We use a combination of numerical simulations and experiments to elucidate the structure of the flow of an electrically conducting fluid past a localized magnetic field, called magnetic obstacle. We demonstrate that the stationary flow pattern is considerably more complex than in the wake behind an ordinary body. The steady flow is shown to undergo two bifurcations (rather than one) and to involve up to six (rather than just two) vortices. We find that the first bifurcation leads to the formation of a pair of vortices within the region of magnetic field that we call inner magnetic vortices, whereas a second bifurcation gives rise to a pair of attached vortices that are linked to the inner vortices by connecting vortices.
This paper presents the analysis of the particle-laden liquid metal wake flow around a cylindrical obstacle at different obstacle Reynolds numbers. Particles in liquid metal are visualized using dynamic neutron radiography. We present the results of particle tracking velocimetry of the obstacle wake flow using an improved version of our image processing and particle tracking code MHT-X. The latter now utilizes divergence-free interpolation of the particle image velocimetry field used for motion prediction and particle trajectory reconstruction. We demonstrate significant improvement over the p…
In this research article we study the wake formation behind 3-Dimensional Multi-scale Porous Obstacles (3DMPOs). Particle Imaging Velocimetry (PIV) is used in a non-shallow ($B/h =1.5$) water flume, with measurements carried out across the $x$ - $y$ plane (at $z$ = 130 mm) and with $Re=70,000$ based on the free-stream velocity ($U_{\infty}$). To characterise the downstream wake characteristics of 3DMPOs the obstacles are split into 3 regimes; (1) non-porous, (2) porous with a single internal scale and (3) porous fractals (based on the Sierpinski carpet). The void fraction ($ϕ=0.7$) and externa…
High-fidelity large-eddy simulations of the flow around two rectangular obstacles are carried out at a Reynolds number of 10,000 based on the free-stream velocity and the obstacle height. The incoming flow is a developed turbulent boundary layer. Mean-velocity components, turbulence fluctuations, and the terms of the turbulent-kinetic-energy budget are analyzed for three flow regimes: skimming flow, wake interference, and isolated roughness. Three regions are identified where the flow undergoes the most significant changes: the first obstacle's wake, the region in front of the second obstacle,…
Formation of recirculating wakes is a prominent feature of inertial flow around bluff bodies. Below the onset of vortex shedding in uniform unbounded flows, the fluid in the recirculating wake region moves on closed planar orbits. The steady wake is thus an isolated zone in the flow and does not exchange fluid with the free stream. In this work, we utilize lattice-Boltzmann simulations and microfluidic experiments to demonstrate that in microchannel inertial flow of Newtonian fluids, the recirculating wake is replaced by a three-dimensional vortical flow. Spiraling streamlines generate a conti…
The turbulent flow past a wall-mounted square cylinder with an aspect ratio of four was investigated with the aid of Spalart-Allmaras improved delayed detached-eddy simulation (S-A IDDES) and proper orthogonal decomposition (POD). The Reynolds number was equal to 12,000 (based on the free-stream velocity and obstacle width). This study focused on analysing the vortical structure of the wake and vortex shedding process along the obstacle height. A quantitative comparison of the first and second-order flow statistics with the available experimental and direct numerical simulation data was used t…
This sequence of fluid dynamics videos illustrates the behavior of a suspension of noncolloidal particles flowing past various bluff body obstacles within a microfluidic device. The polystyrene particles, of 7 μm diameter and volume fraction of 8.4%, are carefully made neutrally buoyant with the suspending liquid composed of a mixture of water and a small fraction of glycerol. The channel depth is 60 μm and the typical length of the obstacles normal to the flow direction is 200 μm. The flow rate is varied to generate Reynolds numbers based on the scale of the obstacle in the approximate range …
It is shown that a channel flow of a dilute polymer solution between two widely spaced cylinders hindering the flow is an important paradigm of an unbounded flow in the case in which the channel wall is located sufficiently far from the cylinders. The quantitative characterization of instabilities in a creeping viscoelastic channel flow between two widely spaced cylinders reveals two elastically driven transitions, which are associated with the breaking of time-reversal and mirror symmetries: Hopf and forward bifurcations described by two order parameters $\mbox{v}_{rms}$ and $\barω$, respecti…
