External Horizontal Magnetic Field Research Articles

Effect of horizontal magnetic field on Küppers–Lortz instability

We investigate the effect of an external horizontal magnetic field on the Küppers–Lortz instability (KLI) in rotating Rayleigh–Bénard convection of Boussinesq fluids using weakly nonlinear theory along with linear theory. By the KLI, we mean the instability where the two-dimensional roll solutions of the system occurring at the onset of convection become unstable against the perturbations by rolls oriented at different angles with the previous one as the rotation rate exceeds a critical value. The governing parameters, namely, the Prandtl number (Pr), the Taylor number (Ta), and the Chandrasekhar number (Q), are varied in the ranges 0.8≤Pr<∞, 0<Ta≤104, and 0≤Q≤104, respectively, by considering the vanishingly small magnetic Prandtl number limit. In the Pr→∞ limit, magnetic field is found to inhibit the KLI by enhancing the critical Taylor number (Tac) for its onset. On the other hand, for finite Prandtl number fluids, the KLI is favored for lower Q, and it is inhibited for higher Q. Interestingly, in the finite Prandtl number range, both KLI and small angle instability are manifested depending on the Prandtl number. No small-angle instability is observed for Pr≥50, and the rotation-induced KLI is inhibited predominantly by the magnetic field, while, for Pr<50, along with the Küppers–Lortz instability, small-angle instability is also observed. However, in this case, the KLI is favored for lower Q, while it is inhibited for higher Q.

Three-dimensional direct numerical simulation of free-surface magnetohydrodynamic wave turbulence.

We report on three-dimensional direct numerical simulation of wave turbulence on the free surface of a magnetic fluid subjected to an external horizontal magnetic field. A transition from capillary-wave turbulence to anisotropic magneto-capillary wave turbulence is observed for an increasing field. At high enough field, wave turbulence becomes highly anisotropic, cascading mainly perpendicularly to the field direction, in good agreement with the prediction of a phenomenological model, and with anisotropic Alfvén wave turbulence. Although surface waves on a magnetic fluid are different from Alfvén waves in plasma, a strong analogy is found with similar wave spectrum scalings and similar magnetic-field dependent dispersionless wave velocities.

Crisis-induced flow reversals in magnetoconvection.

We report the occurrence of flow reversals induced by the attractor-merging crisis in Rayleigh-Bénard convection of electrically conducting low-Prandtl-number fluids in the presence of a uniform external horizontal magnetic field. The simultaneous collision of two coexisting chaotic attractors with an unstable fixed point and its associated stable manifold takes place in the higher-dimensional phase space of the system, leading to a single merged chaotic attractor. The effect of strength of the magnetic field on the flow reversal phenomena is also explored in detail.

NUMERICAL INVESTIGATION OF HORIZONTAL MAGNETIC FIELD EFFECT ON THE FLOW CHARACTERISTICS OF GALLIUM FILLED IN A VERTICAL ANNULUS

In the present numerical study, the effect of an external horizontal magnetic field on the natural convection of an electrically conducting molten metal (gallium) inside a vertical cylindrical crucible has been investigated. The effect of the external magnetic field is evaluated on the flow pattern and also the temperature field of molten gallium in the mold with an aspect ratio of A=1.0 and a radii ratio of λ=3.0. A series of simulations are carried out for Hartmann numbers of 0, 22.5, 112, and 167 and Rayleigh numbers of 104, 105, and 106. The obtained results show that for a given Rayleigh number, increasing the Hartmann number suppresses convection flows in all directions with different intensities. Moreover, it was found that the employed horizontal magnetic field leads to vanishing the axisymmetric pattern of flow structures. This is due to the formation of Roberts and Hartmann layers near the walls parallel (0° and 180°) and normal (90° and 270°) to the magnetic field, respectively. Additionally, it is found that the presence of the magnetic field results in the reduction of convection heat transfer. This reduction is lower in the 90° and 270° directions due to the development of Roberts layers near the walls parallel to an external magnetic field. Finally, the numerical results have been validated against the published reliable data.

