Toroidal Motion Research Articles

Numerical Modeling of Melt Flow and Mixing in an Inductively Stirred Ladle and Comparison with Gas and Mechanical Stirring

Fluid flow and mixing in an inductively stirred ladle are modeled mathematically. The effect of two modes of electromagnetic stirring on motion is simulated; one produces a predominantly swirling motion (as in mechanical, paddle‐stirred ladle), while the other generates an upwelling, toroidal motion (as in gas‐stirred ladle). Two different ANSYS software programs, namely, Maxwell‐3D and Fluent, are applied to carry out numerical simulations. In the former, 3D Maxwell's equations are solved to estimate, a priori, the distribution of Lorentz force within the melt phase due to the imposed three‐phase, alternating current excitation of copper coils, while in the latter, time‐averaged magnetohydrodynamic (MHD) turbulent flow equations are solved to yield the electromagnetically driven flow field. Model predictions are validated against published results and it is shown that the electromagnetic as well as turbulent‐MHD models developed in this work are robust and perform sufficiently accurately. Finally, numerically predicted results together with relevant published work indicated that at equivalent specific input stirring power and identical vessel shape and volume, mixing is fastest in electromagnetic stirring with a traveling magnetic field (producing an upwelling toroidal motion), followed by mechanical agitation, gas stirring, and electromagnetic stirring with a rotating magnetic field (inducing swirling flow).

Efficient physical delamination of Ti3C2Tx MXene under periodic and constant shear field of Taylor vortex flow

Employing Taylor vortex flow (TVF), we have devised an innovative technique for the delamination of MXene without using a chemical intercalant and demonstrated the enhanced optoelectronic characteristics of this delaminated MXene through their successful implementation in light emitting diode (LED). The pairwise toroidal fluid motion of TVF was induced by the rotation of the inner cylinder in the Couette-Taylor (CT) reactor. Due to periodic and constant shear field, TVF was highly efficient for the exfoliation of MXene. So, the continuous exfoliation process using CT reactor always showed 8.1 ∼ 12.5 times higher delaminated MXene (d-Ti3C2Tx) yield than that using a conventional mixing tank (MT) reactor which generated turbulent eddy flow (TEF) by impeller agitation. As such, 8.26 mgּ/mL (42.90 % of recovery ratio) of d-Ti3C2Tx was obtained in CT reactor at 1300 rpm of inner cylinder rotation speed and 24 min of mean residence time (MRT). In comparison, d-Ti3C2Tx in MT reactor at 3000 rpm of agitation speed and 24 min of MRT was 0.66 mgּ/mL (3.42 % of recovery ratio). In addition, d-Ti3C2Tx in TVF was thinner and wider than that in TEF. So, the d-Ti3C2Tx was homogeneously suspended without sedimentation and oxidation in aqueous suspension over 30 days. In addition, d-Ti3C2Tx in the TVF was applied to the transparent conducting electrode of inorganic CsPbBr3 perovskite light emitting diodes (PeLEDs). The transparent conducting oxide-free PeLED had 62.52 cd/A of maximum current efficiency and 14.48 % of maximum external quantum efficiency, which is comparable to the best performance of ITO-based inorganic CsPbBr3 PeLEDs.

Nearly Toroidal, Periodic and Quasi-periodic Motions of Fluid Particles Driven by the Gavrilov Solutions of the Euler Equations

We consider the smooth, compactly supported solutions of the steady 3D Euler equations of incompressible fluids constructed by Gavrilov (Geom Funct Anal (GAFA) 29(1):190–197, 2019), and we study the corresponding fluid particle dynamics. This is an ode analysis, which contributes to the description of Gavrilov’s vector field.

Tokamak plasma equilibrium with relativistic runaway electrons

We consider axisymmetric equilibrium of a tokamak plasma that includes current carried by relativistic runaway electrons (REs). Using a guiding center approach, a qualitative picture of the equilibrium of a pure RE beam is elucidated. In a hot thermal plasma, none of the classical drifts of charged particles contribute to the net field-perpendicular current density, which is purely due to magnetization current. In the case of a runaway beam, however, the curvature drift of REs provides the Lorentz force needed to maintain the centripetal acceleration associated with the relativistic toroidal motion. Two different equilibrium formulations are derived for the general case consisting of a mix of thermal and RE current. At higher RE energies, the shift between flux-surfaces and surfaces of constant generalized angular momentum of REs in such equilibria can exceed the radial extent of a typical magnetohydrodynamic mode such that its stability properties could be altered. Simplified one-dimensional governing equations are derived for the absolute and relative orbit shifts in the case of a circular tokamak, enabling quick estimates of parameter dependencies.

