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In this manuscript, a general formulation of 3-dimensional compressible fluids based on the port-Hamiltonian framework is presented, both for isentropic and non-isentropic assumptions, describing the energy flux between the mechanical, chemical, and thermal domains, with an explicit characterization of the first and the second law of thermodynamics. For isentropic fluids, the conversion of kinetic energy into heat by viscous friction is considered as energy dissipation associated with the rotation and compression of the fluid. A dissipative port-Hamiltonian formulation is derived for this class of fluids, including vorticity boundary conditions in the port variables. For non-isentropic fluids, we consider a fluid mixture with multiple chemical reactions. To describe the energy fluxes, we propose a pseudo port-Hamiltonian formulation, which includes the rate of irreversible entropy creation by heat flux, chemical reaction, diffusion of matter, and viscous friction.

International audience; When two liquid droplets approach at negligible velocity in air, their coalescence spontaneously occurs by jump-to-contact instability and a connecting bridge joining the two facing interfaces at the nanoscale is created. We report experimental investigations of the expansion of this initial bridge by means of high-speed imaging. By considering droplets of water, polydimethylsiloxane or paraffin of a few hundred micrometers, we investigate regimes where inertia takes a major role. Depending on the Ohnesorge number Oh, the dynamics of the bridge differs a lot. For Oh ≈ 1, the initial flow is rapidly attenuated and the connecting bridge between the two droplets adopts a smooth parabolic shape. The maximum interface curvature and the minimum liquid pressure remain at the bridge centre. The expansion is thus caused by the capillary pressure that drives the fluid towards the center. At small Oh, in the inertial regime, the length of the initial bridge grows at constant speed and the bridge expansion can be described by the propagation of non-dispersive capillary wave packets. The central part of the bridge takes a cylindrical shape connected to the droplets by a narrow region of very large curvature. At the resolved scale, the interface exhibits slope discontinuities. By considering dihedral potential flows that result of the presence of the slope discontinuities, we show that the apparent angle made by the interface controls the flow-rate that enters the bridge and thus determines its radial expansion.

Direct numerical simulations are performed to assess the aerodynamic performance of three-dimensional wings undergoing asymmetric hovering flapping flight. A large number of flapping kinematics is investigated, varying the pitch rate and the upstroke and downstroke angles of attack. We show that, for all cases, time-averaged performance is driven, to leading order, by the mean angle of attack over a flapping period despite the increased contribution of drag to vertical force with increased stroke plane angle. We hence suggest that asymmetric hovering is not intrinsically more efficient than normal hovering, conversely to what has been previously reported in the literature. This may explain the under-representation of this flight mode in nature.

International audience; We study the velocity field in the liquid phase during the drying of a porous medium in the capillaritydominated regime with evaporation from the top surface. A simple mass balance in the continuum framework leads to a linear variation of the filtration velocity across the sample. By contrast, the instantaneous slice-averaged velocity field determined from pore network simulations leads to step velocity profiles. The vertical velocity profile is almost constant near the evaporative top surface and zero close to the bottom of the sample. The relative extent of the two regions with constant velocity is dictated by the position of the most unstable meniscus. It is shown that the continuum and pore network results can be reconciled by averaging the velocity field obtained from the pore network simulations over time. This opens up interesting prospects regarding the transport of dissolved species during drying. Also, the study reveals the existence of an edge effect, which is not taken into account in the classical continuum models of drying.

International audience; We present a linear optimal perturbation analysis of streamwise invariant disturbances evolving in parallel round jets. The potential for transient energy growth of perturbations with azimuthal wavenumber $m\geq1$ is analyzed for different values of Reynolds number Re. Two families of steady (frozen) and unsteady (diffusing) base flow velocity profiles have been used, for different aspect ratios $\alpha=R/\theta$, where $R$ is the jet radius and $\theta$ the shear layer momentum thickness. Optimal initial conditions correspond to infinitesimal streamwise vortices, which evolve transiently to produce axial velocity streaks, whose spatial structure and intensity depend on base flow and perturbation parameters. Their dynamics can be characterized by a maximum optimal value of the energy gain $G_{opt}$, reached at an optimal time $\tau_{opt}$ after which the perturbations eventually decays. Optimal energy gain and time are shown to be respectively proportional to Re^2 and Re, regardless of the frozen or diffusing nature of the base flow. Besides, it is found that the optimal gain scales like $G_{opt}\propto 1/m^3$ for all $m$ except $m=1$. This quantitative difference for azimuthal wavenumber $m=1$ is shown to be based on the nature of transient mechanisms. For $m = 1$ perturbations, the shift-up effect [J. I. Jiménez-González et al., “Modal and non-modal evolution of perturbations for parallel round jets,” Phys. Fluids 27, 044105-1–044105-19 (2015)] is active: an initial streamwise vorticity dipole induces a nearly uniform velocity flow in the jet core, which shifts the whole jet radially. By contrast, optimal perturbations with $m\geq2$, are concentrated along the shear layer, in a way that resembles the classical lift-up mechanism in wall-shear flows. The $m=1$ shift-up effect is more energetic than the $m\geq2$ lift-up, but it is slower, with optimal times considerably shorter in the case of $m\geq2$ disturbances. This suggests that these perturbations may emerge very quickly in the flow when injected as initial conditions. When the base flow diffuses, the large timescale for $m=1$ disturbances allows the shear layer to spread and the jet core velocity to decrease substantially, thus lowering the values of corresponding optimal gain and time. For $m\geq2$, results are less affected, since the shorter transient dynamics does not leave room for significant modifications of the base flow velocity profiles, and the scaling laws obtained in the frozen case are recovered. Nevertheless, base flow diffusion hinders the transient growth, as a consequence of a weaker component-wise non-normality and a smoother, radially spread structure of optimal disturbances.

