Axisymmetric Magnetohydrodynamics Research Articles

A Coupled Magnetohydrodynamics (MHD) and Thermal Stress-Strain Model to Explore the Impact of Gas Cooling on Ingot Solidification Shrinkage in Vacuum Arc Remelting (VAR) Process

An advanced 2D axisymmetric magnetohydrodynamics model, including calculations for electromagnetic, thermal, and flow fields, fully coupled with a thermal stress-strain model, allowing the computation of solid mechanical parameters like stress, strain, and deformation within the ingot of the vacuum arc remelting process is presented. This process encounters challenges due to solidification shrinkage, which causes losing contact between the ingot and the mold, reducing the cooling efficiency of the system, resulting in a deeper melt pool and decreasing ingot quality. Herein, the width of the air gap along the ingot, the precise position of contact between the ingot and mold, and the profile of the melt pool, affected by gas cooling, are calculated. The global pattern of transport phenomena, such as (electro-vortex) flow and electromagnetic fields in the bulk of the ingot, is insensitive to helium gas cooling through the shrinkage gap. However, including gas cooling significantly improves heat removal through the mold, which consequently reduces the pool depth of the Alloy 718 ingot, leading to an improvement in the quality of the ingot.

Research on an Equivalent Heat Source Model of the AC Arc in the Short Gap of a Copper-Core Cable and a Fire Risk Assessment Method.

The magnetohydrodynamics (MHD) model of the alternating current (AC) arc is complex, so a simplified equivalent heat source (EHS) model can be used to replace the complex model in studying the AC arc's thermal characteristics and cable fire risk. A 2D axisymmetric AC arc MHD simulation model in the short gap of a copper-core cable is established in this paper. The AC arc voltage and current obtained by the model are consistent with experiments. The AC arc's heat source distribution obtained by the MHD model is fitted to obtain the heat source function Q of the AC arc. Q is divided into 16 independent segmented heat sources, and a correction matrix is constructed to optimize the segmented heat sources. A neural network and a genetic algorithm give the prediction model and the optimal correction matrix of the segmented heat source. The EHS model optimized by the optimal correction matrix can obtain a minimum temperature error of 5.8/4.4/4.2% with the MHD model in different AC arc peak currents 2/4/6 A. The probability of a cable fire is calculated by using AC arc's optimized EHS model when different numbers of AC arcs are generated randomly in AC half-waves. The EHS model can replace the complex MHD model to study the thermal characteristics of AC arcs and quickly calculate the probability of a cable fire caused by random AC arcs.

Numerical simulations of MHD jets from Keplerian accretion disks

Context. The most successful scenario for the origin of astrophysical jets requires a large-scale magnetic field anchored in a rotating object (black hole or star) and/or its surrounding accretion disk. Platform jet simulations, where the mass load onto the magnetic field is not computed by solving the vertical equilibrium of the disk but is imposed as a boundary condition, are very useful for probing the jet acceleration and collimation mechanisms. The drawback of such simulations is the very large parameter space: despite many previous attempts, it is very difficult to determine the generic results that can be derived from them. Aims. We wish to establish a firm link between jet simulations and analytical studies of magnetically driven steady-state jets from Keplerian accretion disks. In particular, the latter have predicted the existence of recollimation shocks – due to the dominant hoop stress –, which have so far never been observed in platform simulations. Methods. We performed a set of axisymmetric magnetohydrodynamics (MHD) simulations of nonrelativistic jets using the PLUTO code. The simulations are designed to reproduce the boundary conditions generally expected in analytical studies. We vary two parameters: the magnetic flux radial exponent α and the jet mass load κ. In order to reach the huge unprecedented spatial scales implied by the analytical solutions, we used a new method allowing us to boost the temporal evolution. Results. We confirm the existence of standing recollimation shocks at large distances. As in self-similar studies, their altitude evolves with the mass load κ. The shocks are weak and correspond to oblique shocks in a moderately high, fast magnetosonic flow. The jet emitted from the disk is focused toward the inner axial spine, which is the outflow connected to the central object. The presence of this spine is shown to have a strong influence on jet asymptotics. We also argue that steady-state solutions with α ≥ 1 are numerically out of range. Conclusions. Internal recollimation shocks may produce observable features such as standing knots of enhanced emission and a decrease in the flow rotation rate. However, more realistic simulations (e.g. fully three-dimensional) must be carried out in order to investigate nonaxisymmetric instabilities and with ejection only from a finite zone in the disk, so as to to verify whether these MHD recollimation shocks and their properties are maintained.