Overstable rotating convection in the presence of a vertical magnetic field

Recently, Banerjee et al. [Phys. Rev. E 102, 013107 (2020)] investigated overstable rotating convection in the presence of an external horizontal magnetic field and reported a rich bifurcation structure near the onset. However, the bifurcation structure near the onset of overstable rotating convection in the presence of a vertical magnetic field has not been explored yet. We address the issue here by performing three dimensional direct numerical simulations and low-dimensional modeling of the system using a Rayleigh–Bénard convection model. The control parameters, namely, the Taylor number (Ta), the Chandrasekhar number (Q), and the Prandtl number (Pr) are varied in the ranges 750≤Ta≤106, 0<Q≤103, and 0<Pr≤0.5. Our investigation reveals two qualitatively different onset scenarios including bistability (coexistence of subcritical and supercritical convections). Analysis of the low-dimensional model shows that a supercritical Hopf bifurcation is responsible for the supercritical onset and a subcritical pitchfork bifurcation is responsible for the subcritical onset. It is also observed that the appearance of a subcritical convection at the onset has strong dependence on all three control parameters: Ta, Q, and Pr. The scenario of a subcritical convection is found to disappear as Pr is increased for fixed Ta and Q. However, most striking findings of the investigation are that the increment in Ta for fixed Q and Pr opposes the subcritical convection, whereas the increment in Q for fixed Ta and Pr favors it. This is in sharp contrast with the earlier results reported in rotating magnetoconvection.

Collisional ferrohydrodynamics of magnetic fluid droplets on superhydrophobic surfaces

The study reports the aspects of post-impact hydrodynamics of ferrofluid droplets on superhydrophobic (SH) surfaces in the presence of a horizontal magnetic field. A wide gamut of dynamics was observed by varying the impact Weber number (We), the magnetic field strength (manifested through the magnetic Bond number (Bom), which is defined as the ratio of magnetic force to surface tension force), and the Hartmann number (Ha), defined as the ratio of magnetic force to the viscous force. For a fixed We ∼ 60, we observed that at moderately low Bom ∼300, droplet rebound off the SH surface is suppressed. The noted We is chosen to observe various impact outcomes and to reveal the consequent ferrohydrodynamic mechanisms. We also show that ferrohydrodynamic interactions lead to asymmetric spreading due to variation in magnitude of the Lorentz force, and the droplet spreads preferentially in a direction orthogonal to the magnetic field lines. We show analytically that during the retraction regime, the kinetic energy of the droplet is distributed unequally in the transverse (orthogonal to the external horizontal magnetic field) and longitudinal (along the direction of the magnetic field) directions. This ultimately leads to the suppression of droplet rebound. We studied the role of Bom at fixed We ∼ 60 and observed that the liquid lamella becomes unstable at the onset of retraction phase, through nucleation of holes, their proliferation and rupture after reaching a critical thickness only on SH surfaces, but is absent on hydrophilic surfaces. We propose an analytical model to predict the onset of instability at a critical Bom. The model shows that the critical Bom is a function of the impact We, and the critical Bom decreases with increasing We. We illustrate a phase map encompassing all the post-impact ferrohydrodynamic phenomena on SH surfaces for a wide range of We and Bom.

Argon bubble flow in liquid gallium in external magnetic field

This paper presents detailed results of neutron imaging of argon bubble flows in a rectangular liquid gallium vessel with and without the application of external horizontal magnetic field. The developed image processing algorithm is presented and its capability to extract physical information from images of low signal-to-noise ratio is demonstrated. Bubble parameters, velocity components, trajectories and relevant statistics were computed and analysed. A simpler version of the code was applied to the output of computational fluid dynamics simulations that reproduced the experiment. This work serves to further validate the neutron radiography as a suitable method for monitoring gas bubble flow in liquid metals, as well as to outline procedures that might help others to extract data from neutron radiography images with a low signal-to-noise ratio resulting from high frame rate acquisitions required to resolve rapid bubble motion.

Investigation of liquid metal drop impingement on a liquid metal surface under the influence of a horizontal magnetic field

Considering the existence of a horizontal magnetic field, we experimentally investigate the process of a liquid metal drop with high surface tension impacting a film of the same liquid. High-speed photography is adopted here to capture the dynamics of the interaction between the drop and the liquid film. We observe three typical outcomes after drop impact on the film, namely, symmetric crown, asymmetric crown, and prompt splashing, among which the asymmetric crown is first discovered by the present experiments. Moreover, the experimental variables, such as the drop size, impact velocity, initial film thickness, and intensity of the magnetic field, are included to study the three outcomes in detail. For crown formation, the external horizontal magnetic field changes the shape of the crown from symmetric to asymmetric during the crown expansion process, while for prompt splashing, the external horizontal magnetic field promotes splashing from the liquid layer where the drop and the liquid film meet and reduces the critical Weber number where prompt splashing occurs. Therefore, the present experimental results conclusively prove that the external horizontal magnetic field affects the process of liquid metal drop impact on a liquid metal film. Finally, by selecting a typical case, we carried out the direct numerical simulation to calculate the distribution of the magnetic-field-induced Lorentz force inside the droplet after impact, which helps us fully understand the phenomena observed.

