improve the mixing properties of the jet. With the purely axisymmetric excitation, the outer and inner Kelvin-Helmholtz vortices appear earlier than for the natural jet and the transition process is faster. This early three-dimensionality growth is due to a rapid appearance of streamwise vortices, stretched between consecutive vortex rings, which lead to enhanced mixing. For the combined axisymmetric and azimuthal excitations, the outer Kelvin-Helmholtz rings appear moreover with an azimuthal deformation from the beginning of the jet. This allows for the early generation of streamwise vortices. The vortex stretching phenomenon takes place near the jet inlet with a growth of the axial component of the vorticity fluctuations. The ejections of species from the outer jet thus appear sooner and with a larger intensity. Finally, the mixing efficiency is studied through the global mixedness and the intensity of segregation.

Direct numerical simulations (DNS) are performed to investigate mixing in free round coaxial jets. A great attention has been put on the influence of upstream conditions upon the global flow structure and the mixing process. The mixing behavior is studied through the spatial and temporal development of the mixture fraction of the annular and the inner fluids, and examined by means of flow visualization and statistics. It is shown that the turbulent mixing process and the mixture fraction field in coaxial jets depend on the upstream conditions, even though a quasi self-similar state is reached. The mixing alterations are explained by the understanding of the flow dynamics modifications implied by the different upstream conditions. These alterations are mainly due to the intense generation of streamwise vortices, favored by high inlet velocity gradients and velocity ratios, as well as low ratios between the inner and the outer jet diameters. This is associated with a high quality of mixing, as far as global mixedness is concerned. It is also shown that the annular fluid reaches the inner fluid and mixes swiftly into it. Conversely, the latter remains confined. Additionally, spots of pure unmixed species are observed at the end of the computational domain, and shown to be due to the annular jet.

International audience; We present large-eddy simulations of the turbulent compressible flow at a low Mach number in curved ducts. The aim is to investigate the influence of the curvature radius R c on the flow. Three simulations are carried out at R c = 3.5 D h , 6.5 D h and 10.5 D h (D h hydraulic diameter). We first validate our computations by comparison with the incompressible experiments performed by Chang et al. (1983, Turbulent flow in a strongly curved U-bend and downstream tangent of square cross-sections. Physico-chemical Hydrodynamics, 4(3), 243–269). We observe that the decrease of the curvature radius is accompanied by a strong intensification of the secondary transverse flows : a rise of 100% of the maximum of their intensity is obtained between the smaller and the higher values of R c . We show that the secondary flows strength is directly related to the radial pressure gradient intensity. We observe a significant modification of the near-wall laws in the vicinity of each curved walls in correlation with the favourable or the adverse streamwise pressure gradient depending on the nature of the curvature. The influence of R c on the coherent vortices is also estimated.

We investigate through large-eddy simulations the effects of different types of upstream forcing in subsonic (Mach 0.7) and supersonic (Mach 1.4) round jets. We have reproduced and tested the different methods of forcing developed in incompressible round jets by Urbin and Métais In Direct and Large-Eddy Simulations II, 1997, P. R. Chollet, J. P. Voke, and L. Kleiser, Kluwer: Dordrecht, pp. 539–542, Danaila and Boersma, Physics of Fluids A, 12, 1255–1257, da Silva and Métais Physics of Fluids, 14, 3798–3819, (see also Lee and Reynolds Bifurcating and blooming jets at high Reynolds number 5th Symposium on Turbulent Shear Flows, New York). Our strategy is to search the optimal excitation that maximizes the jet spreading at Reynolds number Re = 36 000. Four different forcings based on information obtained both instantaneously and statistically. In the subsonic case, and as in the incompressible one, we aimed to favour the flow spreading along one particular plane (bifurcating plane), while maintaining a standard or reduced spreading rate along the bisecting plane, perpendicular to the bifurcating one. The flow response to the excitations is analysed both instantaneously and statistically. In the subsonic case, and as in the incompressible one, the maximum jet spreading is obtained with inlet varicose–flapping perturbations at preferred and first subharmonic frequencies, respectively. The potential core length is reduced by 27% with respect to the natural jet. These results are in good agreement with several laboratory experiments and numerical simulations carried out in incompressible round jets. Indeed, the subsonic jet has a convective Mach number of 0.35, and is weakly affected by compressibility. In the supersonic jet case, on the other hand, the highest spreading rate is found with a flapping excitation at the second subharmonic. The potential core length is now reduced by 28% with respect to the unforced jet.