International audience; Terrestrial and microgravity flow boiling experiments were carried out with the same test rig, comprising a locally heated artificial cavity in the center of a channel near the frontal edge of an intrusive glass bubble generator. Bubble shapes were in microgravity generally not far from those of truncated spheres,which permitted the computation of inertial lift and drag from potential flow theory for truncated spheres approximating the actual shape. For these bubbles, inertial lift is counteracted by drag and both forces are of the same order of magnitude as g-jitter. A generalization of the Laplace equation is found which applies to a deforming bubble attached to a plane wall and yields the pressure difference between the hydrostatic pressures in the bubble and at the wall, �p. A fully independent way to determine the overpressure p is given by a second Euler-Lagrange equation. Relative differences have been found to be about 5% for both terrestrial and microgravity bubbles. A way is found to determine the sum of the two counteracting major force contributions on a bubble in the direction normal to the wall from a single directly measurable quantity. Good agreement with expectation values for terrestrial bubbles was obtained with the difference in radii of curvature averaged over the liquid-vapor interface, �(1/R2 − 1/R1)�, multiplied with the surface tension coefficient, σ. The new analysis methods of force components presented also permit the accounting for a surface tension gradient along the liquid-vapor interface. No such gradients were found for the present measurements.

International audience; Laminar pressure-driven suspensionflows are studied in the situation of neutrally buoyant particles at finite Reynolds number. The numerical method is validated for homogeneous particle distribution (no lateral migration across the channel): the increase of particle slip velocities and particle stress with inertia and concentration is in agreement with former works in the literature. In the case of a two-phase channel flow with freely moving particles, migration towards the channel walls due to the Segré-Silberberg effect is observed, leading to the development of a non-uniform concentration profile in the wall-normal direction (the concentration peaks in the wall region and tends towards zero in the channel core). The particle accumulation in the region of highest shear favors the shear-induced particle interactions and agitation, the profile of which appears to be correlated to the concentration profile. A 1D model predicting particle agitation, based on the kinetic theory of granular flows in the quenched state regime when Stokes number St = O(1) and from numerical simulations when St < 1, fails to reproduce the agitation profile in the wall normal direction. Instead, the existence of secondary flows is clearly evidenced by long time simulations. These are composed of a succession of contra-rotating structures, correlated with the development of concentration waves in the transverse direction. The mechanism proposed to explain the onset of this transverse instability is based on the development of a lift force induced by spanwise gradient of the axial velocity fluctuations. The establishment of the concentration profile in the wall-normal direction therefore results from the combination of the mean flow Segré-Silberberg induced migration, which tends to stratify the suspension and secondary flows which tend to mix the particles over the channel cross section.

International audience; The dynamic behavior of convective motion in a confined porous medium saturated by a pure fluid under the action of mechanical vibration is studied. A redefinition of vibrational Rayleigh number is proposed from which we distinguish the domain of validity of the mean flow. The weakly nonlinear stability analysis performed demonstrates, contrary to published results, that the bifurcation is of supercritical nature and the subcritical branch does not exist. It is emphasized that, in order to find the thermal behavior of the system for the onset of convection, we should separate the vibrational effect from the thermal effect involving the temperature difference.

A linear stability analysis is presented for the Kelvin–Helmholtz instability in a Hele-Shaw cell, an analysis based on the Navier–Stokes equation to improve on the previous Euler–Darcy study that Gondret and Rabaud [Phys. Fluids 9, 3267 (1997)] made of their own experiments.