Transitions near the onset of low Prandtl-number rotating convection in presence of horizontal magnetic field

We investigate the transitions near the onset of thermal convection in electrically conducting low Prandtl-number (Pr) fluids in the presence of rotation about a vertical axis and external horizontal magnetic field. Three-dimensional direct numerical simulations (DNSs) and low dimensional modeling are performed with the Rayleigh–Bénard convection system in the ranges 0 < Q ≤ 1000 and 0 < Ta ≤ 500 of the Chandrasekhar number (Q) and the Taylor number (Ta), respectively, for that purpose. For larger Q(≥32.7), DNSs show substantial enhancement of convective heat transport and only finite amplitude steady two dimensional roll patterns at the onset. On the other hand, for smaller Q(<32.7), very rich dynamics involving different stationary as well as time dependent patterns, including stationary two-dimensional rolls, cross rolls, and oscillatory cross rolls, are observed at the onset of convection. Our investigation uncovers the cause of enhancement of heat transport and the origin of different flow patterns at the onset. We establish that a first order transition to convection occurring at the onset is responsible for the enhancement of the heat transport there. Furthermore, as the Rayleigh number (Ra) is increased beyond the onset, subsequent transitions near it are also explored in detail for smaller Q, and these are found to be associated with a variety of bifurcations including subcritical/supercritical pitchfork, Hopf, imperfect pitchfork, imperfect gluing, and Neimark–Sacker.

A Miniature Resonant and Torsional Magnetometer Based on Lorentz Force.

A microelectromechanical system (MEMS) torsional resonant magnetometer based on Lorentz force was investigated, consisting of torsional structures, torsional beams, metal plates, a coil, and a glass substrate. The Lorentz force, introduced by the interaction between the current in the MEMS coil and an external horizontal magnetic field, leads to displacement of the torsional structure. The strength of the magnetic field is proportional to this displacement, and can be detected with two sensing capacitors fabricated on the torsion structure and the substrate. To improve sensor sensitivity, a folded torsional beam and a double-layer excitation coil were introduced. The fabrication processes included lift-off, anodic bonding, chemical mechanical planarization, silicon nitride (SiNx) deposition, plasma-enhanced chemical vapor deposition, and inductively coupled plasma release. The prototype of the magnetometer was finished and packaged. The sensor performance, including its sensitivity and repeatability, was tested in a low-pressure environment. Additionally, the influences of structural parameters were analyzed, including the resistance of the excitation coil, the initial value of the capacitors, the elastic coefficient of the torsional beam, and the number of layers in the excitation coil. The test results demonstrated that this sensor could meet the requirements for attitude determination systems in low earth orbit satellites.

In-situ fabrication of graded material with the application of a horizontal magnetic field during directional solidification

The present paper proposes a method of graded materials preparation under a low horizontal magnetic field during directional solidification. The external horizontal magnetic field was applied to the mushy zone of the directionally solidified Al-10 wt% Cu and Al-18 wt% Si samples, which was perpendicular to the growth direction. Experimental results demonstrate that the applied horizontal magnetic field produces a gradient size distribution of the primary α(Al) grains in Al-10 wt% Cu alloys and a gradient fraction distribution of primary Si particles in Al-18 wt% Si alloys. 3D numerical simulations indicate that the formation of graded structure should be attributed to the migration of primary phase driven by the thermoelectric magnetic force (TEMF). The formation of segregation channel should be attributed to the TEM convection (TEMC) in the mushy zone. Further, in situ synchrotron X-ray radiography observations of the initial transient of directional solidification show that the primary α(Al) phases were migrated approximately along the direction perpendicular to the magnetic field. These results suggest that the TEM effects can greatly change the growth of primary grains and the solidification structure, and the application of an external horizontal magnetic field would be beneficial to fabricate the graded material during directional solidification.