The near-field behavior of coaxial jets is studied through direct numerical simulation (DNS) with a particular focus on the influence of the inner shear layer steepness characterized by its momentum thickness θ01 thus mimicking the variation in the lip thickness of a real jet nozzle. We investigate the two distinct jet regimes ru>ruc for which a recirculation bubble is present near the jet inlet and ruruc case, variations of θ01 strongly affect the shape and the downstream extent of the recirculation bubble. The DNS allow to show the strong dependency of the inner and outer potential core lengths and of the critical value ruc on the jet inlet velocity profile. We finally revisit the theoretical model originally proposed by Rehab, Villermaux, and Hopfinger [“Flow regimes of large-velocity-ratio coaxial jets,” J. Fluid Mech. 345, 357 (1997)] first aimed at the prediction of the variations of various jet characteristics as a function of ru. The model is extended to determine the dependency of the jet characteristics with θ01. A very good correspondence between the theoretical predictions and the numerical results is obtained.

Large eddy simulations of the turbulent gas flow within ducts of square cross-section are performed. The spatial development of turbulent flow inside a heated straight duct is first considered with a higher temperature suddenly imposed at one of the duct walls. The downstream development of the thermal boundary layer is then studied and compared with the fully developed turbulent case. The gradual increase with temperature of the viscosity near the heated wall yields a progressive enhancement of the turbulent structures and to a single ejection localized near the middle plane of the heated wall. The use of curvilinear coordinates allows to consider ducts of more complex geometries and to investigate the combined effects of heating and curvature. The case of an S-shape duct is then considered exhibiting both convex and concave curvatures. The pressure gradient between the inner and outer wall of the curved sections leads to the apparition of intense counter-rotating Dean vortices associated with an intense transverse flow with a maximum intensity of 22% of the bulk velocity. Downstream of the second curved section of the duct, the flow exhibits a complex distribution of various vortices. In the heated case, the mutual interaction between the heating and the Dean vortices is investigated. The heating is seen to enhance both the size and intensity of the Dean vortices when situated close to the heated wall.

We present Large-Eddy Simulations (LES) of the turbulent compressible flow in a curved and an S-shape duct of square cross section. The aim is to predict the three-dimensional structures which develop inside the cooling channels of heat exchangers and which dominate the heat transfer with the heated wall. We first consider a curved duct with one curvature only and then an S-shape duct with two opposite curvatures. We observe the formation of Görtler vortices which are moved close to the convex wall by the radial pressure gradient between the two curved faces. These are associated with a secondary flow of over 20% of the streamwise velocity. We determine the influence of wall heating and consecutively consider the case of concave wall heating and of convex wall heating. Due to the secondary flow associated with the Görtler vortices, we observe an enhancement of the heat flux in the first case and an inhibition in the second case.

We deal with the prediction of electromagnetically-driven turbulent flows by means of a large-eddy-simulation method (LES). The model is applied in the case of a liquid metal pool submitted to a polyphase linear electromagnetic stirrer. We investigate two cases: (i) the effects of the pulsating part of the Lorentz forces are neglected, the frequency of the applied magnetic field being high enough; (ii) the oscillating part of the electromagnetic forces is taken into account, the frequency of the magnetic field being sufficiently low. The LES predictions agree well with the mean velocity measurements, as does the standard k–ε model. However, as for the turbulent kinetic energy predictions, there is a large discrepancy between the two models. When the oscillating part of the Lorentz forces is taken into account, the computations show that the fluid flow is sensitive to the unsteady part of the forces provided the frequency of the magnetic field is sufficiently low. The mean velocity is not affected by the fluctuating component of the force. As for the turbulence parameters, the presence of the pulsating part leads to a significant reduction of the turbulent kinetic energy, whilst the turbulence length scale decreases. The effect of the oscillating part of the Lorentz forces becomes negligible when the magnetic field frequency exceeds approximately 5 Hz.