Regularity via one vorticity component for the 3D axisymmetric MHD equations

AbstractIn this paper, we investigate the regularity criteria of axisymmetric weak solutions to the three‐dimensional (3D) incompressible magnetohydrodynamics (MHD) equations with nonzero swirl component. By making use of techniques of the Littlewood–Paley decomposition, we show that weak solutions to the 3D axisymmetric MHD equations become regular if the swirl component of vorticity satisfies that , which partially gives a positive answer to the marginal case for the regularity of MHD equations.

Axisymmetric smoothed particle magnetohydrodynamics

ABSTRACT Many astrophysical and terrestrial scenarios involving magnetic fields can be approached in axial geometry. Although the smoothed particle hydrodynamics (SPH) technique has been successfully extended to magnetohydrodynamics (MHD), a well-verified, axisymmetric MHD scheme based on such technique does not exist yet. In this work, we fill that gap in the scientific literature and propose and check a novel axisymmetric MHD hydrodynamic code, that can be applied to physical problems which display the adequate geometry. We show that the hydrodynamic code built following these axisymmetric hypothesis is able to produce similar results than standard 3D-SPMHD codes with equivalent resolution but with much lesser computational load.

On the Global Well-Posedness of the 3D Axisymmetric Resistive MHD Equations

In this paper, we prove the global well-posedness for the three-dimensional magnetohydrodynamics (MHD) equations with zero viscosity and axisymmetric initial data. First, we analyze the problem corresponding to the Sobolev regularities $ H^s\times H^{s-2}$, with $ s>5/2$. Second, we address the same problem but for the Besov critical regularities $ B_{p,1}^{3/p+1}\times B_{1,p}^{3/p-1}$, $2\leq p\leq \infty$. This case turns out to be more subtle as the Beale-Kato-Majda criterion is not known to be valid for rough regularities.

Numerical Simulation of Heat Transfer Flow Subject to MHD of Williamson Nanofluid with Thermal Radiation

In this paper, heat transfer and entropy of steady Williamson nanofluid flow based on the fundamental symmetry is studied. The fluid is positioned over a stretched flat surface moving non-uniformly. Nanofluid is analyzed for its flow and thermal transport properties by consigning it to a convectively heated slippery surface. Thermal conductivity is assumed to be varied with temperature impacted by thermal radiation along with axisymmetric magnetohydrodynamics (MHD). Boundary layer approximations lead to partial differential equations, which are transformed into ordinary differential equations in light of a single phase model accounting for Cu-water and TiO2-water nanofluids. The resulting ODEs are solved via a finite difference based Keller box scheme. Various formidable physical parameters affecting fluid movement, difference in temperature, system entropy, skin friction and Nusselt number around the boundary are presented graphically and numerically discussed. It has also been observed that the nanofluid based on Cu-water is identified as a superior thermal conductor rather than TiO2-water based nanofluid.

A 2-D Axisymmetric Magneto-Hydrodynamic Model of a DC Arc Plasma Torch and Its Solution Methodology

The behavior of dynamic plasma is governed by the magneto-hydrodynamic (MHD) equation, and the efficient solution is still an open challenging issue in computational electromagnetics. In this article, to efficiently predict the behavior of an engineering direct current (dc) arc plasma torch, a 2-D axisymmetric MHD model is introduced and its solution methodology is proposed. In the methodology, the initial temperature field of the MHD model is estimated based on a predicted trajectory of the plasma arc, determined by using the single-particle orbital theory; a simple yet efficient iterative procedure using a prediction-correction approach to determine the magnetic field and to solve the corresponding 2-D finite-element equations of the mass, momentum, and energy conservations is proposed; and an approach to solve the extremely small conductivity near the electrodes is introduced. Finally, a finite element method code is developed and used to compute the multi-physics fields of the plasmas with promising results.

Multiple Slip Effects on Magnetohydrodynamic Axisymmetric Buoyant Nanofluid Flow above a Stretching Sheet with Radiation and Chemical Reaction

The present article investigates the effect of multiple slips on axisymmetric magnetohydrodynamics (MHD) buoyant nano-fluid flow over a stretching sheet with radiation and chemical effect. The non-linear partial differential equations were transformed to a non-linear control equation using an appropriate similarity transformation. The governing equations were solved through the finite element method. The influence of physical parameters such as multiple slips, magnetic, thermal radiation, Prandtl number, stretching, Brownian motion, thermophoresis, Schmidt number, Lewis number and chemical reaction on the radial velocity, temperature, solutal concentration and nano-fluid volume fraction profile were investigated. We noted that the boundary layers increases in the presence of multiple slip effects whereas, the effect of thermal slip on Nusselt number increases with the increasing values of magnetic and thermal radiation. To verify the convergence of the numerical solution, the computations were made by reducing the mesh size. Finally, our results are parallel to previous scholarly contributions.