The turbulent flow inside a rotating channel provided with transverse ribs along one wall is studied by means of two-dimensional time-resolved particle image ve- locimetry. The measurement set-up is mounted on the same rotating disk with the test section, allowing to obtain the same accuracy and resolution as in a non-rotating rig. The Reynolds number is 15 000, and the rotation number is 0.38. As the ribbed wall is heated, both the Coriolis force and the centrifugal force play a role in the fluid dynamics. The mean velocity fields highlight the major impact of the rotational buoyancy (characterized by a buoyancy number of 0.31) on the flow along the lead- ing side of the duct. In particular, since the flow is directed radially outward, the near-wall layers experience significant centripetal buoyancy. The recirculation area behind the obstacles is enlarged to the point of spanning the whole inter-rib space. Also the turbulent fluctuations are significantly altered, and overall augmented, with respect to the non-buoyant case, resulting in higher turbulence levels far from the rib. On the other hand the centrifugal force has little or no impact on the flow along the trailing wall. Vortex identification, proper orthogonal decomposition, and two-point correlations are used to highlight rotational effects, and in particular to determine the dominant scales of the turbulent unsteady flow, the time-dependent behavior of the shear layer and of the recirculation bubble behind the wall-mounted obstacles, the lifetime and advection velocity of the coherent structures.

International audience; This article investigates the structural stability and sensitivity properties of the confined turbulent wake behind an elongated D-shaped cylinder of aspect-ratio 10 at Re = 32 000. The stability analysis is performed by linearising the incompressible Navier-Stokes equations around the numerically computed and the experimentally measured mean flows. We found that the vortex-shedding frequency is very well captured by the leading unstable global mode, especially when the additional turbulent diffusion is modelled in the stability equations by means of a frozen eddy-viscosity approach. The sensitivity maps derived from the computed and the measured mean flows are then compared, showing a good qualitative agreement. The careful inspection of their spatial structure highlights that the highest sensitivity is attained not only across the recirculation bubble but also at the body blunt-edge, where tiny pockets of maximum receptivity are found. The impact of the turbulent diffusion on the obtained results is investigated. Finally, we show how the knowledge of the unstable adjoint global mode of the linearised mean-flow dynamics can be exploited to design an active feedback control of the unsteady turbulent wake, which leads, under the adopted numerical framework, to completely suppress its low-frequency oscillation.

International audience; Analysis of the helical vortices measured behind a model wind turbine in a water channel are reported. Phase-locked measurements using planar particle image ve- locimetry are taken behind a Glauert rotor to investigate the evolution and breakdown of the helical vortex structures. Existing linear stability theory predicts helical vortex filaments to be susceptible to three unstable modes. The current work presents tip and root vortex evolution in the wake for varying tip speed ratio and shows a breaking of the helical symmetry and merging of the vortices due to mutual inductance between the vortical filaments. The merging of the vortices is shown to be steady with rotor phase, however, small-scale non-periodic meander of the vortex positions is also ob- served. The generation of the helical wake is demonstrated to be closely coupled with the blade aerodynamics, strongly influencing the vortex properties which are shown to agree with theoretical predictions of the circulation shed into the wake by the blades. The mutual inductance of the helices is shown to occur at the same non-dimensional wake distance.

International audience; We consider the growth rate of the height of the connecting bridge in rapid surface-tension-driven coalescence of two identical droplets attached on a partially wetting substrate. For a wide range of contact angle values, the height of the bridge grows with time following a power law with a universal exponent of 2/3, up to a threshold time, beyond which a 1/2 exponent results, that is known for coalescence of freely-suspended droplets. In a narrow range of contact angle values close to 90◦, this threshold time rapidly vanishes and a 1/2 exponent results for a 90◦ contact angle. The argument is confirmed by three-dimensional numerical simulations based on a diffuse interface method with adaptive mesh refinement and a volume-of-fluid method.

International audience; In this paper, evaporation of a volatile, perfectly wettingliquid confined in an initially filled capillary tube of square internal cross section is studied, when conditions are such that liquid films develop along the tube internal corners under the effect of capillary forces, as the bulk meniscus recedes inside the tube. More precisely, the emphasis is on the moment when the liquid film tips depin from the tube top once they have reached a critical length, a phenomenon observed in experiments. A model taking into account liquid corner flow and phase change at the film tip is proposed in order to predict the critical film length at depinning. The model is found to be in good agreement with experimental data and highlights that the critical film length depends strongly on the degree of roundedness of the tube internal corners. Thus, it is crucial to take into account this purely geometrical factor when modeling evaporation in polygonal capillary tubes or, more generally, corner flows in a rounded wedge.

International audience; An experimental study of a turbulent free-surface shallow flow over an inclined sinusoidal bottom with a fixed corrugation amplitude is presented. A parametric analysis is performed by varying both the inclination angle and the Reynolds number. We show that a "Pulse-Waves" regime, dominant for Reynolds smaller than 4 000, coexists with a "Roll-Waves" regime, which becomes dominant above this value. The relative energy of the waves is quantified in the parameter space. At Reynolds numbers larger than 8 000, these wave instabilities disappear.