Large Eddy Simulations of a passive scalar were done using wall-functions for both wall-friction and wall heat flux on the plane channel flow configuration with solid walls. Conjugate heat-transfer simulations have been carried out at low (Re τ = 150) and high (Re τ = 395) Reynolds numbers using a wall-function strategy. Attention was not only paid on the temperature fluctuations in the fluid and inside the solid wall, but also on the temperature signal spectrum inside the solid as well as in the first off wall point in the fluid. The main purpose of this work is intended to stress on the misleading effects (especially when focusing on temperature fluctuations) of wall-function type meshes in the fluid-solid thermal interaction frame-work.

Direct numerical simulations are performed to analyse the instability, transition scenario and resulting topology from high velocity ratio coaxial jets (ru = 3.3 and 23.5). The inner and outer shear layers roll up into axisymmetric vortex rings due to the Kelvin–Helmholtz instability. For ru = 3.3 the outer primary vortices evolve according to the theory considering an isolated mixing layer profile, and impose their evolution upon the inner structures which are ‘locked’ into the outer ones. For ru = 23.5 there is a big recirculation region that does not affect the development of the Kelvin–Helmholtz instabilities. The preferred mode for simple (non-coaxial) round jets is well recovered at the end of the potential core region in the case ru = 3.3 but not when ru = 23.5 due to the presence of the backflow region. The structure of the preferred mode is the same in both cases, however, and consists in a helical arrangement (m = 1). Finally, when the bubble is present one can see that the inner streamwise structures, corresponding to the secondary instabilities, are stretched by the presence of the bubble which acts as an additional source of axial vorticity production.

Large-eddy simulations of a compressible turbulent square duct flow at low Mach number are described. First, we consider the isothermal case with all the walls at the same temperature: good agreement with previous incompressible DNS and LES results is obtained both for the statistical quantities and for the turbulent structures. A heated duct with a higher temperature prescribed at one wall is then considered and the intensity of the heating is varied widely. The increase of the viscosity with temperature in the vicinity of the heated wall turns out to play a major rôle. We observe an amplification of the near-wall secondary flows, a decrease of the turbulent fluctuations in the near-wall region and, conversely, their enhancement in the outer wall region. The increase of the viscous thickness with heating implies a significant augmentation of the size of the characteristic flow structures such as the low- and high-speed streaks, the ejections and the quasi-longitudinal vorticity structures. For strong enough heating, the size limitation imposed by the lateral walls leads to a single low-speed streak located near the duct central plane surrounded by two high-speed streaks on both sides. Violent ejections of slow and hot fluid from the heated wall are observed, linked with the central low-speed streak. A selective statistical sampling of the most violent ejection events reveals that the entrainment of cold fluid, originated from the duct core, at the base of the ejection and its subsequent expansion amplifies the ejection intensity.

International audience; Direct and large-eddy simulations (DNS/LES) are performed to analyze the vortex dynamics and the statistics of bifurcating jets. The Reynolds number ranges from ReD=1.5×103 to ReD=5.0×104. An active control of the inlet conditions of a spatially evolving round jet is performed with the aim of favoring the jet spreading in one particular spatial direction, thus creating a bifurcating jet. Three different types of forcing, based on the information provided by a LES of a natural (unforced) jet, are superimposed to the jet inlet in order to cause its bifurcation. The different forcing types mimic the forcing methods used in experimental bifurcating jets (Lee and Reynolds, Parekh et al., Suzuki et al.), but using excitations with relatively low amplitudes, which could be used in real industrial applications. The three-dimensional coherent structures resulting from each specific forcing are analyzed in detail and their impact on the statistical behavior of bifurcating jets is explained. In particular we focus on the influence of the forcing frequency and of the Reynolds number on the jet control efficiency. Analysis of the coherent vortex dynamics shows that an inlet excitation which combines an axisymmetric excitation at the preferred frequency and a so-called flapping excitation at the subharmonic frequency is the most efficient strategy for jet control, even at high Reynolds numbers.

