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Microscopic active droplets are able to swim autonomously in viscous flows: this puzzling feature stems from solute exchanges with the surrounding fluid via surface reactions or their spontaneous solubilisation, and the interfacial flows resulting from these solutes' gradients. Contrary to asymmetric active colloids, these isotropic droplets swim spontaneously by exploiting the nonlinear coupling of solute transport with self-generated Marangoni flows, which is also responsible for secondary transitions to more complex individual and collective dynamics. Thanks to their simple design and their sensitivity to physico-chemical signals, they are fascinating physicists, chemists, biologists and fluid dynamicists alike to analyse viscous self-propulsion and collective dynamics in active matter systems, to develop synthetic cellular models or to perform targeted biomedical or engineering applications. I review here the most recent and significant developments of this rapidly-growing field, focusing on the mathematical and physical modelling of these intringuing droplets, together with its experimental design and characterisation., Comment: 26 pages, 8 figures, to appear in Annual Review of Fluid Mechanics

A rotational version of the fluid-mechanical sewing machine (FMSM) is investigated experimentally. A thin thread of silicon oil was dispensed at a constant flow rate Q from a height H and fell on a table rotating at an angular speed ω, at a distance R from the axis. In all experimental runs, the values of Q and H were kept constant while the radius R was changed manually after each full rotation. Preliminary results show that the usual stitching patterns ensue as the local linear speed V=ωR approaches the critical transition speeds seen in the FMSM scenario but with subtle asymmetries introduced by rotational (centrifugal) effects. In some instances, arcs and loops of the traces were noticeably more pronounced when directed outward compared to those pointing toward the axis of rotation. Moreover, we observed stitching patterns not reported before. Overall, the symmetry-breaking features, while clearly visible, were rather subtle. Their morphological characteristics, such as differences in local curvature of traces relative to those in FMSM, are estimated to be below 10% in most cases.

International audience; Shock waves in viscous flows present thick and diffuse shock layers that merge with the boundary layer. These specific characteristics make detection and analysis difficult and inaccurate. To improve shock-wave detection, a method based on Fourier self-deconvolution (FSD) is presented in this paper. Test cases consider a concrete application with a test case obtained in a supersonic rarefied flow around a cylinder. In a first step, the method was validated with numerical flow fields calculated with the DS2V code based on a Monte Carlo algorithm. Then, the FSD method was applied to experimental flows operating at Mach 2 and Mach 4 in the low-density MARHy facility. The experimental flow fields were measured using the glow discharge technique, and shock-wave detection was validated against pressure profiles measured with a Pitot tube. The proposed method makes it possible to identify three characteristic zones of the shock: the shock foot, its centre and the maximum density zone, making it possible to deduce its thickness and obtain a precise estimation of the standoff distance. In addition to being completely non-intrusive, the method appears to be parameter free, robust and easy to implement.

Accepted: 2019-07-18, 資料番号: SA1190230000

Experiments and theory concern the behaviour of a small bubble carried through an orifice by a very viscous liquid. The liquid was polybutene oil, of viscosity about 70 Pa s, i.e. 70,000 times that of water. The Reynolds number of the flow is substantially less than one, hence the flow pattern is approximately radial flowing into, and away from, the orifice. These flow patterns have profound effects on the shape of an entrained bubble. On the upstream side, the acceleration of the liquid, as it approaches the orifice, causes elongation of the bubble since the front of the bubble moves faster than the back. On the downstream side, the reverse occurs: the back of the bubble moves fast than the front. Thus the height of the bubble diminishes as it moves away from the orifice, leading to the formation of a ‘crescent-moon’ shape. The shape of these bubbles can be predicted by considering the motion of a droplet of the same liquid replacing the bubble: the resulting geometric theory gives good predictions of bubble deformation approaching the orifice and of ‘crescent-moon’ formation downstream of the orifice.

In the present paper, a Vortex Particle Method is combined with a Boundary Element Method for the study of viscous incompressible planar flow around solid bodies. The method is based on Chorins operator splitting approach for the Navier–Stokes equations written in vorticity–velocity formulation, and consists of an advection step followed by a diffusion step. The evaluation of the advection velocity exploits the Helmholtz–Hodge Decomposition, while the no-slip condition is enforced by an indirect boundary integral equation. The above decomposition and splitting are discussed in comparison to the analogous decomposition for the pressure-velocity formulation of the governing equations. The Vortex Particle Method is implemented with a completely meshless algorithm, as neither advection nor diffusion requires topological connection of the point lattice. The results of the meshless approach are compared with those obtained by a mesh-based Finite Volume Method, where the pseudo-compressible iteration is exploited to enforce the solenoidal constraint on the velocity field. Several benchmark tests were performed for verification and validation purposes. In particular, we analyzed the two-dimensional flow past a circle, past an ellipse with incidence and past a triangle for different Reynolds numbers.