Direct numerical simulations are used to study the interaction of a stream of small heavy inertial particles with the laminar and turbulent wakes of an immobile sphere facing an incompressible uniform inflow. Particles that do not collide with the obstacle but move past it, are found to form preferential concentrations both in the sphere boundary layer and in its wake. In the laminar case, the upstream diverging flow pattern is responsible for particle clustering on a cylinder that extends far downstream the sphere. The interior of this surface contains no particles and can be seen as a shadow…
Large eddy simulations (LES) are employed to investigate the role of time-varying currents on the form drag and vortex dynamics of submerged 3D topography in a stratified rotating environment. The current is of the form $U_c+U_t \sin(2πf_t t)$, where $U_c$ is the mean, $U_t$ is the tidal component and $f_t$ is its frequency. A conical obstacle is considered in the regime of low Froude number. When tides are absent, eddies are shed at the natural shedding frequency $f_{s,c}$. The relative frequency $f^*=f_{s,c}/f_t$ is varied in a parametric study which reveals states of high time-averaged form…
Lattice Boltzmann Method (LBM) simulations for turbulent flows over a fractal and non-fractal obstacles are presented. The wake hydrodynamics are compared and discussed in terms of flow relaxation, Strouhal numbers and wake length for different Reynolds numbers. Three obstacle topologies are studied, Solid (SS), Porous Regular (PR) and Porous Fractal (FR). In particular we observe that the oscillation present in the case of the solid square can be annihilated or only pushed downstream depending on the topology ot the porous obstacle. The Lattice Boltzmann Method (LBM) is implemented over a ran…
Dynamic similarity of vortex shedding in a superfluid flowing past a penetrable obstacle
Seoul National University（首尔大学）；NextQuantum, Seoul National University（NextQuantum，首尔大学）；Institute of Applied Physics, Seoul National University（首尔大学应用物理研究所）
The fluid flow around a bluff body is complex and time dependent, which also contains a wide range of time and length scales. The first few eigenmodes of the proper orthogonal decomposition (POD) of such a flow provide significant insight into the flow structure, and can form the basis of a low-dimensional representation of certain turbulent flows. In this article, the direct-forcing immersed boundary method is considered to model the wake flow generated by arbitrary shaped obstacles. Based on the POD analysis of wakes behind cylinders, airfoils, and rotors, a reduced order model (ROM) for the…
The Reynolds number provides a characterization of the transition to turbulent flow, with wide application in classical fluid dynamics. Identifying such a parameter in superfluid systems is challenging due to their fundamentally inviscid nature. Performing a systematic study of superfluid cylinder wakes in two dimensions, we observe dynamical similarity of the frequency of vortex shedding by a cylindrical obstacle. The universality of the turbulent wake dynamics is revealed by expressing shedding frequencies in terms of an appropriately defined superfluid Reynolds number, ${\rm Re}_s$, that ac…
This investigation analyzes the effect of vortex wakes on the Lagrangian displacement of particles induced by the passage of an obstacle in a two-dimensional incompressible and inviscid fluid. In addition to the trajectories of individual particles, we also study their drift and the corresponding total drift areas in the Föppl and Kirchhoff potential flow models. Our findings, which are obtained numerically and in some regimes are also supported by asymptotic analysis, are compared to the wakeless potential flow which serves as a reference. We show that in the presence of the Föppl vortex wake…
Many wind farms are placed near coastal regions or in proximity of orographic obstacles. The meso-scale gradients that develop in these zones make wind farms operating in velocity fields that are rarely uniform. However, all existing wake-merging methods in engineering wind-farm wake models assume a homogeneous background velocity field in and around the farm, relying on a single wind-speed value usually measured several hundreds of meters upstream of the first row of turbines. In this study, we derive a new momentum-conserving wake-merging method capable of superimposing the waked flow on a h…