Selected presentations from the Euromech Colloquium 412, Munich Univ. of Technology 4-6 October; International audience; Terms from the transport equations of the grid-scale (GS) and subgrid-scale (SGS) kinetic energy are analyzed both instantaneously and statistically in order to understand the role of the coherent vortices in the GS/SGS interactions in free shear flows. In the end, a new light emerges on the role played by these structures in these complex processes. The implications for SGS modeling are discussed.

We propose a modified version of the selective structure function (SSF) model originally proposed by David (1993 PhD Thesis National Polytechnic Institute, Grenoble). As compared with the SSF model, the modified selective structure function (MSSF) model respects in a better way the energetic exchanges between the supergrid and the subgrid scales and automatically adjusts itself to the discretization thinness of the most energetic scales. Using the PRICELES industrial code, we first simulate decaying homogeneous isotropic turbulence at high Reynolds number. The MSSF model is shown not to dissipate the supergrid scale energy when the kinetic energy is present at large scale only. It leads to a good prediction of the time decay law and to kinetic energy spectra with a well defined k −5/3 spectral range extending up to the cut-off wavenumber. The results of the MSSF model are found to be very close to those obtained with Smagorinsky's dynamic model of Germano et al (1991 Phys. Fluids A 3 1760-5). For low Reynolds number isotropic turbulence, a very satisfactory comparison with the experimental data of Comte-Bellot and Corrsin (1971 J. Fluid Mech. 48 273-337) is obtained. In the turbulent channel flow, the MSSF model was shown to allow for a much better prediction of the friction velocity owing to its less dissipative character in the near-wall region as compared to the SSF model.

Large Eddy Simulations of a spatially growing thermal boundary layer in a heated square duct at low Mach number are described. The temperature of one of the wall of the spatial duct,T h , is higher than the temperature of the other three walls. Turbulent inlet conditions are provided by the LES of an isothermal temporal duct. Both ducts are computed simultaneously and they are linked by a boundary condition of characteristic type proposed by Poinsot & Lele (1992).

Direct and Large-eddy simulations (DNS/LES) were used to analyze the vortex dynamics and statistical behavior of bifurcating jets. The Reynolds numbers analyzed go from Re D 1.5 × 103 to Re D 5.0 × 104. The jet bifurcation was achieved by means of an active jet control superimposed to a spatially evolving round jet. Three types of forcing were analyzed, which reproduce the forcing methods used in experimental bifurcating jets [8], although using a much lower amplitude forcing, more realistic in terms of potential industrial applications. The study analyses coherent structures resulting from each of the forcing types and explains their impact in the statistical behavior of the bifurcating jets. Special emphasis is made in the influence of increasing Reynolds number in the spatial evolution of each excited jet. Finally, this work addressed also the dynamics of the near field coherent structures in a coaxial by means of DNS. The Reynolds number was Re D1 = 3000. The interaction between the inner and outer shear layers and its consequences for the transition process was analyzed in detail. In particular t is postulated that the inner streamwise vortex pairs are stretched by the central backflow region.

This paper studies aspects of particle dispersion and vortex formation in stably stratified turbulence with rotation using the direct numerical simulation of the (non-dimensionalized) Navier-Stokes equations within the Boussinesq approximation.

Large Eddy Simulations of a compressible turbulent square duct at low Mach number are described. First, the isothermal case with all the walls at the same temperature is considered. Good agreement with previous incompressible DNS and LES results is obtained both for the mean and turbulent statistics. The heated duct with a larger temperature prescribed at one wall is then considered. We observe an amplification of the near wall secondary flows, a decrease of the turbulent fluctuations in the near wall region and, conversely, an enhancement of the latter in the outerwall region. This can be explained by the increase of the dominant turbulence structures (ejections) and by the changes in the fluid properties associated with heating. A detailed investigation of the ejection mechanism is presented.