International audience; The current work reports on a numerical and experimental study of the evolution of decaying dipolar vortices in a shallow fluid layer. The dynamics and the structure of such vortices are investigated as a function of both their Reynolds number Re and the aspect ratio of vertical and horizontal length scales δ. By quantifying the strength of the secondary motions (vertical motions and nonzero horizontal divergence) with respect to the swirling motions of the primary vortex cores, it was found that the three-dimensionality of a shallow (δ << 1) dipolar vortex only depends on a single parameter: δ²Re. Depending on the value of this parameter, three flow regimes are observed for shallow dipolar vortices: (1) a quasi-two-dimensional regime where the structure of the dipolar vortex remains almost unchanged throughout its lifetime, (2) a transitional regime where the structure presents some three-dimensional characteristics but remains coherent, and (3) a three-dimensional regime where the structure of the dipolar vortex acquires a complicated three-dimensional shape with a persistent spanwise vortex at its front.

International audience; High-transonic unsteady flows around an airfoil at zero angle of incidence and moderate Reynolds numbers are characterized by an unsteadiness induced by the von Kármán instability and buffet phenomenon interaction. These flows are investigated by means of low-dimensional modeling approaches. Reduced-order dynamical systems based on proper orthogonal decomposition are derived from a Galerkin projection of two-dimensional compressible Navier-Stokes equations. A specific formulation concerning density and pressure is considered. Reduced-order modeling accurately predicts unsteady transonic phenomena.

International audience; In this paper, we study the effect of a homogeneous longitudinal through flow on the onset of convection in a horizontal porous layer saturated by a binary fluid and heated from below or above. The layer boundaries are subjected to a constant heat flux. The investigation is made by taking the Soret effect into account. It is found that in the case of positive separation ratio when the denser component moves toward the cooler wall, through flow has no effect on the stability threshold but exerts an orientating effect on the convective patterns. For negative separation ratio, a strong destabilization occurs of the spatially homogeneous state with respect to long-wave disturbances. The stability range for long-wavelength convective rolls is defined.

International audience; Longitudinal low-frequency thermoacoustic unstable modes in combustion chambers have been intensively studied experimentally, numerically, and theoretically, leading to significant progress in both understanding and controlling these acoustic modes. However, modern annular gas turbines may also exhibit azimuthal modes, which are much less studied and feature specific mode structures and dynamic behaviors, leading to more complex situations. Moreover, dealing with 10–20 burners mounted in the same chamber limits the use of high fidelity simulations or annular experiments to investigate these modes because of their complexity and costs. Consequently, for such circumferential acoustic modes, theoretical tools have been developed to uncover underlying phenomena controlling their stability, nature, and dynamics. This review presents recent progress in this field. First, Galerkin and network models are described with their pros and cons in both the temporal and frequency framework. Then, key features of such acoustic modes are unveiled, focusing on their specificities such as symmetry breaking, non-linear modal coupling, forcing by turbulence. Finally, recent works on uncertainty quantifications, guided by theoretical studies and applied to annular combustors, are presented. The objective is to provide a global view of theoretical research on azimuthal modes to highlight their complexities and potential.

International audience; A global Linear Stability Analysis (LSA) of the three-dimensional flow past a nearly oblate spheroidal gas bubble rising in still liquid is carried out, considering the actual bubble shape and terminal velocity obtained for various sets of Galilei (Ga) and Bond (Bo) numbers in axisymmetric numerical simulations. Hence, this study extends the stability analysis approach of Tchoufag et al. [“Linear stability and sensitivity of the flow past a fixed oblate spheroidal bubble,” Phys. Fluids 25, 054108 (2013) and “Linear instability of the path of a freely rising spheroidal bubble,” J. Fluid Mech. 751, R4 (2014)] (which considered perfectly spheroidal bubbles with an arbitrary aspect ratio) to the case of bubbles with a realistic fore-aft asymmetric shape (i.e., a flatter front and a more rounded rear). The critical curve separating stable and unstable regimes for the straight vertical path is obtained both in the (Ga,Bo) and the (Re,χ) planes, where Re is the bubble Reynolds number and χ its aspect ratio (i.e., the major-to-minor axes length ratio). This provides new insight into the effect of the shape asymmetry on the wake instability of bubbles held fixed in a uniform stream and on the path instability of freely rising bubbles, respectively. For the range of Ga and Bo explored here, we find that the flow past a bubble with a realistic shape is generally more stable than that past a perfectly spheroidal bubble with the same aspect ratio. This study also provides the first critical curve for the onset of path instability that can be compared with experimental observations. The tendencies revealed by this critical curve agree well with those displayed by available data. The quantitative agreement is excellent for O(1) Bond numbers. However, owing to two simplifying assumptions used in the LSA scheme, namely, the steadiness of the base state and the uncoupling between the bubble shape and the flow disturbances, quantitative discrepancies (up to 20%–30%) with experimental threshold values of the Galilei number remain for both small and large Bond numbers.