This paper demonstrates particle tracking velocimetry performed for a model system wherein particle-laden liquid metal flow about a cylindrical obstacle was studied. We present the image processing methodology developed for particle detection in images with disparate and often low signal- and contrast-to-noise ratios, and the application of our MHT-X tracing algorithm for particle trajectory reconstruction within and about the wake flow of the obstacle. Preliminary results indicate that the utilized methods enable consistent particle detection and recovery of long, representative particle traj…
We consider the time-dependent Navier-Stokes equations in a half-space with boundary data on the line $(x,y)=(x_0,y)$ assumed to be time-periodic (or stationary) with a fixed asymptotic velocity ${\bf u}_{\infty}=(1,0)$ at infinity. We show that there exist (locally) unique solutions for all data satisfying a compatibility condition in a certain class of fuctions. Furthermore, we prove that asymptotically the vorticity decompose itself in a dominant stationary part on the parabolic scale $y\sim\sqrt{x}$ and corrections of order $x^{-{3/2}+ε}$, while the velocity field decompose itself in a dom…
The excitation of wake waves by a relativistic homogeneous electron bunch passing through cold magnetized plasma at equilibrium is studied for arbitrary values of the ratio of bunch density to plasma density. The analysis is based on the assumption that the magnetic field is sufficiently strong ($ω_B\gg ω_p$, where $ω_p$ and $ω_B$ are the electron plasma and cyclotron frequences respectively). The periodic and nonperiodic solutions for the momentum of plasma electrons inside and outside the bunch are analyzed. It was shown that the presence of strong external magnetic field may increase the am…
At low Reynolds numbers, the wind flow in the wake of a single wind turbine is generally not turbulent. However, turbines in wind farms affect each other's wakes so that a turbulent flow can arise. In the present work, an analogue of this effect for the massless charge carrier flow around obstacles in graphene is outlined. We use a relativistic hydrodynamic simulation to analyze the flow in a sample containing impurities. Depending on the density of impurities in the sample, we indeed find evidence for potentially turbulent flow and discuss experimental consequences.
Analogies are elaborated in the qualitative description of two systems: the magnetohydrodynamic (MHD) flow moving through a region where an external local magnetic field (magnetic obstacle) is applied, and the ordinary hydrodynamic flow around a solid obstacle. The former problem is of interest both practically and theoretically, and the latter one is a classical problem being well understood in ordinary hydrodynamics. The first analogy is the formation in the MHD flow of an impenetrable region -- core of the magnetic obstacle -- as the interaction parameter $N$, i.e. strength of the applied m…
It is known that obstacles can hydrodynamically trap bacteria and synthetic microswimmers in orbits, where the trapping time heavily depends on the swimmer flow field and noise is needed to escape the trap. Here, we use experiments and simulations to investigate the trapping of microrollers by obstacles. Microrollers are rotating particles close to a bottom surface, which have a prescribed propulsion direction imposed by an external rotating magnetic field. The flow field that drives their motion is quite different from previously studied swimmers. We found that the trapping time can be contro…
Rich recirculation patterns have been recently discovered in the electrically conducting flow subject to a local external magnetic termed "the magnetic obstacle" [Phys. Rev. Lett. 98 (2007), 144504]. This paper continues the study of magnetic obstacles and sheds new light on the core of the magnetic obstacle that develops between magnetic poles when the intensity of the external field is very large. A series of both 3D and 2D numerical simulations have been carried out, through which it is shown that the core of the magnetic obstacle is streamlined both by the upstream flow and by the induced …
Many practical applications exploit an external local magnetic field -- magnetic obstacle -- as an essential part of their constructions. Recently, it has been demonstrated that the flow of an electrically conducting fluid influenced by an external field can show several kinds of recirculation. The present paper reports a 3D numerical study whose some results are compared with an experiment about such a flow in a rectangular duct.
