Vortex Wall Research Articles

Vortex dynamics and wall shear stress behaviour associated with an elliptic jet impinging upon a flat plate

Vortical structures and dynamics of a Re h = 2100 elliptic jet impinging upon a flat plate were studied at H/d h = 1, 2 and 4 jet-to-plate separation distances. Flow investigations were conducted along both its major and minor planes using laser-induced fluorescence and digital particle image velocimetry techniques. Results show that the impingement process along the major plane largely consists of primary jet ring-vortex and wall-separated secondary vortex formations, where they subsequently separate from the flat plate at smaller H/d h = 1 and 2 separation distances. Key vortex formation locations occur closer to the impingement point as the separation distance increases. Interestingly, braid vortices and rib structures begin to take part in the impingement process at H/d h = 4 and wave instabilities dominate the flow field. In contrast, significantly more coherent primary and secondary vortices with physically larger vortex core sizes and higher vortex strengths are observed along the minor plane, with no signs of braid vortices and rib structures. Lastly, influences of these different flow dynamics on the major and minor plane instantaneous and mean skin friction coefficient levels are investigated to shed light on the effects of separation distance on the wall shear stress distributions.

Flow field features of fractal impinging jets at short nozzle to plate distances

An experimental analysis of the flow field generated by an impinging jet equipped with a fractal grid insert located at the nozzle exit is carried out by means of Tomographic Particle Image Velocimetry. The Reynolds number based on the nozzle exit section diameter d is set to 15,000. The presence of the grid leads to a non uniform curvature of the jet shear layer. As a consequence, azimuthal instabilities are triggered in proximity of the nozzle exit section, causing the production of streamwise vortices. Furthermore, the organization of the coherent structures in proximity of the impinged wall is discussed and related to the convective heat transfer distribution. Owing to the presence of counter rotating wall vortices along the diagonals of the on-plate imprint of the fractal grid, a region of minimum in the scalar transfer map can be detected. In addition to that, similarly to the well known vortex rings that characterize the case of round jet without turbulence promoter, the presence of azimuthally coherent structures that might be generated by Kelvin–Helmholtz instability of the jet shear layer is presented and discussed.

Evolution of vortical structures in a curved artery model with non-Newtonian blood-analog fluid under pulsatile inflow conditions

Steady flow and physiological pulsatile flow in a rigid 180° curved tube are investigated using particle image velocimetry. A non-Newtonian blood-analog fluid is used, and in-plane primary and secondary velocity fields are measured. A vortex detection scheme (d 2-method) is applied to distinguish vortical structures. In the pulsatile flow case, four different vortex types are observed in secondary flow: deformed-Dean, Dean, Wall and Lyne vortices. Investigation of secondary flow in multiple cross sections suggests the existence of vortex tubes. These structures split and merge over time during the deceleration phase and in space as flow progresses along the 180° curved tube. The primary velocity data for steady flow conditions reveal additional vortices rotating in a direction opposite to Dean vortices—similar to structures observed in pulsatile flow—if the Dean number is sufficiently high.

Numerical visualization of shock tube-generated vortex–wall interaction using a fifth-order upwind scheme

Numerical visualization of shock tube-generated vortex–wall interaction using a fifth-order upwind scheme

Window purifying ventilator using a cross-flow fan: Simulation and optimization

The window purifying ventilator is a relatively new idea that involves replacing one part of the window frame with a ventilator, for which the core component is a cross-flow fan (CFF). When a CFF is applied to the window purifying ventilator, a filter should be added, and its casing should be modified. In this paper, first, time-accurate solutions with a sliding mesh technique were developed for modelling the two-dimensional viscous and incompressible model of CFF. Three prevalent two-equation turbulence models (Standard, RNG and Realizable k–e models) for CFF simulation were compared and validated in the experiments, and the most suitable model for this type CFF was found. Based on the time-accurate simulation, the formation of flow construction inside the CFF was also observed and explained. Next, the CFF was optimized for window purifying ventilator by redesigning and modifying the shape and location of vortex wall and rear wall, both numerically and experimentally. From the research results, the vortex wall’s position has a great influence on the ventilator’s performance by determining the position and intensity of eccentric vortex, and the shape of the rear wall also affects the ventilator’s performance by determining the flow pattern and internal flow resistance. Through appropriate designing the vortex and rear wall, finally, the CFF could apply to the window purifying ventilator with acceptable flow rates.