Direct-numerical simulation of turbulence (DNS) consists of solving explicitly all the scales of motion, from the largest l I to the Kolmogorov dissipative scale l D . It is well known from the statistical theory of turbulence that l I /l D scales like \( R_l^{3/4}\), where R l is the large-scale Reynolds number u’l I / v based upon the rms velocity fluctuation u’. Therefore, the total number of degrees of freedom necessary to represent the whole span of scales of a three-dimensional turbulent flow is of the order of \( R_l^{9/4}\) in three dimensions. With the presently available computers, the DNS is then limited to Reynolds numbers which are several orders of magnitude smaller than those encountered in the ocean, the atmosphere, or most of the industrial facilities. In order to increase the Reynolds number in the simulations, it is necessary to introduce a subgrid-scale model representing the action of scales smaller than Δx, the computational mesh, upon the explicitly resolved scales. This is the basis of the Large-Eddy Simulation (LES) techniques.

We present a statistical and topological study of the spatial growth of a round jet up to twelve diameters downstream from the nozzle. The use of large-eddy simulations allow us to reach high Reynolds number values: here, Re = 25000. It is shown that, at a reasonable computational cost, good comparisons with experimental data can be achieved. We successively consider the case of the “natural” unexcited jet and the case of the jet excited with specified inflow perturbations at the nozzle. The natural jet alternatively exhibits axisymmetric (rings) and helicoidal vortex structures. Further downstream, we observe that the alternate inclination of the rings yields localized alternated pairings. We have showed that this structure can be forced to appear from the nozzle with an adhoc excitation leading to the preferential development of the jet in one particular direction. When axisymmetric excitation is applied, after vortex rings have formed, pairs of counter-rotating longitudinal vortices appear linked with primary rings and these create horizontal side jets. Longitudinal vortices are still present when a helicoidal excitation is imposed.

Most atmospheric and oceanic turbulence and eddies originate from the development of instabilities resulting from the combined effects of density gradients and rotation. We present here numerical Direct Numerical Simulations (DNS) and Large-Eddy Simulations (LES) of turbulent flows of atmospheric and oceanic interest. We first investigate the effects of solid-body rotation on free-shear flows, wall-bounded flows, and homogeneous turbulence, and show the drastic modification of the flow topology. Stably-stratified rotating turbulence is then numerically investigated with energy injection at small scales. We observe inverse cascades corresponding to a well defined k−5/3 spectral range for the geostrophic part of both the kinetic and available potential energy spectra. The applications to the observed mesoscale atmospheric spectrum are discussed. We finally show how DNS and LES techniques can be applied to the computation of synoptic and frontal scale cyclogenesis.

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.

The spectral eddy-viscosity and eddy-diffusivity closures derived from the eddy-damped quasinormal Markovian (EDQNM) theory, and one of its physical space counterparts, i.e., the structure function model [Metais and Lesieur, J. Fluid Mech. 239, 157 (1992)], are revisited to account for molecular viscosity and diffusivity effects. The subgrid-scale Schmidt number (usually set to Sct≈0.6) is analytically derived from the EDQNM theory and shown to be Reynolds number dependent, a property of utmost importance for flows involving scalar transport at moderate Reynolds numbers or during the transition to turbulence. A priori tests in direct numerical simulation of homogeneous isotropic turbulence [da Silva and Pereira, Phys. Fluids 19, 035106 (2007)] and in spatially evolving turbulent plane jets [da Silva and Metais, J. Fluid Mech. 473, 103 (2002)], as well as a posteriori (large eddy simulation) tests in a round jet are carried out and show that the present viscous structure function model improves the results...