Within the framework of natural configurations developed by Rajagopal and Srinivasa, evolution within continuum thermodynamics is formulated as evolution of a natural configuration linked with the current configuration. On the other hand, withing the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework, the evolution is split into Hamiltonian mechanics and (generalized) gradient dynamics. These seemingly radically different approaches have actually a lot in common and we show their compatibility on a wide range of models. Both frameworks are illustrated on isotropic and anisotropic rate-type fluid models. We propose an interpretation of the natural configurations within GENERIC and vice versa (when possible).

International audience; When transported in confined geometries rigid fibers show interesting transport dynamics induced by friction with the top and bottom walls. Fiber flexibility causes an additional coupling between fiber deformation and transport and is expected to lead to more complex dynamics. A first crucial step for their understanding is the characterization of the deformed fiber shape. Here we characterize this shape for a fiber transported in a confined plug flow perpendicular to the flow direction using a combination of microfluidic experiments and numerical simulations. In the experiments, size, initial orientation, and mechanical properties of the fibers are controlled using microfabrication techniques and in situ characterization methods. The numerical simulations use modified Brinkman equations as well as full three-dimensional simulations. We show that the bending of a perpendicular fiber results from the force distribution acting on the elongated object and is proportional to the elasto-viscous number, which compares viscous to elastic forces. We quantitatively characterize the influence of the confinement on the fiber deformation. The precise understanding of the deformation of a flexible fiber in a confined geometry can also be used in future to understand the deformation and transport of more complex deformable particles in confined flows, such as vesicles or red blood cells.

We present in this double contribution two different reduced order strategies for incompressible parameterized Navier-Stokes equations characterized by varying Reynolds numbers. The first strategy deals with low Reynolds number (laminar flow) and is based on a stabilized finite element method during the offline stage followed by a Galerkin projection on reduced basis spaces generated by a greedy algorithm. The second methodology is based on a full order finite volume discretization. The latter methodology will be used for flows with moderate to high Reynolds number characterized by turbulent patterns. For the treatment of the mentioned turbulent flows at the reduced order level, a new POD-Galerkin approach is proposed. The new approach takes into consideration the contribution of the eddy viscosity also during the online stage and is based on the use of interpolation. The two methodologies are tested on classic benchmark test cases.

The method of numerical flow simulation in diesel engine spray devices channels is reviewed in the article. The efficiency of conformal mappings use for converting the flow domain to a parametric rectangle with orthogonal grid is declared and illustrated. In this method, the reduced boundary value problem for Navier-Stokes equations for velocity and pressure fields is solved in this rectangle. The numerical conformal mapping, based on Finite Element Method (FEM) is described. Boundary value problems of Laplace equations for real and imaginary component of mapping function are solved by FEM algorithm. The proposed simulation and qualitative estimation method for various configurations of the flow channel of the spray head is analyzed in the article. The influence of the angle of deflection from the axis channel sprayer nozzle on the flow velocity in the channel is described. The capacities of a software package for numerical conformal mapping are presented.

Dynamics and breakup of an axi-symmetric liquid jet injected upwards into another stationary or co-flowing immiscible liquid is investigated numerically. Simulations are done using an in-house code based on a novel DGLSM (dual grid level set method). Furthermore, a novel procedure – based upon physical interpretation of the various functions in Level Set Method – is demonstrated here as a powerful numerical tool to calculate certain parameters (diameter as well as frequency of drop formation and temporal variation of jet length at the axis), which characterize the unsteady interface-dynamics. Six different combination of the dispersed and continuous fluid are subjected to various injection velocity, resulting in a large variation in the non-dimensional governing parameters such as viscosity-ratio and Weber number. From the temporal variation of jet length and instantaneous interface, three drop formation regimes are proposed: Periodic Uniform Drop formation (P-UD), Quasi-Periodic Non-Uniform Drop formation (QP-NUD) and Chaotic Non-Uniform Drop formation (C-NUD); demarcated in a drop formation regime map for various Weber number and viscosity ratio. Their effect on the mean value of jet breakup length ( L d , m ), detached drop diameter ( D d , m ) and drop formation frequency ( St m ) is also studied. After a more detailed study on stationary continuous fluid, the effect of co-flowing continuous fluid is studied; and is found to stabilize the drop formation regime and increase the frequency of drop formation.

The main interest of the present investigation is to generate exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow motion and stability due to disks moving towards each other or in opposite directions with a constant velocity. Making use of the analytic solution, the description of possible conditions of motion is based on the exact solutions of the Navier-Stokes equations. Both stationary and transient cases have been considered. The stability of motion is analyzed for different initial perturbations. Different types of stability were found according to whether the disks moved towards or away from each other.