Comparisons of MHD propeller model with observations of cataclysmic variable AE Aqr

ABSTRACT We have developed a numerical magnetohydrodynamic (MHD) model of the propeller candidate star AE Aqr using axisymmetric MHD simulations. We suggest that AE Aqr is an intermediate polar-type star, where the magnetic field is relatively weak and an accretion disc may form around the white dwarf. The star is in the propeller regime, and many of its observational properties are determined by the disc–magnetosphere interaction. Comparisons of the characteristics of the observed versus modelled AE Aqr star show that the model can explain many observational properties of AE Aqr. In a representative model, the magnetic field of the star is B ≈ 3.3 × 105 G and the time-averaged accretion rate in the disc is 5.5 × 1016 g s−1. Most of this matter is ejected into conically shaped winds. The numerical model explains the rapid spin-down of AE Aqr through the outflow of angular momentum from the surface of the star to the wind, corona, and disc. The energy budget in the outflows, 9 × 1033 erg s−1, is sufficient for explaining the observed flaring radiation in different wavebands. The time-scale of ejections into the wind matches the short time-scale variability in the light curves of AE Aqr.

Axisymmetric benchmarks of impurity dynamics in extended-magnetohydrodynamic simulations

A verification benchmark has been carried out between the M3D-C1 and NIMROD extended-magnetohydrodynamic codes for simulations of impurity-induced disruption mitigation. Disruptions are a significant concern for future tokamaks and high-fidelity simulations are required in order to ensure the success of disruption mitigation techniques (e.g. shattered-pellet injection) in large-scale fusion reactors. Both magnetohydrodynamic (MHD) codes have been coupled to the Killer Pellet RADiation code for impurity dynamics. The codes show excellent agreement in four axisymmetric, nonlinear simulations, particularly during the thermal quench. This agreement is seen in the time histories of global plasma quantities such as thermal energy, radiated power, and total number of electrons, as well as 2D contours of temperature and current density. The simulations predict that, given the same number of atoms injected, argon quenches the plasma two-to-three times as fast as neon. Furthermore, the inclusion of temperature-dependent Spitzer resistivity causes the current to diffuse and to decay, inducing axisymmetric MHD instabilities that result in a current quench. This work represents an important verification of the coupled impurity and MHD models implemented in M3D-C1 and NIMROD, giving greater confidence in the ability of both codes to perform more sophisticated disruption mitigation simulations.

Axisymmetric MHD viscous flows bounded by a solid plane normal to a uniform ambient magnetic field: fundamental flows and application to a solid sphere translating normal to the wall

This work first determines two axisymmetric fundamental Magneto Hydrodynamic (MHD) flows induced, in a conducting Newtonian liquid domain bounded by a plane wall, by distributing either radial or a...

Behavior of thin disk crystalline morphology in the presence of corrections to ideal magnetohydrodynamics.

We analyze an axisymmetric magnetohydrodynamics configuration, describing the morphology of a purely differentially rotating thin plasma disk, in which linear and nonlinear perturbations are triggered associated with microscopic magnetic structures. We study the evolution of the nonstationary correction in the limit in which the corotation condition (i.e., the dependence of the disk angular velocity on the magnetic flux function) is preserved and the poloidal velocity components are neglected. The main feature we address here is the influence of ideal (finite electron inertia) and collisional (resistivity, viscosity, and thermal conductivity) effects on the behavior of the flux function perturbation and of the associated small-scale modifications in the disk. We analyze two different regimes in which resistivity or viscosity dominates and study the corresponding linear and nonlinear behaviors of the perturbation evolution, i.e., when the backreaction magnetic field is negligible or comparable to the background one, respectively. We demonstrate that when resistivity dominates, a radial oscillating morphology (crystalline structure) emerges and it turns out to be damped in time, in both the linear and nonlinear regimes, but in such a way that the resulting transient can be implemented in the description of relevant astrophysical processes, for instance, associated with jet formation or cataclysmic variables. When the viscosity effect dominates the dynamics, only the nonlinear regime is available and a very fast instability is triggered.