We first review mechanisms leading to primary and secondary instabilities originating from a thermal front in a rotating stably stratified atmosphere or ocean. This is done in particular in the light of the work by Garnier et al (1996 C. R. Acad. Sci., Paris B 323 161–8; 1998 J. Atmos. Sci. 55 1316–35), where direct-numerical simulations (DNS) and large-eddy simulations (LES) of Navier–Stokes equations within the Boussinesq approximation were carried out. In these articles, braids of intense cyclonic vertical relative vorticity stretched in the fronts reconnecting the primary vortices were found at the ground and under the lid of the computational domain. We present an animation of primary-vortex and front formation in the DNS, and give an interpretation of the vortex braids using the equations of motion and potential-vorticity conservation. Afterwards, the results of Garnier et al using LES, which showed an instability of the braids yielding very intense secondary vortices forming along the cold front, a...

Results of large-eddy simulations (LES) of oceanic deep convection resulting from localized cooling applied at the surface are presented. The present LES exhibit a very good quantitative agreement with the laboratory experiments by Maxworthy and Narimousa (1994 J. Phys. Oceanogr. 24 865–87). As with the experimental observations, a critical Rossby number such that (Ro *)1/2 ≈ 0.28 is observed under which the flow is dominated by the rotation effects. Three very distinct flow regimes are identified: low, moderate and high rotation regimes. A detailed investigation of the vertical vorticity generation mechanisms demonstrates that the vertical stretching constitutes the main production term and it initiates an asymmetry between cyclonic and anticyclonic vertical vorticity. For the moderate rotation regime, average quantities show a dominance of cyclonic vorticity. However, a more detailed investigation based, in particular, on flow animations reveals the presence of an anticyclonically rotating cold bottom c...

We first recall the concepts of spectral eddy viscosity and diffusivity, derived from the two-point closures of turbulence, in the framework of large-eddy simulations in Fourier space. The case of a spectrum which does not decrease as (Ck is Kolmogorov's constant), with α ≈ 1.32.

International audience; In this paper, Unsteady RANS (URANS) simulations and Large Eddy Simula- tions (LES) in the draft tube of a bulb turbine are presented with the objective to understand and locate the head losses in this turbine component. Three operating points of the turbine are considered. Numerical results are compared with experimental velocity measurements for validation. Thanks to a detailed analysis of the energy balance in the draft tube, the physical and hydrodynamic phenomena responsible for head losses in the draft tube are identified. Head losses are due to transfer of mean kinetic energy to the turbulent flow and viscous dissipation of kinetic energy. This occurs mainly in the central vortex structure and next to the walls in the draft tube. Head losses prediction is found to be dependent on the turbulence model used in the simulations, especially in URANS simulations. Using this analysis, the evolution of head losses between the three operating points is understood.

Flow prediction in a bulb turbine draft tube is conducted for two operating points using Unsteady RANS (URANS) simulations and Large Eddy Simulations (LES). The inlet boundary condition of the draft tube calculation is a rotating two dimensional velocity profile exported from a RANS guide vane- runner calculation. Numerical results are compared with experimental data in order to validate the flow field and head losses prediction. Velocity profiles prediction is improved with LES in the center of the draft tube compared to URANS results. Moreover, more complex flow structures are obtained with LES. A local analysis of the predicted flow field using the energy balance in the draft tube is then introduced in order to detect the hydrodynamic instabilities responsible for head losses in the draft tube. In particular, the production of turbulent kinetic energy next to the draft tube wall and in the central vortex structure is found to be responsible for a large part of the mean kinetic energy dissipation in the draft tube and thus for head losses. This analysis is used in order to understand the differences in head losses for different operating points. The numerical methodology could then be improved thanks to an in-depth understanding of the local flow topology.

We propose a new mixed model for Large Eddy-Simulation based on the 3D spatial velocity increment. This approach blends the non-linear properties of the Increment model (Brun & Friedrich (2001)) with the eddy viscosity characteristics of the Structure Function model (Metais & Lesieur (1992)). The behaviour of this subgrid scale model is studied both via a priori tests of a plane jet at ReH=3000 and Large Eddy-Simulation of a round jet at ReD=25000. This approach allows to describe both forward and backward energy transfer encountered in transitional shear flows.