High Magnetic Reynolds Number Research Articles

A checkerboard-free symmetry-preserving conservative method for magnetohydrodynamic flows

Simulating MHD flows at high Hartmann numbers and low magnetic Reynolds numbers is of high interest for the design of a nuclear fusion breeding blanket, for which high accuracy and conservation of physical properties are of great importance. In this work, a solver is developed that offers these properties through the symmetry-preserving method, while at the same time warranting unconditional stability. Since this method uses predictor values for the pressure and electric potential fields, it can be prone to checkerboarding. Therefore it is extended to include a dynamical checkerboarding solution, which balances this problem with numerical dissipation. This is done through run-time measurements of the intensity of checkerboarding, which is then used as a negative feedback onto the predictor values. The symmetry-preserving discretisation and the dynamical solution to checkerboarding were successfully tested using an magnetohydrodynamic Taylor-Green vortex. The newly introduced method shows results free from numerical dissipation in smooth cases, whereas it avoids checkerboarding in more challenging cases. Finally, the method shows to be unconditionally stable, even on highly distorted meshes.

The gap-size influence on the excitation of magnetorotational instability in cylindricTaylor–Couette flows

The excitation conditions of the magnetorotational instability (MRI) are studied for axially unbounded Taylor–Couette (TC) flows of various gap widths between the cylinders. The cylinders are considered as made from both perfect-conducting or insulating material and the conducting fluid with a finite but small magnetic Prandtl number rotates with a quasi-Keplerian velocity profile. The solutions are optimized with respect to the wavenumber and the Reynolds number of the rotation of the inner cylinder. For the axisymmetric modes, we find the critical Lundquist number of the applied axial magnetic field: the lower, the wider the gap between the cylinders. A similar result is obtained for the induced cell structure: the wider the gap, the more spherical the cells are. The marginal rotation rate of the inner cylinder – for a fixed size of the outer cylinder – always possesses a minimum for not too wide and not too narrow gap widths. For perfect-conducting walls the minimum lies at $r_{{\rm in}}\simeq 0.4$ , where $r_{{\rm in}}$ is the ratio of the radii of the two rotating cylinders. The lowest magnetic field amplitudes to excite the instability are required for TC flows between perfect-conducting cylinders with gaps corresponding to $r_{{\rm in}}\simeq ~0.2$ . For even wider and also for very thin gaps the needed magnetic fields and rotation frequencies are shown to become rather huge. Also the non-axisymmetric modes with $|m|=1$ have been considered. Their excitation generally requires stronger magnetic fields and higher magnetic Reynolds numbers in comparison with those for the axisymmetric modes. If TC experiments with too slow rotation for the applied magnetic fields yield unstable modes of any azimuthal symmetry, such as the currently reported Princeton experiment (Wang et al., Phys. Rev. Lett., vol. 129, 115001), then also other players, including axial boundary effects, than the MRI-typical linear combination of current-free fields and differential rotation should be in the game.

Vorticity and magnetic dynamo from subsonic expansion waves

Context. The main driving forces supplying energy to the interstellar medium (ISM) are supernova explosions and stellar winds. Such localized sources are assimilable to curl-free velocity fields as a first approximation. They need to be combined with other physical processes to replicate real galactic environments, such as the presence of turbulence and a dynamo-sustained magnetic field in the ISM. Aims. This work is focused on the effect of an irrotational forcing on a magnetized flow in the presence of rotation, baroclinicity, shear, or a combination of any of the three. It follows an earlier analysis with a similar focus, namely, subsonic spherical expansion waves in hydrodynamic simulations. By including magnetic field in the model, we can evaluate the occurrence of dynamo on both small and large scales. We aim to identify the minimum ingredients needed to trigger a dynamo instability as well as the relation between dynamo and the growth of vorticity. Methods. We used the Pencil code to run resistive magnetohydrodynamic direct numerical simulations, exploring the ranges of values of several physical and numerical parameters of interest. We explored Reynolds numbers up to a few hundreds. We analyzed the temporal evolution of vorticity, kinetic, and magnetic energy, as well as their features in Fourier space. Results. We report the absence of a small-scale dynamo in all cases where only rotation is included, regardless of the given equation of state and rotation rate. Conversely, the inclusion of a background sinusoidal shearing profile leads to an hydrodynamic instability that produces an exponential growth of the vorticity at all scales, starting from small ones. This is know as vorticity dynamo. The onset of this instability occurs after a rather long temporal evolution of several thousand turbulent turnover times. The vorticity dynamo in turn drives an exponential growth of the magnetic field, first at small scales, followed by large ones. The instability is then saturated and the magnetic field approximately reaches equipartition with the turbulent kinetic energy. During the saturation phase, we can observe a winding of the magnetic field in the direction of the shearing flow. By varying the intensity of the shear, we see that the growth rates of this instability change. The inclusion of the baroclinic term has the main effect of delaying the onset of the vorticity dynamo, but then leads to a more rapid growth. Conclusions. Our work demonstrates how even purely irrotational forcing may lead to dynamo action in the presence of shear, thus amplifying the field to an equipartition level. At the same time, we confirm that purely irrotational forcing alone does not lead to any growth in terms of the vorticity, nor the magnetic field. This picture does not change in the presence of rotation or baroclinicity, at least up to a resolution of 2563 mesh points. To further generalize such a conclusion, we will need to explore how this setup works both at higher magnetic Reynolds numbers and with different prescriptions of the irrotational forcing.