Flow structure evolution for laminar vortex rings impinging onto a fixed solid wall

Laser Induced Fluorescence (LIF) and Particle Image Velocimetry (PIV) techniques are used to investigate the synthetic jet actuated laminar vortex rings impinging onto a solid wall. Four cases with different stroke lengths (19mm⩽L0⩽50mm) are adopted to generate laminar vortex rings with Reynolds number (ReV0≈151) and orifice-to-wall distance (H=40mm) unchanged. It is found that the dimensionless stroke length normalized by the orifice-to-wall distance (L0/H) has a significant influence on the evolution of near wall flow structure of the impinging synthetic jet. Specifically, as the stroke length is relatively small (L0/H=0.475 and 0.775), the impinging vortex ring could only induce a weak secondary vorticity near the wall, which cannot roll up into a coherent structure. It is illustrated with LIF visualization and Finite Time Lyapunov Exponents (FTLEs) that a large-scale spiral vortex ring is generated in the near wall region for these two cases, which is explored for the first time. However, as the stroke length becomes larger (L0/H=0.95 and 1.25), the strong secondary vorticity rolls up and pairs with the impinging vortex ring to form a vortex dipole. As a result, the impinging vortex rings are prevented to merge with the vorticity clustering near the wall causing a rapid reduction of the near wall vortex strength. The analysis of the radial wall jet shows that the induced large-scale spiral vortex ring at the case of the smaller stroke length could slow down both the decay rates of radial mass flow rate and momentum flux, and this might be of benefit for the mass and heat transfer of wall surface when applying the impinging synthetic jet.

Magnetic domain-wall dynamics in wide permalloy strips

Domain walls in soft permalloy strips may exhibit various equilibrium micromagnetic structures depending on the width and thickness of the strip, ranging from the well-known transverse and vortex walls in narrow and thin strips to double and triple vortex walls recently reported in wider strips [V. Est\'evez and L. Laurson, Phys. Rev. B {\bf 91}, 054407 (2015)]. Here we analyze the field driven dynamics of such domain walls in permalloy strips of widths from 240 nm up to 6 $\mu$m, using the known equilibrium domain wall structures as initial configurations. Our micromagnetic simulations show that the domain wall dynamics in wide strips is very complex, and depends strongly on the geometry of the system, as well as on the magnitude of the driving field. We discuss in detail the rich variety of the dynamical behaviors found, including dynamic transitions between different domain wall structures, periodic dynamics of a vortex core close to the strip edge, transitions towards simpler domain wall structures of the multi-vortex domain walls controlled by vortex polarity, and the fact that for some combinations of the strip geometry and the driving field the system cannot support a compact domain wall.

Numerical simulation of a compressible vortex–wall interaction

The wall interaction of isolated compressible vortices generated from a short driver section shock tube has been simulated numerically by solving the Navier–Stokes equations in axisymmetric form. The dynamics of shock-free (incident shock Mach number $$M = 1.36$$ ) and shock-embedded $$(M = 1.57)$$ compressible vortices near the wall has been studied in detail. The AUSM+ scheme with a fifth-order upwind interpolation formula is used for the convective fluxes. Time integration is performed using a low dissipative and dispersive fourth-order six-stage Runge–Kutta scheme. The evolution of primary and wall vortices has been shown using the velocity field, vorticity field, and numerical schlierens. The vortex impingement, shocklets, wall vortices, and their lift-off are clearly identified from the wall pressure time history. It has been observed that the maximum vorticity of the wall vortices reaches close to 30 % of the primary vortex for $$M = 1.36$$ and it reaches up to 60 % for $$M = 1.57$$ . The net pressure force on the wall due to incident shock impingement is dominant compared to the compressible vortex impingement and their evolution.

Nano magnetic vortex wall guide

A concept of nano magnetic vortex wall guide is introduced. Two architectures are proposed. The first one is properly designed superlattices while the other one is bilayer nanostrips. The concept is verified by micromagnetic simulations. Both guides can prevent the vortex core in a magnetic vortex wall from colliding with sample surface so that the information stored in the vortex core can be preserved during its transportation from one location to another one through the guides.

Vorticity Generation by Rough Walls in 2D Decaying Turbulence

In this work we present Lattice Boltzmann simulations of a decaying vortex array in a 2D rectangular domain, which is bounded by a random rough wall from one side. In order to separate the effects of the collisions with the rough wall, the opposite (smooth) rigid wall is placed at a larger distance from the center of the vortex array. Periodic boundary condition is imposed in the perpendicular direction. Well defined random roughness is generated by the widely studied Wolf–Villain surface growth algorithm. The main finding is that collisions with a rough wall generate excess vorticity compared with a smooth boundary, while the kinetic energy decreases monotonously. A proper measure is the integrated excess enstrophy, which exhibits an apparent maximum at an “optimal” roughness range. Numerical values of the excess enstrophy are very sensitive to a particular configuration (wall shape and vortex lattice randomization), however the “optimal” roughness exhibits surface features of similar characteristic sizes than that of the decaying vortices.