International audience; We present an analytical and numerical stability analysis of Soret-driven convection in a porous cavity saturated by a binary fluid. Both the mechanical equilibrium solution and the monocellular flow obtained for particular ranges of the physical parameters of the problem are considered. The porous cavity, bounded by horizontal infinite or finite boundaries, is heated from below or from above. The two horizontal plates are maintained at different constant temperatures while no mass flux is imposed. The influence of the governing parameters and more particularly the role of the separation ratio, characterizing the Soret effect and the normalized porosity, are investigated theoretically and numerically. From the linear stability analysis, we find that the equilibrium solution loses its stability via a stationary bifurcation or a Hopf bifurcation depending on the separation ratio and the normalized porosity of the medium. The role of the porosity is important, when it decreases, the stability of the equilibrium solution is reinforced. For a cell heated from below, the equilibrium solution loses its stability via a stationary bifurcation when the separation ratio >0(Le,), while for 0, while a stationary or an oscillatory bifurcation occurs if mono the monocellular flow loses stability via a Hopf bifurcation. As the Rayleigh number increases, the resulting oscillatory solution evolves to a stationary multicellular flow. For a cell heated from above and

Sedimenting and sheared bidisperse homogeneous suspensions of non-Brownian particles are investigated by numerical simulations in the limit of vanishing small Reynolds number and negligible inertia of the particles. The numerical approach is based on the solution of the three-dimensional Stokes equations forced by the presence of the dispersed phase. Multi-body hydrodynamic interactions are achieved by a low order multipole expansion of the velocity perturbation. The accuracy of the model is validated on analytic solutions of generic flow configurations involving a pair of particles. The first part of the paper aims at investigating the dynamics of monodisperse and bidisperse suspensions embedded in a linear shear flow. The macroscopic transport properties due to hydrodynamic and non hydrodynamic interactions (short range repulsion force) show good agreement with previous theoretical and experimental works on homogeneous monodisperse particles. Increasing the volumetric concentration of the suspension leads to an enhancement of particle fluctuations and self-diffusion. The velocity fluctuation tensor scales linearly up to 15% concentration. Multi-body interactions weaken the correlation of velocity fluctuations and lead to a diffusion like motion of the particles. Probability density functions show a clear transition from Gaussian to exponential tails while the concentration decreases. The behavior of bidisperse suspensions is more complicated, since the respective amount of small and large particles modifies the overall response of the flow. Our simulations show that, for a given concentration of both species, when the size ratio varies from 1 to 2.5, the fluctuation level of the small particles is strongly enhanced. A similar trend is observed on the evolution of the shear induced self-diffusion coefficient. Thus for a fixed and total concentration, increasing the respective volume fraction of large particles can double the velocity fluctuation of small particles. In the second part of the paper, the sedimentation of a single test particle embedded in a suspension of monodisperse particles allows the determination of basic hydrodynamic interactions involved in a bidisperse suspension. Good agreement is achieved when comparing the mean settling velocity and fluctuations levels of the test sphere with experiments. Two distinct behaviors are observed depending on the physical properties of the particle. The Lagrangian velocity autocorrelation function has a negative region when the test particle has a settling velocity twice as large as the reference velocity of the surrounding suspension. The test particle settles with a zig-zag vertical trajectory while a strong reduction of horizontal dispersion occurs. Then, several configurations of bidisperse settling suspensions are investigated. Mean velocity depends on concentration of both species, density ratio and size ratio. Results are compared with theoretical predictions at low concentration and empirical correlations when the assumption of a dilute regime is no longer valid. For particular configurations, a segregation instability sets in. Columnar patterns tend to collect particles of the same species and eventually a complete separation of the suspension is observed. The instability threshold is compared with experiments in the case of suspensions of buoyant and heavy spheres. The basic features are well reproduced by the simulation model.

The problem of the diffusion of turbulence from a plane source is addressed in the context of two-equation eddy-viscosity models and Reynolds-stress-transport models. In the steady state, full analytic solutions are given. At second order, they provide the equilibrium value of the anisotropy level obtained with different combinations of return-to-isotropy and turbulent-diffusion schemes and confirm the results obtained by Straatman et al. [AIAA J. 36, 929 (1998)] in an approximate analysis. In addition, all the characteristics of the turbulence decrease can be determined and it is shown that a special constraint on the value of the modeling constants should hold if turbulence fills the whole surrounding space. In a second step, precise results can be given for the unsteady model problem at the first-order-closure level. The evolution cannot be described with a single set of characteristic scales and one has to distinguish the cases of short and large times. In the short-time regime, the flow is governed by the characteristic scales of turbulence at the source and contamination of the flow proceeds as t^1/2. At large times, the flow is governed by time-dependent characteristic scales that correspond to the solution of the steady problem at the instantaneous location of the front. Contamination of the flow proceeds as a power of time that can be related to the value of the modeling constants. The role of a combination of these constants is emphasized whose value can be specified to produce a solution that matches simultaneously the experimental data for the decrease of turbulent kinetic energy in the steady state and the exponent of the propagation velocity in the transient regime.