Self-Consistent Simulation of the Excitation of Compressional Alfvén Eigenmodes and Runaway Electron Diffusion in Tokamak Disruptions.

Alfvénic modes in the current quench (CQ) stage of the tokamak disruption have been observed in experiments. In DIII-D the excitation of these modes is associated with the presence of high-energy runaway electrons (REs), and a strong mode excitation is often associated with the failure of RE plateau formation. In this work we present results of self-consistent kinetic-MHD simulations of RE-driven compressional Alfvén eigenmodes (CAEs) in DIII-D disruption scenarios, providing an explanation of the CQ modes. Simulation results reveal that high energy trapped REs can have resonance with the Alfvén mode through their toroidal precession motion, and the resonance frequency is proportional to the energy of REs. The mode frequencies and their relationship with the RE energy are consistent with experimental observations. The perturbed magnetic fields from the modes can lead to spatial diffusion of REs including the nonresonant passing ones, thus providing the theoretical basis for a potential approach for RE mitigation.

Acoustic predation in a sailfish-flying fish cloak

When a sailfish circles to corral a school of flying fish in a vortex near the ocean surface, a tiny patch of arced surface waves confined to oppositely placed 70° sectors appears dispersing coherently, but why? It is modeled that, when the fish motions stop suddenly, the corralled school compacts, the tail shed propulsion vortices touch, break and radiate the pressure released from the centrifugal vortex rotation creating an acoustic monopole. The surface-wave patch is a section of the sphere of radiation. The oppositely placed curved bodies of the sailfish and the flying fish act as concave acoustic mirrors about the monopole creating a reverberating bell-shaped cloak in between which vibrates the ear bones and bladders of the flying fish disorienting them. A cup of water firmly struck on a table induces a similar vibration of a purely radial mode. The sailfish circles around the school at a depth where the wind induced underwater toroidal motion in the vertical plane becomes negligible such that the flying fish is unable to sense the tailwind direction above, limiting the ability to swim up and emerge in the right direction to glide. Experiments confirm that the flying fish tail rigidity is too low for a quick ballistic exit, which is not called for either.

Facile recyclable process of high-quality single layer graphene oxide via waste graphite anode scrap

Here we report a facile reusable method for graphene oxide (GO) from the oxidation of waste graphite anode scrap (WGAS), which was synthesized by Couette–Taylor flow reactor. The toroidal motion of fluids generated by the mechanical and structural specificity of the reactor increased the intercalation rate and oxidation efficiency of the WGAS, resulting in high production yield (95 ± 1%) of GO within 90 min reaction time. In addition, the as-synthesized GO nanosheets were extensively characterized using a variety of techniques, which allowed the identification of two-dimensional monolayers (∼1.3 nm) and successfully functionalized high-quality graphene oxides. Our approach of the high-efficiency oxidation and exfoliation of recycled GO with WGAS may find potential application in numerous industrial fields, such as catalysis and electrodes in energy conversion and storage systems, and conductive materials in electronic devices.

The ignition and combustion of mixtures of a gaseous hydrocarbon fuel in air when fluidising a bed of sand

Previous work has been examined here to arrive at a proper criterion for when a mixture of a hydrocarbon gas and air ignites, when it is used to fluidise a bed of e.g. silica sand. It was concluded that, even when the bed has been warmed up to ≈ 900 °C, combustion of such a mixture of gases is usually prevented in the bed's particulate phase, i.e. in the gas moving interstitially between particles of sand. This is caused by free radicals recombining on the surfaces of the fluidised particles. As for the bubble phase, combustion in a bubble of a hydrocarbon gas, pre-mixed with air, is inevitably delayed by the chemistry involving a sequence of straight and branched chain reactions. Also, there can be a toroidal motion of gas inside a bubble; this enhances the transport of heat and radicals from the torus to the sand and so inhibits ignition of a bubble's contents. The result is that for a stoichiometric mixture of propane and air at atmospheric pressure, ignition occurs when a bubble's diameter has grown by coalescence to:db ∼ 3 Umf tig ∼ 2.7 × 10–9Umf exp (158 kJ mol–1 / RT)Here Umf is the superficial velocity of the fluidising gas for incipient fluidisation; tig is the autoignition delay for the particular fluidising gas mixture. This approximate statement is for both slow and fast bubbles; it is very similar to a criterion deduced previously by a different route. The above relationship is based on ignition occurring in a bubble, whenever the residence time in the gas passing up through the bubble along its vertical axis exceeds the ignition delay.