Magnetic domain-wall velocity enhancement induced by a transverse magnetic field

Spin dynamics of field-driven domain walls (DWs) guided by permalloy nanowires are studied by high-speed magneto-optic polarimetry and numerical simulations. DW velocities and spin configurations are determined as functions of longitudinal drive field, transverse bias field, and nanowire width. Nanowires having cross-sectional dimensions large enough to support vortex wall structures exhibit regions of drive-field strength (at zero bias field) that have enhanced DW velocity resulting from coupled vortex structures that suppress oscillatory motion. Factor of 10 enhancements of the DW velocity are observed above the critical longitudinal drive-field (that marks the onset of oscillatory DW motion) when a transverse bias field is applied. Nanowires having smaller cross-sectional dimensions that support transverse wall structures also exhibit a region of higher mobility above the critical field, and similar transverse-field induced velocity enhancement but with a smaller enhancement factor. The bias-field enhancement of DW velocity is explained by numerical simulations of the spin distribution and dynamics within the propagating DW that reveal dynamic stabilization of coupled vortex structures and suppression of oscillatory motion in the nanowire conduit resulting in uniform DW motion at high speed. The enhanced velocity and drive field range are achieved at the expense of a less compact DW spin distribution.

Nanoscale switch for vortex polarization mediated by Bloch core formation in magnetic hybrid systems.

Vortices are fundamental magnetic topological structures characterized by a curling magnetization around a highly stable nanometric core. The control of the polarization of this core and its gyration is key to the utilization of vortices in technological applications. So far polarization control has been achieved in single-material structures using magnetic fields, spin-polarized currents or spin waves. Here we demonstrate local control of the vortex core orientation in hybrid structures where the vortex in an in-plane Permalloy film coexists with out-of-plane maze domains in a Co/Pd multilayer. The vortex core reverses its polarization on crossing a maze domain boundary. This reversal is mediated by a pair of magnetic singularities, known as Bloch points, and leads to the transient formation of a three-dimensional magnetization structure: a Bloch core. The interaction between vortex and domain wall thus acts as a nanoscale switch for the vortex core polarization.

Third type of domain wall in soft magnetic nanostrips.

Magnetic domain walls (DWs) in nanostructures are low-dimensional objects that separate regions with uniform magnetisation. Since they can have different shapes and widths, DWs are an exciting playground for fundamental research, and became in the past years the subject of intense works, mainly focused on controlling, manipulating, and moving their internal magnetic configuration. In nanostrips with in-plane magnetisation, two DWs have been identified: in thin and narrow strips, transverse walls are energetically favored, while in thicker and wider strips vortex walls have lower energy. The associated phase diagram is now well established and often used to predict the low-energy magnetic configuration in a given magnetic nanostructure. However, besides the transverse and vortex walls, we find numerically that another type of wall exists in permalloy nanostrips. This third type of DW is characterised by a three-dimensional, flux closure micromagnetic structure with an unusual length and three internal degrees of freedom. Magnetic imaging on lithographically-patterned permalloy nanostrips confirms these predictions and shows that these DWs can be moved with an external magnetic field of about 1 mT. An extended phase diagram describing the regions of stability of all known types of DWs in permalloy nanostrips is provided.

Nonmonotonic effects of perpendicular magnetic anisotropy on current-driven vortex wall motions in magnetic nanostripes**Project supported by the National Natural Science Foundation of China (Grant Nos. 11247026 and 11374253).

In a magnetic nanostripe, the effects of perpendicular magnetic anisotropy (PMA) on the current-driven horizontal motion of vortex wall along the stripe and the vertical motion of the vortex core are studied by micromagnetic simulations. The results show that the horizontal and vertical motion can generally be monotonously enhanced by PMA. However, when the current is small, a nonmonotonic phenomenon for the horizontal motion is found. Namely, the velocity of the horizontal motion firstly decreases and then increases with the increase of the PMA. We find that the reason for this is that the PMA can firstly increase and then decrease the confining force induced by the confining potential energy. In addition, the PMA always enhances the driving force induced by the current.

Role of spin diffusion in current-induced domain wall motion for disordered ferromagnets