International audience; We present a numerical and analytical study of diffusive convection in a rectangular saturated porous cell heated from below and subjected to high frequency vibration. The configuration of the Horton–Rogers–Lapwood problem is adopted. The classical Darcy model is shown to be insufficient to describe the vibrational flow correctly. The relevant system is described by time-averaged Darcy–Boussinesq equations. These equations possess a pure diffusive steady equilibrium solution provided the vibrations are vertical. This solution is linearly stable up to a critical value of the stability parameter depending on the strength of the vibration. The solutions in the neighborhood of the bifurcation point are described analytically as a function of the strength of vibration, and the larger amplitude states are computed numerically using a spectral collocation method. Increasing the vibration amplitude delays the onset of convection and may even create subcritical solutions. The majority of primary bifurcations are of a special type of symmetry-breaking bifurcation even if the system is subjected to vertical vibration

International audience; In the present work, we study the onset of double-diffusive convective regimes in a tilted rectangular cavity, filled with a porous medium, saturated by a binary fluid. Two opposite walls are maintained at different but uniform temperatures and concentrations while the two other walls are impermeable and adiabatic. When the thermal and solutal buoyancy forces are comparable in intensity but have opposite signs, the motionless double-diffusive regime with linear temperature and concentration profiles is a solution of the problem. The first part of the study consists of a linear stability analysis of the motionless regime. We determine the critical thermal Rayleigh number for the onset of stationary and oscillatory convection. Indeed, we point out that there exist primary Hopf bifurcations for the studied problem in porous medium, while in the same configuration with a fluid medium only primary stationary bifurcations exist. When the first primary bifurcation creates a steady state branch of solutions, the bifurcation is either transcritical or pitchfork depending on the aspect ratio, A and the tilt, φ of the cavity. The onset of oscillatory convection (Hopf bifurcation) depends not only on A and φ but also on the Lewis number, Le and the normalized porosity, ε. Then, we determine the parts of the (Le, ε) parameter space for which the first primary bifurcation is stationary or oscillatory. In particular, it is found that in the case Le⩾1 and for ε Le21 only stationary primary bifurcations exist. In the case Le

International audience; We compute the spatial optimal energy amplification of steady inflow perturbations in a non-parallel wake and analyse their stabilizing action on the global mode instability. The optimal inflow perturbations, which are assumed spanwise periodic and varicose, consist in streamwise vortices that induce the downstream spatial transient growth of streamwise streaks. The maximum energy amplification of the streaks increases with the spanwise wavelength of the perturbations, in accordance with previous results obtained for the temporal energy growth supported by parallel wakes. A family of increasingly streaky wakes is obtained by forcing optimal inflow perturbations of increasing amplitude and then solving the nonlinear Navier-Stokes equations. We show that the linear global instability of the wake can be completely suppressed by forcing optimal perturbations of sufficiently large amplitude. The attenuation and suppression of self-sustained oscillations in the wake by optimal 3D perturbations is confirmed by fully nonlinear numerical simulations. We also show that the amplitude of optimal spanwise periodic (3D) perturbations of the basic flow required to stabilize the global instability is much smaller than the one required by spanwise uniform (2D) perturbations despite the fact that the first order sensitivity of the global eigenvalue to basic flow modifications is zero for 3D spanwise periodic modifications and non-zero for 2D modifications. We therefore conclude that first-order sensitivity analyses can be misleading if used far from the instability threshold, where higher order terms are the most relevant

International audience; We study the distribution of ions in a drying porous medium up to the formation of first crystals at the surface. The study is based on comparisons between numerical simulations and experiments with packings of glass beads. The experimental configuration, which is representative of many previous drying experiments, is characterized by the formation of an efflorescence fairy ring at the surface of the porous medium. The preferential formation of crystals at the periphery is explained by the combined effect of higher evaporation fluxes at the surface periphery, as in the classical coffee ring problem, and variations in the porosity near the wall bordering the packing. It is shown that both effects have a great impact on the time marking the occurrence of first crystals, which is referred to as the first crystallization time. The experiments indicate that the first crystallization time increases with a decreasing bead size for a given initial ion concentration. This is explained by the variation with bead size of the characteristic size of the near wall region where a preferential desaturation of the sample occurs as a result of the porosity increase near the wall. The study also reveals a significant salt supersaturation effect. This represents a noticeable fact in relation with salt weathering issues.

The presence of finite-size particles in a channel flow close to the laminar-turbulent transition is simulated with the Force Coupling Method which allows two-way coupling with the flow dynamics. Spherical particles with channel height-to-particle diameter ratio of 16 are initially randomly seeded in a fluctuating flow above the critical Reynolds number corresponding to single phase flow relaminarization. When steady-state is reached, the particle volume fraction is homogeneously distributed in the channel cross-section (ϕ ≅ 5%) except in the near-wall region where it is larger due to inertia-driven migration. Turbulence statistics (intensity of velocity fluctuations, small-scale vortical structures, wall shear stress) calculated in the fully coupled two-phase flow simulations are compared to single-phase flow data in the transition regime. It is observed that particles increase the transverse r.m.s. flow velocity fluctuations and they break down the flow coherent structures into smaller, more numerous and sustained eddies, preventing the flow to relaminarize at the single-phase critical Reynolds number. When the Reynolds number is further decreased and the suspension flow becomes laminar, the wall friction coefficient recovers the evolution of the laminar single-phase law provided that the suspension viscosity is used in the Reynolds number definition. The residual velocity fluctuations in the suspension correspond to a regime of particulate shear-induced agitation.