Interaction between energetic-ions and internal kink modes in a weak shear tokamak plasma

Based on the conventional tokamak HL-2A-like parameters and profiles, the linear properties and the nonlinear dynamics of non-resonant kink mode (NRK) and non-resonant fishbone instability (NRFB) in reversed shear tokamak plasmas are investigated by using the global hybrid kinetic-magnetohydrodynamic nonlinear code M3D-K. This work mainly focuses on the effect of passing energetic-ions on the NRK and NRFB instabilities, which is different from the previous works. It is demonstrated that the NRFB can be destabilized by the passing energetic-ions when the energetic-ion beta β h exceeds a critical value. The transition from NRK to NRFB occurs when the energetic-ion beta β h increases to above a critical value. The resonance condition responsible for the excitation of NRFB is interestingly found to be satisfied at ω t + ω p ≈ ω, where ω t is the toroidal motion frequency, ω p is the poloidal motion frequency and ω is the mode frequency. The nonlinear evolutions of NRFB’s mode structures and Poincaré plots are also analyzed in this work and it is found that the NRFB can induce evident energetic-ion loss/redistribution, which can degrade the performance of the plasmas. These findings are conducive to understanding the mechanisms of NRFB induced energetic-ion loss/redistribution through nonlinear wave-particle interaction.

A new 3-D multi-fluid model with the application in bubble dynamics using the adaptive mesh refinement

Violent pulsating bubbles behave diversely in different circumstances. It is a multi-scale problem in both space and time. In 3-D problems, the numerical simulation is usually too expensive to implement in practice with a fixed grid. In this paper, a 3-D multi-fluid model is established based on the Eulerian finite element method and the adaptive mesh refinement technique to investigate the bubble evolution and its toroidal motion near a solid vertical wall. The mixture formula for compressible multi-fluid flow is adopted to ensure conservativeness. By means of the block-based adaptive mesh refinement, the accuracy and the efficiency of the simulation are well balanced. The present model is validated by comparing the results with an underwater explosion experiment and the existing numerical results. The results agree well and a fast convergence is observed. Then, several cases with different buoyancy parameters are simulated, and the toroidal bubble motion and their pressure load on the solid wall are analyzed. The bubble’s motion exhibits complex physics, such as the formation of the crescent-shaped bubble, the air cushion effect during the jet penetration, and the nonlinear relationship between the jet impact pressure and the angle between the jet and the opposite bubble surface.

Constraints on Mantle Viscosity From Intermediate‐Wavelength Geoid Anomalies in Mantle Convection Models With Plate Motion History

AbstractThe Earth's long‐ and intermediate‐wavelength geoid anomalies are surface expressions of mantle convection and are sensitive to mantle viscosity. While previous studies of the geoid provide important constraints on the mantle radial viscosity variations, the mantle buoyancy in these studies, as derived from either seismic tomography or slab density models, may suffer significant uncertainties. In this study, we formulate 3‐D spherical mantle convection models with plate motion history since the Cretaceous that generate dynamically self‐consistent mantle thermal and buoyancy structures, and for the first time, use the dynamically generated slab structures and the observed geoid to place important constraints on the mantle viscosity. We found that non‐uniform weak plate margins and strong plate interiors are critical in reproducing the observed geoid and surface plate motion, especially the net lithosphere rotation (i.e., degree‐1 toroidal plate motion). In the best‐fit model, which leads to correlation of 0.61 between the modeled and observed geoid at degrees 4–12, the lower mantle viscosity is ∼1.3–2.5 × 1022 Pa⋅s and is ∼30 and ∼600–1,000 times higher than that in the transition zone and asthenosphere, respectively. Slab structures and the geoid are also strongly affected by slab strength, and the observations prefer moderately strong slabs that are ∼10–100 times stronger than the ambient mantle. Finally, a thin weak layer below the 670‐km phase change on a regional scale only in subduction zones produces stagnant slabs in the mantle transition zone as effectively as a weak layer on a global scale.