Current-induced spin transfer torque and magnetization dynamics in the presence of spin diffusion in disordered magnetic textures is studied theoretically. We demonstrate using tight-binding calculations that weak, spin-conserving impurity scattering dramatically enhances the nonadiabaticity. To further explore this mechanism, a phenomenological drift-diffusion model for incoherent spin transport is investigated. We show that incoherent spin diffusion indeed produces an additional spatially dependent torque of the form $\ensuremath{\sim}{\ensuremath{\nabla}}^{2}[\mathbf{m}\ifmmode\times\else\texttimes\fi{}(\mathbf{u}\ifmmode\cdot\else\textperiodcentered\fi{}\ensuremath{\nabla})\mathbf{m}]+\ensuremath{\xi}{\ensuremath{\nabla}}^{2}[(\mathbf{u}\ifmmode\cdot\else\textperiodcentered\fi{}\ensuremath{\nabla})\mathbf{m}]$, where $\mathbf{m}$ is the local magnetization direction, $\mathbf{u}$ is the direction of injected current, and $\ensuremath{\xi}$ is a parameter characterizing the spin dynamics (precession, dephasing, and spin-flip). This torque, which scales as the inverse square of the domain wall width, only weakly enhances the longitudinal velocity of a transverse domain wall but significantly enhances the transverse velocity of vortex walls. The spatial-dependent spin transfer torque uncovered in this study is expected to have significant impact on the current-driven motion of abrupt two-dimensional textures such as vortices, skyrmions, and merons.

Current induced vortex wall dynamics in helical magnetic systems

Nontrivial topology of interfaces separating anti-chiral phases in helical magnets result in new effects as they interact with spin polarized current. These interfces or vortex walls consist of a one dimensional array of vortex lines. Topological Hall effect comes as a natural expectation. Also Lenz's law will result in a new damping mechanism in these systems. We study the dynamics of these wall interacting with electric current and use fundamental electromagntic laws to calculate this effect. On the other hand discrete nature of these walls affects their pinning and result in low depinning current density. We predict the value of this currnt using collective pinnng theory. Finally throughout this study we propose possible standard experiments that may distinguish our theoretical findings.

Head-to-head domain wall structures in wide permalloy strips

We analyze the equilibrium micromagnetic domain wall structures encountered in Permalloy strips of a wide range of thicknesses and widths, with strip widths up to several micrometers. By performing an extensive set of micromagnetic simulations, we show that the equilibrium phase diagram of the domain wall structures exhibits in addition to the previously found structures (symmetric and asymmetric transverse walls, vortex wall) also double vortex and triple vortex domain walls for large enough strip widths and thicknesses. Also several metastable domain wall structures are found for wide and/or thick strips. We discuss the details of the relaxation process from random magnetization initial states towards the stable domain wall structure, and show that our results are robust with respect to changes of e.g. the magnitude of the Gilbert damping constant and details of the initial conditions.

Effects of Edge Taper on Domain Wall Structure and Current-Driven Walker Breakdown in a Ferromagnetic Thin Film Wire

Domain walls in a ferromagnetic thin film wire with rectangular cross section adopt transverse wall (TW) or vortex wall (VW) geometries depending on the magnetic material and the wire width and thickness. However, experimentally wires can have a trapezoidal cross section if they are made by liftoff using an undercut resist profile. Micromagnetic modeling shows that tapering of the wire not only promotes the formation of a TW over a VW, but also increases the critical current value and the domain wall velocity at which Walker breakdown occurs, providing a potential route to higher speed domain wall devices.

Limitations in artificial spin ice path selectivity: the challenges beyond topological control

Magnetic charge is carried through nanowire networks by domain walls, and the micromagnetic structure of a domain wall provides an opportunity to manipulate its movement. We have shown previously that magnetic monopole defects exist in artificial spin ice (ASI) and result from two bar switching at a vertex. To create and manipulate monopole defects and indeed magnetic charge in general, path selectivity of the domain wall at a vertex is required. We have recently shown that in connected ASI structures, transverse wall chirality (or topology) determines wall path direction, but a mechanism known as Walker breakdown, where a wall mutates into a wall of opposite chirality partially destroys selectivity. Recently it has been claimed that in isolated Y-shaped junctions that support vortex walls, selectivity is entirely determined by chirality (or topology), the suggestion being that vortex wall chirality is robust in the Walker breakdown process. Here we demonstrate that in Y-shaped junctions, magnetic switching in the important topologically protected regime exists only for a narrow window of field and bar geometry, and that it will be challenging to access this regime in field-driven ASI. This work has implications for the wider field of magnetic charge manipulation for high density memory storage.

Analytical Modelling of Magnetic DW Motion

The main analytical model for describing the motion of magnetic domain walls is the 1-D model formulated based on the profile of a Bloch wall. This model qualitatively describes the motion of magnetic domain wall in nanowires, while it may fail to match experimental and numerical results quantitatively. In recent years, the 1-D model has been further generalized by the introduction of terms such as spin transfer torques and spin orbit torques. It has also been used to describe the motion of different domain walls, including vortex walls. It seems that in many such attempts, formalisms are not followed accurately and the main assumptions of the model (such as the Bloch wall profile used in developing the model) are underestimated. In this paper, we first derive an analytical model to describe the motion of a tilting Bloch wall in perpendicularly magnetized materials using four collective coordinates. We then compare the energy landscape predicted by this model to that of micromagnetic simulations, highlighting the possibility of using such comparisons to develop corrections for the 1-D model.