Multi-particle collision dynamics (MPCD) is a particle based Navier-Stokes solver and in the last ten years it has been largely used to analyze meso- scopic systems where both hydrodynamics and ther- mal effects have to be taken into account, typical ex- amples being colloidal suspensions and polymer solu- tions. Though the soundness of this approach is well documented, only a few studies present a systematic validation of the method as a Navier-Stokes solver for relatively complex flows (e.g. unsteady, non-uniform). In this study we use MPCD to simulate an unsteady periodic flow (second Stokes’ problem) and a two di- mensional flow (lid-driven cavity). Quantitative com- parisons with analytical and finite difference results show that MPCD is able to correctly reproduce the hy- drodynamics of these systems in a wide range of nu- merical parameter values, allowing the applications of MPCD to the analysis of complex fluids in confined geometries such as in Lab-On-a-Chip microfluidic de- vices. Discrepancies for certain parameter ranges and in specific flow conditions are singled out and discussed.

A pseudospectral matrix-element (PSME) numerical model is described for the simulation of rotating flows in a three-dimensional annular cavity. Temporal discretisation is implemented using a second-order semi-implicit scheme. Modified compressibility is invoked to handle the coupling between velocity and pressure while maintaining the incompressibility constraint. The governing continuity and Navier-Stokes momentum equations and boundary conditions are discretised using Chebyshev and Fourier collocation formulae. The model is validated against numerical results from alternative schemes and experimental data on rotating flows in an annular cavity. A base flow regime and instability patterns are observed, in accordance with other previously published investigations. It is demonstrated that the PSME model provides an accurate representation of rotating flows in an annular cavity.

Industrial design and optimization processes rely increasingly on powerful and well-engineered CFD tools. Compressible solution methods, which perform very well at transonic and supersonic flow speeds, display a dramatic degradation of convergence as well as of solution quality as the incompressibility limit is approached (very low flow speeds). In many technical applications, especially in turbomachinery, the flow conditions vary strongly within the computational domain and with time. When the incompressibility limit is approached, a large disparity arises between the smallest and largest eigenvalues of the systems characteristic matrix. In order to overcome these problems low-Mach preconditioning methods have been devised to rescale the eigenvalues of the characteristic matrix of the system of governing equations and, hence, reduce the large inequality in the acoustic and convective flow speeds. Frequently, low flow speeds are observed in low Reynolds environments. As noted by several authors, often instability issues in these regions, such as cavities and boundary layers, arise by preconditioning. Often, this problem is due to an overestimation of the maximum allowable timestep size. In fact, in a low Reynolds regime, the influence of viscous effects on time marching schemes predominates. An important role in the determination of viscous time steps plays the von Neumann number (VNN), whereas the Courant Friedrichs Lewy criteria (CFL) influences the inviscid time step behaviour. The objective of this work is the presentation of the theoretical background and results of a consistent Low-Mach preconditioning scheme based on a preconditioner proposed by Turkel, which has been extended to a wide range of Reynolds numbers. Furthermore, the interaction of low-Mach preconditioning, the von Neumann and Courant Friedrichs Lewy numbers on the convergence history and quality of results will be discussed. Its implementation is illustrated using DLR’s in-house CFD code TRACE. To prove the robustness and correctness of the algorithm, we discuss a set of test cases like the lid-driven cavity at different Reynolds numbers influenced by CFL and VNN.

The flow in the stern region of a fully appended hull is analyzed by both computational and experimental fluid dynamics. The study is focused on the velocity field induced by the rotating propellers. Measurements have been performed by laser Doppler velocimetry (LDV) on the vertical midplane of the rudder and in two transversal planes behind the propeller and behind the rudder. In the numerical approach, the real geometry of the propeller has been considered. To this purpose, a dynamic overlapping grids method has been used, which is implemented in the unsteady Reynolds averaged Navier–Stokes equations (URANSE) solver developed at INSEAN. Uncertainty analysis has been performed on both data sets and the results from the two approaches are compared. The agreement between the two data sets is found to be good, the deviation in the velocity and vorticity fields lying within the evaluated uncertainties. Numerical data allowed the analysis of further details of the flow that could not be measured, like load conditions of the single blades, interaction of the propeller wake with the rudder, and pressure oscillations induced by the propeller on the vault of the stern.

A theoretical analysis on the performance, close to a free surface, of the most used SPH formulations for Newtonian viscous terms is carried out in this paper. After an introduction of the SPH formalism, the SPH expressions for the viscous term in the momentum equation are analyzed in their continuous form. Using a Taylor expansion, a reformulation of those expressions is undertaken which allows to characterize the behavior of the viscous term close to the free surface. Under specific flow conditions, we show that the viscous term close to the free surface is singular when the spatial resolution is increased. This problem is in essence related to the incompleteness of the kernel function close to the free surface and appears for all the formulations considered. In order to assess the impact of such singular behavior, an analysis of the global energy dissipation is carried out, which shows that such a free-surface singularity vanishes when the integral quantities are considered. Notwithstanding that, not all the SPH viscous formulas allow the correct evaluation of the energy dissipation rate and, consequently, they may lead to an inaccurate modelling of viscous free-surface flows.