General-relativistic Simulations of Four States of Accretion onto Millisecond Pulsars

Abstract Accreting neutron stars can power a wide range of astrophysical phenomena including short- and long-duration gamma-ray bursts, ultra-luminous X-ray sources, and X-ray binaries. Numerical simulations are a valuable tool for studying the accretion-disk–magnetosphere interaction that is central to these problems, most clearly for the recently discovered transitional millisecond pulsars. However, magnetohydrodynamic (MHD) methods, widely used for simulating accretion, have difficulty in highly magnetized stellar magnetospheres, while force-free methods, suitable for such regions, cannot include the accreting gas. We present an MHD method that can stably evolve essentially force-free, highly magnetized regions, and describe the first time-dependent relativistic simulations of magnetized accretion onto millisecond pulsars. Our axisymmetric general-relativistic MHD simulations for the first time demonstrate how the interaction of a turbulent accretion flow with a pulsar’s electromagnetic wind can lead to the transition of an isolated pulsar to the accreting state. This transition naturally leads to the formation of relativistic jets, whose power can greatly exceed the power of the isolated pulsar’s wind. If the accretion rate is below a critical value, the pulsar instead expels the accretion stream. More generally, our simulations produce for the first time the four possible accretion regimes, in order of decreasing mass accretion rate: (a) crushed magnetosphere and direct accretion; (b) magnetically channeled accretion onto the stellar poles; (c) the propeller state, where material enters through the light cylinder but is prevented from accreting by the centrifugal barrier; (d) almost perfect exclusion of the accretion flow from the light cylinder by the pulsar wind.

A new method for extending solutions to the self-similar relativistic magnetohydrodynamic equations for black hole outflows

The paradigm in which magnetic fields play a crucial role in launching/collimating outflows in many astrophysical objects continues to gain support. However, semi-analytical models including the effect of magnetic fields on the dynamics and morphology of jets are still missing due to the intrinsic difficulties in integrating the equations describing a collimated, relativistic flow in the presence of gravity. Only few solutions have been found so far, due to the highly nonlinear character of the equations together with the need to blindly search for singularities. These numerical problems prevented a full exploration of the parameter space. We present a new integration scheme to solve r-self-similar, stationary, axisymmetric magnetohydrodynamics equations describing collimated, relativistic outflows crossing smoothly all the singular points (Alfven point and modified slow/fast points). For the first time, we are able to integrate from the disk mid-plane to downstream of the modified fast point. We discuss an ensemble of jet solutions, emphasising trends and features that can be compared to observables. We present, for the first time with a semi-analytical MHD model, solutions showing counter-rotation of the jet for a substantial fraction of its extent. We find diverse jet configurations with bulk Lorentz factors up to 10 and potential sites for recollimation between $10^3-10^7$ gravitational radii. Such extended coverage of the intervals of quantities, such as magnetic-to-thermal energy ratios at the base or the heights/widths of the recollimation region, makes our solutions suitable for application to many different systems where jets are launched.

On Unsteady Three-Dimensional Axisymmetric MHD Nanofluid Flow with Entropy Generation and Thermo-Diffusion Effects on a Non-Linear Stretching Sheet

The entropy generation in unsteady three-dimensional axisymmetric magnetohydrodynamics (MHD) nanofluid flow over a non-linearly stretching sheet is investigated. The flow is subject to thermal radiation and a chemical reaction. The conservation equations are solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasi-linearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account. The nanofluid particle volume fraction on the boundary is passively controlled. The results show that as the Hartmann number increases, both the Nusselt number and the Sherwood number decrease, whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with respect to some physical parameters.

Steady-state axisymmetric nonlinear magnetohydrodynamic solutions with various boundary conditions

Axisymmetric magnetohydrodynamics (MHD) can be invoked for describing astrophysical magnetized flows and formulated to model stellar magnetospheres including main sequence stars (e.g. the Sun), compact stellar objects [e.g. magnetic white dwarfs (MWDs), radio pulsars, anomalous X-ray pulsars (AXPs), magnetars, isolated neutron stars etc.], and planets as a major step forward towards a full three-dimensional model construction. Using powerful and reliable numerical solvers based on two distinct finite-difference method (FDM) and finite-element method (FEM) schemes of algorithm, we examine axisymmetric steady-state or stationary MHD models in Throumoulopoulos & Tasso (2001), finding that their separable semi-analytic nonlinear solutions are actually not unique given their specific selection of several free functionals and chosen boundary conditions. The multiplicity of nonlinear steady MHD solutions gives rise to differences in the total energies contained in the magnetic fields and flow velocity fields as well as in the asymptotic behaviours approaching infinity, which may in turn explain why numerical solvers tend to converge to a nonlinear solution with a lower energy than the corresponding separable semi-analytic one. By properly adjusting model parameters, we invoke semi-analytic and numerical solutions to describe different kind of scenarios, including nearly parallel case and the situation in which the misalignment between the fluid flow and magnetic field is considerable. We propose that these MHD models are capable of describing the magnetospheres of MWDs as examples of applications with moderate conditions (including magnetic field) where the typical values of several important parameters are consistent with observations. We discuss the challenges of developing numerical extrapolation MHD codes in view of nonlinear degeneracy.