Simulation of heat transfer and entropy generation of MHD natural convection of non-Newtonian nanofluid in an enclosure

In this paper, heat transfer and entropy generation on laminar natural convection of non-Newtonian nanofluids in the presence of an external horizontal magnetic field in a square cavity has been analyzed by Finite Difference Lattice Boltzmann Method (FDLBM). The cavity is filled with water and nanoparticles of copper (Cu) while the mixture shows shear-thinning behavior. This study has been conducted for the certain pertinent parameters of Rayleigh number (Ra=104–105), power-law index (n=0.6–1), Hartmann number (Ha=0–90) and the volume fraction has been studied from φ=0 to 0.04. Results indicate that the augmentation of the power-law index causes heat transfer to drop in the absence of the magnetic field, by contrast, the heat transfer increases with the rise of power-law index in the presence of the magnetic field. The addition of nanoparticle augments heat transfer for multifarious studied parameters. The heat transfer drops with the increase in Hartmann number generally and also affects the power-law index and nanoparticles influences on heat transfer. Augmentation of the volume fraction and Rayleigh number enhance all kinds of entropy generations of heat transfer, fluid friction, and the magnetic field in different studied parameters. The increase in the Hartmann number causes the total entropy generation to drop and affects the influences of the power-law index and the volume fraction on the entropy generations.

Oscillatory instability and routes to chaos in Rayleigh-Bénard convection: Effect of external magnetic field

We investigate oscillatory instability and routes to chaos in Rayleigh-Bénard convection of electrically conducting fluids in the presence of an external horizontal magnetic field. Three dimensional direct numerical simulations (DNS) of the governing equations are performed for the investigation. DNS shows that oscillatory instability is inhibited by the magnetic field. The supercritical Rayleigh number for the onset of oscillation is found to scale with the Chandrasekhar number Q as in DNS with α = 1.8 for low Prandtl numbers (Pr). Most interestingly, DNS shows Q-dependent routes to chaos for low-Prandtl-number fluids like mercury (Pr = 0.025). For low Q, period-doubling routes are observed, while, quasiperiodic routes are observed for high Q. The bifurcation structure associated with Q-dependent routes to chaos is then understood by constructing a low-dimensional model from the DNS data. The model also shows similar scaling laws as DNS. The bifurcation analysis of the low-dimensional model shows that the origin of different routes is associated with the bifurcation structure near the primary instability. These observations show a similarity with the previous results of convection experiments performed with mercury.

External Magnetic Field Effects on the Rayleigh-Taylor Instability in an Inhomogeneous Rotating Quantum Plasma

The effects of external magnetic field effects on the Rayleigh-Taylor instability in an inhomogeneous stratified quantum plasma rotating uniformly are investigated. The external magnetic field is considered in both horizontal and vertical direction. The linear growth rate is derived for the case where a plasma with exponential density distribution is confined between two rigid planes at z=0 and z=h, by solving the linear QMHD equations into normal mode. Some special cases are particularized to explain the roles that play the variables of the problem. The results show that, the presence of both external horizontal and vertical magnetic field beside the quantum effect will bring about more stability on the growth rate of unstable configuration. The maximum stability will happen in the case of wave number parallels to or in the same direction of external horizontal magnetic field.

Hydromagnetic Double-Diffusive Laminar Natural Convection in a Radiatively Participating Fluid

ABSTRACT Two-dimensional hydromagnetic double-diffusive convection of a radiatively participating fluid confined in a rectangular enclosure is studied numerically for fixed Prandtl, Rayleigh, and Lewis numbers, Pr = 13.6, Ra = 105, Le = 2. Uniform temperatures and concentrations are imposed along the vertical walls, while the horizontal walls are assumed to be adiabatic and impermeable. The damping and stabilization effects of an external horizontal magnetic field are studied for three different optical thicknesses of the semitransparent fluid as well as for an opaque medium. For moderate optical thickness, a steady compositionally dominated flow is observed for all values of Hartmann number considered, and the magnetic damping is remarkably lower than in the opaque medium, for which the flow is always thermally dominated. For optically thin and optically thick media, the thermally dominated flow is stabilized and becomes compositionally dominated as soon as the Hartmann number is increased.