Analytical Solution of Magnetically Dominated Astrophysical Jets and Winds: Jet Launching, Acceleration, and Collimation

Abstract We present an analytical solution of a highly magnetized jet/wind flow. The left side of the general force-free jet/wind equation (the “pulsar” equation) is separated into a rotating and a nonrotating term. The two equations with either term can be solved analytically, and the two solutions match each other very well. Therefore, we obtain a general approximate solution of a magnetically dominated jet/wind, which covers from the nonrelativistic to relativistic regimes, with the drift velocity well matching the cold plasma velocity. The acceleration of a jet includes three stages. (1) The jet flow is located within the Alfvén critical surface (i.e., the light cylinder), has a nonrelativistic speed, and is dominated by toroidal motion. (2) The jet is beyond the Alfvén critical surface where the flow is dominated by poloidal motion and becomes relativistic. The total velocity in these two stages follows the same law vΓ = ΩR. (3) The evolution law is replaced by , where θ is the half-opening angle of the jet and 0 ≤ ν ≤ 2 is a free parameter determined by the magnetic field configuration. This is because the earlier efficient acceleration finally breaks the causality connection between different parts in the jet, preventing a global solution. The jet has to carry local charges and currents to support an electromagnetic balance. This approximate solution is consistent with known theoretical results and numerical simulations, and it is more convenient to directly compare with observations. This theory may be used to constrain the spin of black holes in astrophysical jets.

Study on the Harmonic Loss of Permanent Magnet Toroidal Space Motor for Hybrid Electric Vehicles

Based on magnetic gear transmission principle, permanent magnet toroidal space motor for hybrid electric vehicles with dual-rotor drive is proposed in this paper, harmonic loss caused by toroidal space relative motion of two rotors is conducted in hybrid drive mode. According to the structural principle of toroidal space motor, the speed of permanent magnet teeth of planet and worm inner rotor are decomposed to the revolution and rotation planes respectively. On the two planes, the frequency of alternating magnetic field at toroidal stator, planet and worm inner rotor are derived. At iron core and permanent magnetic teeth of stator and rotor, the magnetic field of revolution and rotation components are simulated. Combining with the speed relationship of toroidal space motor, the harmonic losses of revolution component and rotation component are analyzed in hybrid drive mode. The influence of speed matching of two rotors and toroidal stator material on harmonic loss are discussed. The results indicate that harmonic loss of permanent magnet toroidal space motor for hybrid electric vehicles can be reduced effectively by reducing relative speed of two rotors and adopting amorphous alloy for toroidal stator.

Waves in gas centrifuges: a review

Waves in gas centrifuges are generated by scoops for withdrawal of the gas. The physics of the waves and their role in the gas dynamics are under discussion. Strong centrifugal and Coriolis forces have dramatic impact on the properties and dispersion relation of the waves. The conventional sound, vertex and entropy waves split into 3 families with different dispersion. The entropy wave has zero velocity of propagation but variation of temperature in this wave is accompanied by toroidal motion. Pressure is not perturbed. The rest two families of the waves have nonzero velocities of propagation. Upper family has frequency above doubled frequency of rotation of the rotor with exceptional case of the wave (named acoustic wave) propagating exactly in the axial direction. This wave propagates with the conventional sound velocity and is polarized only in the axial direction. Unique property of this wave is the weakest damping due to the molecular viscosity and heat conductivity. All other waves are damped on distances compared with their wavelength. At the conventional parameters of the IGUASU centrifuge the acoustic waves are damped predominantly due to the viscous interaction and heat exchange with the wall of the rotor. This wave is able to propagate on the distance of ≤ 1 m. Numerical experiments show that the waves can affect the axial circulation and gas content in the centrifuge and produce phenomena of resonances. Possible impact of the waves on the process of separation of the isotopes is also under discussion.

Inferring the internal structure of γ Doradus variables from Rossby modes

A unique type of oscillation modes has recently been identified in γ Doradus variables. These low-frequency modes are called Rossby modes (or r modes) because they consist of Rossby waves in each spherical layer. These waves are characterised by toroidal motions that are restored by the latitudinal variation in the Coriolis force. The horizontal oscillations are weakly coupled in the radial direction. We show that these modes can be used to probe the interior of the stars. The method of the ν − √Δν diagram, which has originally been developed to analyse another type of modes, Kelvin g-modes (or prograde sectoral g-modes), is extended to take Rossby modes into account. We first show based on a theoretical model and then on two stars, KIC 3240967 and KIC 12066947, that the method can be adapted to Rossby modes straightforwardly. In addition, we demonstrate that simultaneous analysis of Kelvin and Rossby modes results in (1) smaller uncertainties in the internal rotation rate and the characteristic period of gravity modes, and (2) a substantial reduction of the correlation between the estimates of the two parameters.