FREQUENCY AND DAMPING RATE OF FAST SAUSAGE WAVES

We investigate the frequency and damping rate of fast axisymmetric waves that are subject to wave leakage for a one-dimensional magnetic cylindrical structure in the solar corona. We consider the ideal magnetohydrodynamic (MHD) dispersion relation for axisymmetric MHD waves superimposed on a straight magnetic cylinder in the zero β limit, similar to a jet or loop in the solar corona. An analytic study accompanied by numerical calculations has been carried out to model the frequency, damping rate, and phase speed of the sausage wave around the cut-off frequency and in the long wavelength limit. Analytic expressions have been obtained based on equations around the points of interest. They are linear approximations of the dependence of the sausage frequency on the wave number around the cut-off wavelength for both leaky and non-leaky regimes and in the long wavelength limit. Moreover, an expression for the damping rate of the leaky sausage wave has been obtained both around the cut-off frequency and in the long wavelength limit. These analytic results are compared with numerical computations. The expressions show that the complex frequencies are mainly dominated by the density ratio. In addition, it is shown that the damping eventually becomes independent of the wave number in the long wavelength limit. We conclude that the sausage mode damping directly depends on the density ratios of the internal and external media where the damping declines in higher density contrasts. Even in the long wavelength limit, the sausage mode is weakly damped for high-density contrasts. As such, sausage modes could be observed for a significant number of periods in high-density contrast loops or jets.

Line formation in the inner winds of classical T Tauri stars: testing the conical-shell wind solution

We present the emission line profile models of hydrogen and helium based on the results from axisymmetric magnetohydrodynamics (MHD) simulations of the wind formed near the disk-magnetosphere boundary of classical T Tauri stars (CTTSs). We extend the previous outflow models of `the conical-shell wind' by Romanova et al. to include a well defined magnetospheric accretion funnel flow which is essential for modelling the optical and near-infrared hydrogen and helium lines of CTTSs. The MHD model with an intermediate mass-accretion rate shows outflows in conical-shell shape with a half opening angle about 35 degrees. The flow properties such as the maximum outflow speed in the conical-shell wind, maximum inflow speed in the accretion funnel, mass-accretion and mass-loss rates are comparable to those found in a typical CTTS. The density, velocity and modified temperature from the MHD simulations are used in a separate radiative transfer model to predict the line profiles and test the consistency of the MHD models with observations. The line profiles are computed with various combinations of X-ray luminosities, temperatures of X-ray emitting plasma, and inclination angles. A rich diversity of line profile morphology is found, and many of the model profiles are very similar to those found in observations. We find that the conical-shell wind may contribute to the emission in some hydrogen lines (e.g. H-alpha, H-beta, Pa-beta and Pa-gamma) significantly when the temperature in the wind is relatively high (e.g. \sim 10^{4} K); however, the wind contribution decreases rapidly when a lower wind temperature is adopted. The model well reproduces a relatively narrow and low-velocity blueshifted absorption component in He I (10830), which are often seen in observations.

SYNCHROTRON RADIATION OF SELF-COLLIMATING RELATIVISTIC MAGNETOHYDRODYNAMIC JETS

The goal of this paper is to derive signatures of synchrotron radiation from state-of-the-art simulation models of collimating relativistic magnetohydrodynamic (MHD) jets featuring a large-scale helical magnetic field. We perform axisymmetric special relativistic MHD simulations of the jet acceleration region using the PLUTO code. The computational domain extends from the slow magnetosonic launching surface of the disk up to 6000^2 Schwarzschild radii allowing to reach highly relativistic Lorentz factors. The Poynting dominated disk wind develops into a jet with Lorentz factors of 8 and is collimated to 1 degree. In addition to the disk jet, we evolve a thermally driven spine jet, emanating from a hypothetical black hole corona. Solving the linearly polarized synchrotron radiation transport within the jet, we derive VLBI radio and (sub-) mm diagnostics such as core shift, polarization structure, intensity maps, spectra and Faraday rotation measure (RM), directly from the Stokes parameters. We also investigate depolarization and the detectability of a lambda^2-law RM depending on beam resolution and observing frequency. We find non-monotonic intrinsic RM profiles which could be detected at a resolution of 100 Schwarzschild radii. In our collimating jet geometry, the strict bi-modality in polarization direction (as predicted by Pariev et al.) can be circumvented. Due to relativistic aberration, asymmetries in the polarization vectors across the jet can hint to the spin direction of the central engine.