International audience; Characteristic formulations for boundary conditions have demonstrated their effectiveness to handle inlets and outlets, especially to avoid acoustic wave reflections. At walls, however, most authors use simple Dirichlet or Neumann boundary conditions, where the normal velocity (or pressure gradient) is set to zero. This paper demonstrates that there are significant differences between characteristic and Dirichlet methods at a wall and that simulations are more stable when using walls modelled with a characteristic wave decomposition. The derivation of characteristic methods yields an additional boundary term in the continuity equation, which explains their increased stability. This term also allows to handle the two acoustic waves going towards and away from the wall in a consistent manner. Those observations are confirmed by stability matrix analysis and one- and two-dimensional simulations of acoustic modes in cavities.

An algorithm is proposed for the simulation of unsteady viscous stratified compressible flows. The advantage of the method is its capability to deal with a broad range of subsonic Mach numbers, including nearly incompressible flows, with a single modelling, based on the fully compressible Navier-Stokes equations. The method is second-order accurate both in space and time. To remove the stiffness of the numerical problem due to the large disparity between the flow and the acoustic wave speeds at low Mach number, an approximate Newton method, based on artificial compressibility, is used. After a detailed description of the method, the accuracy of the algorithm is checked by computing compressible and incompressible benchmark test cases. Results of flows over a backward facing step with or without stratification effects for a Reynolds number of 800 are compared with the steady solution of incompressible methods, The computation of a compressible natural convection allows to evaluate the accuracy of the method for flow including significant compressibility effects, whereas numerical results of a Poiseuille-Benard channel flow for a Reynolds number of 10 demonstrate the efficiency of the present algorithm to compute unsteady hows. (C) 2000 Elsevier Science Ltd. All rights reserved.

An oscillatory instability has been observed experimentally on an horizontal cylinder free to move and rotate between two parallel vertical walls of distance H. The vertical motion of the cylinder, its rotation about its axis, and its transverse motion across the gap have been investigated as a function of its diameter D, its density ρs, of the mean vertical velocity U of the fluid, and of its viscosity ν. The relevant Reynolds number Re is shown to be based on the cell aperture H and on the relative velocity Vr between the fluid and the cylinder. For a blockage ratio D/H above 0.5 and Re above 20, oscillations of the rolling angle of the cylinder about its axis and of its transverse coordinate in the gap were observed together with periodic variations of the vertical velocity. For a given fluid-cylinder pair, the relative velocity Vr as well as the frequency f and the amplitude of the transverse velocity for these oscillations are nearly independent of the flow velocity U. For given cylinder density and fluid characteristics, f is also nearly independent of the ratio D/H in the range investigated. The oscillations could be observed down to values of Re as low as 30: this is lower than usual values for vortex shedding in confined geometries, which suggests that one might deal with a different instability mechanism. Fil: D'angelo, María Verónica. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Física. Grupo de Medios Porosos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Hulin, Jean-Pierre. Universite Pierre et Marie Curie; Francia. Universite Paris Sud; Francia. Centre National de la Recherche Scientifique; Francia Fil: Auradou, Harold. Universite Pierre et Marie Curie; Francia. Universite Paris Sud; Francia. Centre National de la Recherche Scientifique; Francia

We report the experimental observation of a robust horizontal mean flow induced by internal gravity waves. A wave beam is forced at the lateral boundary of a tank filled with a linearly stratified fluid initially at rest. After a transient regime, a strong jet appears in the wave beam, with horizontal recirculations outside the wave beam. Using multiple scale analysis, we present a simple physical mechanism predicting the growth rate of the mean flow and its initial spatial structure. We find good agreement with experimental results. These results show that a mean flow with non-zero vertical vorticity can be generated by Reynolds stresses if the wave fulfils two conditions: (1) the wave amplitude must vary along its propagation direction, which is the case in the presence of viscosity; (2) the wave amplitude must vary in the lateral direction, which is the case when the wave generator is localized in space.

International audience; The aim of this study was to develop a numerical model to simulate the surface erosion occurring at a fluid/soil interface subject to a flow process. We used a penalization procedure to compute flow around obstacles. A fictitious domain method allowed the use of fast and efficient finite volumes approximations on Cartesian meshes and avoided unstructured body-fitted meshes. The water/soil interface evolution was described with a Level Set function. Several numerical simulations confirmed the model's ability to predict the interfacial erosion of soils.