Systematics of toroidal dipole modes in Ca, Ni, Zr, and Sn isotopes

We analyze the relation between isoscalar toroidal modes and so-called pygmy dipole resonance (PDR) which both appear in the same region of low-energy dipole excitations. To this end, we use a theoretical description within the fully self-consistent Skyrme quasiparticle random-phase approximation (QRPA). Test cases are spherical nuclei $^{40,48}$Ca, $^{58,72}$Ni, $^{90,100}$Zr, and $^{100,120,132}$Sn which cover four different elements and for each element at least two isotopes with different neutron excess, one small and another large. The structure of the modes is investigated in terms of strength functions, transition densities (TD) and transition currents (TC). For all considered nuclei, we see that, independently on whether PDR strength exists or not, the flow pattern in the lower part of the "PDR energy region" is basically the isoscalar vortical toroidal motion with a minor irrotational fraction. A one-to-one correspondence between calculated TD and TC can be established. The toroidal flow appears already in the uncoupled two-quasiparticle (2qp) excitations and becomes definitively strong for the QRPA modes. Altogether, we find that low-lying dipole strength often denoted as isoscalar PDR is actually an oversimplified imitation of the basically toroidal motion in nuclei with a sufficient neutron excess.

Test particle dynamics in low-frequency tokamak turbulence

We study the evolution of one million test particles in a turbulent plasma simulation, using the gyrokinetic code Trapped Element REduction in Semi-Lagrangian Approach (TERESA), as a method to get insights into the type of transport governing the plasma. TERESA (Trapped Element REduction in Semi-Lagrangian Approach) is a collisionless global 4D code which treats the trapped particles kinetically, while the passing particles are considered adiabatic. The Vlasov-Poisson system of equations is averaged over the cyclotron and the trapped particle's bounce motion, and thus, the model focuses on slow phenomena of the order of the toroidal precession motion of the banana orbits. We initialize the test particles, which are de facto “test banana-centers,” at a time of the simulation when the plasma is turbulent. We impose an initial temperature and density gradients, and only the Trapped Ion Mode (TIM) instability can develop in this system. We then calculate the Mean Squared Displacement of the test particles as a function of time in order to obtain a random walk diffusion coefficient. We observe that the radial diffusion of the test particles depends on their toroidal precession kinetic energy (E), in such a way that the transport of particles is dominated by a strong, relatively narrow peak at the resonant energies. A radial particle diffusion flux is then calculated and compared to the total radial particle flux accounting for all the transport processes such as diffusion and advection which is obtained directly from the TERESA code. We can thus compare the diffusive contribution to the particle flux against the nondiffusive contributions. The results show that the total flux is essentially diffusive which is consistent with our simulation setup aiming for “global turbulence.” Both fluxes present a peak around a resonance energy ER≈1.74Ti between the TIM and the particles. Both thermal and high-energy particles do not contribute significantly to radial transport.

Three-dimensional particle behavior using defocusing method in micro-toroidal vortex generated by optoelectrokinetic flow

This paper demonstrates a technique to realize multiphysics simulation and experimental validation of micro-toroidal vortex and utilizing the defocusing method to obtain the three-dimensional particles trajectory using a single camera. Fluorescent polystyrene particles were suspended at a concentration of 3.7 × 108 count mL−1 solution diluted with DI water. These were carried by the toroidal vortex fluid motion and showed an optoelectrokinetic phenomenon. We used a defocusing method to trace the three-dimensional trajectory of the particles. The size of the ring pattern increased as particles moved far away from the focusing plane and close to the objective lens. By recording the ring pattern size of one particle in every continuous frame, we successfully implemented the described techniques to obtain the three-dimensional trajectory of particles in an optoelectrokinetic experiment. Simulation results in COMSOL® Multiphysics (v4.3a) were compared to the trajectory and particle velocity variation in the experiment.

Nuclear Electromagnetic Generator: Introduction in Neutron Algebra and Elements of Neutron Kinetics

In the work, the problem of neutron kinetics in general view taking into account the all groups of delayed neutrons is solved. Conception of the matrix of complete neutron kinetics is introduced and are determined its properties. In the task about a finding of overt form for the solution of kinetic equations, the separation method and the reducing method of integrodifferential task to integral task with the aid of matched theorem are used. Diffusion of neutrons in the toroidal nuclear electric generator (nuclegen) is investigated also. Important conclusion about the practically complete absence of the diffusion of neutrons and charged fission particles (ionites) through the external boundary under toroidal motion is substantiated when solving of corresponding diffusion equation with the aid of Fourier’s standard separation method.

Diffusion of neutrons in the toroidal nuclear electrogenerator

Diffusion of neutrons in the toroidal nuclear electrogenerator (nuclegen) is investigated. Important conclusion about the practically complete absence of the diffusion of neutrons and charged fission particles through the external boundary under toroidal motion is substantiated by the solution of corresponding equation diffusion with the aid of Fourier’s standard division method.