ADJOINT VARIABLE METHOD FOR THE THERMAL DESIGN OF EUTECTIC DIRECTIONAL SOLIDIFICATION PROCESSES IN AN OPEN-BOAT CONFIGURATION

A computational method for the inverse design of a directional solidification process of a near-eutectic binary alloy driven by the coupled action of buoyancy, thermocapillary, and electromagnetic convection is presented. The objective is to calculate the mold cooling/heating conditions such that a stable desired interface growth with growth velocity vf and thermal gradient G is achieved. The interface velocity vf and thermal gradient G are chosen such that a diffusion-based growth is obtained in the presence of melt convection. Morphological stability is enforced by imposing an appropriate magnitude of G/|vf|, which is determined a-priori based on the constitutional stability criterion. The design problem is posed as a functional optimization problem. The cost functional is defined so as to represent the deviation of the freezing interface thermal conditions from thermodynamic equilibrium. An appropriate continuum adjoint problem is defined such that an analytical expression for the gradient of the objective function is obtained. The conjugate gradient method coupled with the finite element solutions of the continuum direct, sensitivity, and adjoint problems is employed for solving the inverse problem. The method is demonstrated with an example of calculating the boundary thermal fluxes for the directional growth of an Sb-8.6% Ge melt in an open-boat configuration under the influence of an external horizontal magnetic field such that a stable vertical interface advances from left to right with a desired growth velocity.

Ising wall instability in a nematic liquid crystal

A new instability for a splay-bend Ising wall was found in a 5CB nematic liquid crystal layer. This instability, which occurs in the presence of an external horizontal magnetic field, is driven by the elastic anisotropy of the liquid crystal material. Depending on the homogeneity of the magnetic field, the unstable straight interface evolves towards a new steady state or undergoes a spinodal decomposition into facets. Energy arguments are given in order to explain these physical phenomena.

Natural oscillations of a liquid of finite electrical conduction in the presence of an external magnetic field

The effect of the finite electrical conduction (finiteness of the magnetic Reynolds number), which is considered a dissipative factor, on small natural oscillations of an ideal heavy liquid of finite depth whose free surface borders on vacuum is studied. A constant external horizontal magnetic field is applied to the liquid. The energy-balance equation is derived, and the theorem of wave attenuation with time is proved. Numerical calculations and the resulting asymptotic formulas give a complete pattern of the spectrum, including its continuous part. The amplitude-frequency characteristics of the wave modes are presented.

Hydromagnetic stability analysis of a Solar prominence suspended in an external horizontal magnetic field

AbstractAmong the observed characteristics of quiescent solar prominences, stability is perhaps the most important requirement for theoretical models of these coronal structures. Only stable equilibria can explain the presence of such cool and dense plasma sheets for extended periods of time. Utilizing the MHD‐Energy Principle (Bernstein et al. 1958) we investigate the linear stability properties of the two‐dimensional prominence equilibrium of Osherovich (1985). Incorporating a finite magnetic energy and a continous magnetic field, this model takes into account explicitly an external horizontal magnetic field in which the prominence is suspended. The presented numerical calculations indicate that the prominence model of Osherovich is stable and can explain the main features of reported oscillations. Instabilities occur only when model parameters are unrealistic for physical conditions in solar prominences.

Solar prominence model based on eigenvalue solutions. I - Isolated filaments and their properties under the influence of external horizontal magnetic field

view Abstract Citations (14) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Solar prominence model based on eigenvalue solutions. I - Isolated filaments and their properties under the influence of external horizontal magnetic field Osherovich, V. A. Abstract The magnetohydrostatic equilibrium of solar prominences is treated analytically. The set of exact eigenvalue solutions that describes topologically different magnetic configurations is found. These solutions correspond to magnetic configurations with continuous magnetic field and finite magnetic energy per unit length of filament. The influence of a horizontal magnetic field on a filament is considered in detail. With thermodynamic parameters observed by Landman, the magnetic field and total mass of a prominence with a simple magnetic topology are estimated. Publication: The Astrophysical Journal Pub Date: October 1985 DOI: 10.1086/163530 Bibcode: 1985ApJ...297..314O Keywords: Eigenvalues; Magnetic Field Configurations; Solar Magnetic Field; Solar Physics; Solar Prominences; Filaments; Ground State; Magnetic Flux; Magnetohydrostatics; Solar Physics full text sources ADS |