Natural doubly diffusive convection in a three-dimensional vertical enclosure with square cross-section in the horizontal is studied. Convection is driven by imposed temperature and concentration differences between two opposite vertical walls. These are chosen such that a pure conduction state exists. No-flux boundary conditions are imposed on the remaining four walls, with no-slip boundary conditions on all six walls. Numerical continuation is used to compute branches of spatially localized convection. Such states are referred to as convectons. Two branches of three-dimensional convectons with full symmetry bifurcate simultaneously from the conduction state and undergo homoclinic snaking. Secondary bifurcations on the primary snaking branches generate secondary snaking branches of convectons with reduced symmetry. The results are complemented with direct numerical simulations of the three-dimensional equations.

International audience; Buoyancy-driven turbulent mixing of fluids of slightly different densities [At = Δρ/(2〈ρ〉) = 1.15×10−2] in a long circular tube tilted at an angle θ = 15° from the vertical is studied at the local scale, both experimentally from particle image velocimetry and laser induced fluorescence measurements in the vertical diametrical plane and numerically throughout the tube using direct numerical simulation. In a given cross section of the tube, the axial mean velocity and the mean concentration both vary linearly with the crosswise distance z from the tube axis in the central 70% of the diameter. A small crosswise velocity component is detected in the measurement plane and is found to result from a four-cell mean secondary flow associated with a nonzero streamwise component of the vorticity. In the central region of the tube cross section, the intensities of the three turbulent velocity fluctuations are found to be strongly different, that of the streamwise fluctuation being more than twice larger than that of the spanwise fluctuation which itself is about 50% larger than that of the crosswise fluctuation. This marked anisotropy indicates that the turbulent structure is close to that observed in homogeneous turbulent shear flows. Still in the central region, the turbulent shear stress dominates over the viscous stress and reaches a maximum on the tube axis. Its crosswise variation is approximately accounted for by a mixing length whose value is about one-tenth of the tube diameter. The momentum exchange in the core of the cross section takes place between its lower and higher density parts and there is no net momentum exchange between the core and the near-wall regions. A sizable part of this transfer is due both to the mean secondary flow and to the spanwise turbulent shear stress. Near-wall regions located beyond the location of the extrema of the axial velocity (|z|≳0.36 d) are dominated by viscous stresses which transfer momentum toward (from) the wall near the top (bottom) of the tube.

We analyze the results of a direct numerical simulation of the turbulent buoyancy-driven flow that sets in after two miscible fluids of slightly different densities have been initially superimposed in an unstable configuration in an inclined circular pipe closed at both ends. In the central region located midway between the end walls, where the flow is fully developed, the resulting mean flow is found to exhibit nonzero secondary velocity components in the tube cross section. We present a detailed analysis of the generation mechanism of this secondary flow which turns out to be due to the combined effect of the lateral wall and the shear-induced anisotropy between the transverse components of the turbulent velocity fluctuations.

The interaction between a free-slip surface with unsheared but sustained turbulence is investigated in a series of direct numerical simulations. By changing (i) the distance between the (plane) source of turbulence and the surface, and (ii) the value of the viscosity, a set of five different data sets has been obtained in which the value of the Reynolds-number varies by a factor of 4. The observed structure of the interaction layer is in agreement with current knowledge, being made of three embedded sublayers: a blockage layer, a slip layer, and a Kolmogorov layer. Practical measures of the different thicknesses are proposed that lead to a new Reynolds-number scaling based on easy-to-evaluate surface quantities. This scaling is consistent with previous proposals but makes easier the comparison between free-surface flows when they differ by the characteristics of the distant turbulent field. Its use will be straightforward in a turbulence-modeling framework.

The evolution of the concentration and flow fields resulting from the gravitational mixing of two interpenetrating miscible fluids placed in a tilted tube or channel is studied by using direct numerical simulation. Three-dimensional (3D) geometries, including a cylindrical tube and a square channel, are considered as well as a purely two-dimensional (2D) channel. Striking differences between the 2D and 3D geometries are observed during the long-time evolution of the flow. We show that these differences are due to those existing between the 2D and 3D dynamics of the vorticity field. More precisely, in two dimensions, the strong coherence and long persistence of vortices enable them to periodically cut the channels of pure fluid that feed the front. In contrast, in 3D geometries, the weaker coherence of the vortical motions makes the segregational effect due to the transverse component of buoyancy strong enough to preserve a fluid channel near the front of each current. This results in three different regimes for the front velocity (depending on the tilt angle), which is in agreement with the results of a recent experimental investigation. The evolution of the front topology and the relation between the front velocity and the concentration jump across the front are investigated in planar and cylindrical geometries and highlight the differences between 2D and 3D mixing dynamics.