The force on a test charge moving through a strongly magnetized plasma is calculated using linear response theory. Strong magnetization is found to generate a component of the force perpendicular to the velocity of the particle in the plane formed by the velocity and magnetic field vectors. This transverse force is generated by an asymmetry with respect to the velocity vector in the induced electrostatic wake potential that is associated with the action of the Lorentz force on the background plasma. The direction depends on the speed of the test charge. If it is faster than a critical speed ch…
We study a predator-prey model of plankton dynamics in the two and three-dimensional wakes of turbulent flows behind a cylinder, focusing on the impact of the three-dimensional character of the carrying velocity field on population variance spectra and spatial distributions. By means of direct numerical simulations, we find that the qualitative behavior of the biological dynamics is mostly independent of the space dimensionality, which suggests that only the relation between the typical flow and biological timescales is crucial to observe persistent blooms. Similarly, in both cases, we find th…
The flow transformation and the generation of vortex structures by a strong magnetic dipole field in a liquid metal duct flow is studied by means of three-dimensional direct numerical simulations. The dipole is considered as the paradigm for a magnetic obstacle which will deviate the streamlines due to Lorentz forces acting on the fluid elements. The duct is of square cross-section. The dipole is located above the top wall and is centered in spanwise direction. Our model uses the quasi-static approximation which is applicable in the limit of small magnetic Reynolds numbers. The analysis covers…
We investigate the two-dimensional flow of a liquid foam around circular obstacles by measuring all the local fields necessary to describe this flow: velocity, pressure, bubble deformations and rearrangements. We show how our experimental setup, a quasi-2D "liquid pool" system, is adapted to the determination of these fields: the velocity and bubble deformations are easy to measure from 2D movies, and the pressure can be measured by exploiting a specific feature of this system, a 2D effective compressibility. To describe accurately bubble rearrangements, we propose a new, tensorial descriptor.…
Plankton constitutes the productive base of aquatic ecosystems and plays an essential role in the global carbon cycle. The impact of hydrodynamic conditions on the biological activity of plankton species can manifest in a variety of different ways and the understanding of the basic effects due to multiscale complex flows still appears incomplete. Here, we consider a predator-prey model of plankton dynamics in the presence of a turbulent flow past an idealized island, to investigate the conditions under which an algal bloom is observed, and the resulting patchiness of plankton distributions. By…
Three-dimensional foam flow resolved by fast X-ray tomographic microscopy
CNRS（法国国家科学研究中心）；Institut de Physique de Rennes（雷恩物理研究所）；Institute for Biomedical Engineering, University and ETH Zurich（苏黎世联邦理工学院生物医学工程研究所）；ETH Zurich（苏黎世联邦理工学院）；Swiss Light Source, Paul Scherrer Institute（瑞士光子源，保罗谢尔研究所）；Laboratoire de Physique, ENS Lyon（里昂高等师范学校物理实验室）
A neutral boundary layer was generated in the laboratory to analyze the mean velocity field and the turbulence field within and above an array of two-dimensional obstacles simulating an urban canopy. Different geometrical configurations were considered in order to investigate the main characteristics of the flow as a function of the aspect ratio (AR) of the canopy. To this end, a summary of the two-dimensional fields of the fundamental turbulence parameters is given for AR ranging from 1 to 2. The results show that the flow field depends strongly on AR only within the canyon, while the outer f…
We investigate the effects of helical swimmer shape (i.e., helical pitch angle and tail thickness) on swimming dynamics in a constant viscosity viscoelastic (Boger) fluid via a combination of particle tracking velocimetry, particle image velocimetry and 3D simulations of the FENE-P model. The 3D printed helical swimmer is actuated in a magnetic field using a custom-built rotating Helmholtz coil. Our results indicate that increasing the swimmer tail thickness and pitch angle enhances the normalized swimming speed (i.e., ratio of swimming speed in the Boger fluid to that of the Newtonian fluid).…