We investigate the migration of bubbles in several flow patterns occurring within the gap between a rotating inner cylinder and a concentric fixed outer cylinder. The time-dependent evolution of the two-phase flow is predicted through three-dimensional Euler-Lagrange simulations. Lagrangian tracking of spherical bubbles is coupled with direct numerical simulation of the Navier-Stokes equations. We assume that bubbles do not influence the background flow (one-way coupling simulations). The force balance on each bubble takes into account buoyancy, added-mass, viscous drag and shear-induced lift forces. For increasing velocities of the rotating inner cylinder, the flow in the fluid gap evolves from the purely azimuthal steady Couette flow to Taylor toroidal vortices and eventually a wavy vortex flow. The migration of bubbles is highly dependent on the balance between buoyancy and centripetal forces (mostly due to the centripetal pressure gradient) directed toward the inner cylinder and the vortex cores. Depending on the rotation rate of the inner cylinder, bubbles tend to accumulate alternatively along the inner wall, inside the core of Taylor vortices or at particular locations within the wavy vortices. A stability analysis of the fixed points associated with bubble trajectories provides a clear understanding of their migration and preferential accumulation. The location of the accumulation points is parameterized by two dimensionless parameters expressing the balance of buoyancy, centripetal attraction toward the inner rotating cylinder, and entrapment in Taylor vortices. A complete phase diagram summarizing the various regimes of bubble migration is built. Several experimental conditions considered by Djéridi et al.1 are reproduced; the numerical results reveal a very good agreement with the experiments. When the rotation rate is further increased, the numerical results indicate the formation of oscillating bubble strings, as observed experimentally by Djéridi et al.2. After a transient state, bubbles collect at the crests or troughs of the wavy vortices. An analysis of the flow characteristics clearly indicates that bubbles accumulate in the low-pressure regions of the flow field.

We report a study of the capillary pinching of a gas bubble by a wetting liquid inside a pinched channel. The capillary pinching induces very reproducible bubbling, at a very well-defined frequency. There are two regimes associated with drip and jet bubbling. In the latter, we show that highly monodispersed bubbles are formed by our pinched channel. The dynamics of the bubble formation also shows two distinct regimes: a long-duration elongation of the air bubble and a rapid relaxation of the interface after interface breakup. The slow regime depends on the flux imposed and the channel geometry. The rapid deformation dynamic regime depends very weakly on the boundary conditions. Scaling arguments are proposed in the context of the lubrication approximation to describe the two regimes.

“Oseen–Poiseuille” equations are developed from an asymptotic formulation of the three-dimensional Navier–Stokes equations in order to study the influence of weak inertia on flows between rough surfaces. The impact of the first correction on macroscopic flow due to inertia has been determined by solving these equations numerically. From the numerical convergence of the asymptotic expansion to the three-dimensional Navier–Stokes flows, it is shown that, at the macroscopic scale, the quadratic correction to the Reynolds equation in the weak-inertial regime vanishes generalizing a similar result in porous media.

The possibility to take into account the effects of the Coriolis acceleration on turbulence is examined in the framework of two-equation eddy-viscosity models. General results on the physical consistency of such turbulence models are derived from a dynamical-system approach to situations of time-evolving homogeneous turbulence in a rotating frame. Application of this analysis to a (k,epsilon) model fitted with an existing Coriolis correction [J. H. G. Howard, S. V. Patankar, and R. M. Bordynuik, "Flow prediction in rotating ducts using Coriolis-modified turbulence models", ASME Trans. J. Fluids Eng. 102, (1980)] is performed. Full analytical solutions are given for the flow predicted with this model in the situation of homogeneously sheared turbulence subject to rotation. The existence of an unphysical phenomenon of blowup at finite time is demonstrated in some range of the rotation-to-shear ratio. A direct connection is made between the slope of the mean-velocity profile in the plane-channel flow with spanwise rotation, and a particular fixed point of the dynamical system in homogeneously sheared turbulence subject to rotation. The general analysis, and the understanding of typical inaccuracies and misbehavior observed with the existing model, are then used to design a new model which is free from the phenomenon of blowup at finite time and able to account for both of the main influences of rotation on turbulence: the inhibition of the spectral transfer to high wave numbers and the shear/Coriolis instability.

In an attempt to improve the poor prediction of our previous theory, we examine corrections from the small region in a Hele-Shaw cell near the meniscus where the flow is three dimensional. At larger Reynolds numbers, we find an O(1) change to the effective boundary condition for mass conservation which is to be applied to the large scale flow outside the small region.