Approximate Deconvolution with Correction – A High Fidelity Model for Magnetohydrodynamic Flows at High Reynolds and Magnetic Reynolds Numbers

Abstract We propose a model for magnetohydrodynamic flows at high Reynolds and magnetic Reynolds numbers. The system is written in the Elsässer variables so that the decoupling method of [C. Trenchea, Unconditional stability of a partitioned IMEX method for magnetohydrodynamic flows, Appl. Math. Lett. 27 (2014), 97–100] can be used. This decoupling method is only first-order accurate, so the proposed model aims at improving the temporal accuracy (from first to second order), as well as reducing the modeling error of the existing turbulence model. This is done in the framework of the recently developed LES-C turbulence models [A. E. Labovsky, Approximate deconvolution with correction: A member of a new class of models for high Reynolds number flows, SIAM J. Numer. Anal. 58 (2020), 5, 3068–3090]. We show the model to be unconditionally stable and numerically verify its superiority over its most natural competitor.

Large eddy simulations of inhomogeneous high-magnetic Reynolds number magnetohydrodynamic flows

Large eddy simulations of inhomogeneous high-magnetic Reynolds number magnetohydrodynamic flows

Entropy generation in unsteady stagnation flow through porous media in the presence of a high magnetic Reynolds number with a uniform heat source: renewable energy applications

The present model’s major focus is on entropy production and Newtonian, incompressible two-dimensional temperature-dependent stagnation point with uniform heat source factors in a porous channel. Furthermore, the induced magnetic field (IMF) is employed in this flow analysis, which is created by the movement of electrically conducting fluid. Entropy generation (EG) is an important aspect of any heat transfer development since it helps to reduce the irreversibility factor in a system. EG analysis has several applications in traditional industrial fields requiring fluid flows and heat transfer. As a result, the current study is concerned with the effects of EG. The relevant similar transformations are used to convert partial governing equations arising in the present model into ordinary differential equations (ODE). The bvp4c built-in code in MATLAB programming is then utilized to crack highly nonlinear equations. We arrive at numerical solutions by employing thebvp4c built-in code in MATLAB software. The results are plotted and discussed for various embedded parameters. It is discovered that because of low friction, the porosity parameter decreases the velocity and induces the magnetic boundary layer. Unsteady parameter and heat source parameters accelerate Bejan number, whereas the heat source and porosity constraints accelerate entropy analysis.

Onset of instability with collapse observed in relatively high density and medium beta regions of LHD

Edge MHD instabilities with pressure collapse are found in relatively high beta and low magnetic Reynolds number regions with a magnetic axis torus outward-shifted configuration of the large helical device (LHD), and characteristics and onset conditions of the instability are investigated. The instability has a radial structure with an odd parity around the resonant surface, which is different from that of the interchange instability typically observed in the LHD. The onset condition dependence on the magnetic axis location shows that the onset beta increases as the magnetic axis location moves more torus inwardly, and the instability appears only in limited configurations where the magnetic axis is located between 3.65 and 3.775 m. In such configurations, the resonant surface location is close to an index of the plasma boundary. This fact suggests that the distance between the resonant surface location and the plasma boundary plays an important role in the onset, and a possibility that the instability is driven by an external mode.

MHD wake around a cylinder for different values of the magnetic Reynolds number

The wake around a cylinder is well known and relatively well documented. The flow configuration depends on the Reynolds number and exhibits the classical von Karman street when this number reaches a sufficiently high value. When we consider a conducting liquid, the flow configuration becomes sensitive to the action of a magnetic field. In this work, we were interested in a general configuration when the magnetic field is aligned with the flow at infinity downstream, for a cylinder with the axis perpendicular to the flow and magnetic field direction. The problem was treated numerically for small and high magnetic Reynolds numbers. In the present work, results for both are proposed and obtained by numerical simulation. Figs 14, Refs 11.

Kinetic thermal ion effects on maintaining high beta plasmas above the Mercier criterion in the Large Helical Device

It is found that kinetic thermal ions have a significant stabilizing effect on Large Helical Device (LHD) plasmas from the kinetic magnetohydrodynamic (MHD) simulations. The simulation results for the LHD plasmas at high magnetic Reynolds number show that the high beta plasmas can be maintained since the saturation level of the pressure-driven MHD instabilities is significantly reduced by the kinetic thermal ions. This results from the fact that the response of the trapped ions to the instabilities is weakened by the precession drift motion in the three-dimensional magnetic field. Thus the supercritical stability of the LHD plasmas well above the Mercier criterion can be attributed to the precession drift motion of the trapped ions in the three-dimensional magnetic field.

Large eddy simulations of high-magnetic Reynolds number magnetohydrodynamic turbulence for non-helical and helical initial conditions: A study of two sub-grid scale models

Pseudo-spectral large eddy simulation (LES) calculations of high-magnetic Reynolds number (Rem) incompressible magnetohydrodynamic (MHD) turbulence are carried out for two initial conditions, namely, the non-helical Orszag–Tang vortex and the strongly helical Arnold–Beltrami–Childress (ABC) flows using two eddy-viscosity-based sub-grid scale (SGS) approaches: the cross-helicity (CH) and dynamic Smagorinsky (DS) models. Validation is conducted through comparisons of 1923 LES calculations with in-house 5123 direct numerical simulations (DNS) at Reynolds number, Re=Rem=800. The results show that the CH model performs better than the DS model. The performance of the SGS models at higher Re is further evaluated by carrying out 3843 LES calculations at Re=Rem=7500. Various quantities including turbulent kinetic energy, turbulent magnetic energy, cross-helicity, helicity, vorticity structures, cosine of angle between velocity and magnetic field, cosine of angle between velocity and vorticity field, kinetic and magnetic energy spectra, and energy fluxes are analyzed to understand the capability of the two LES models in predicting the evolution of MHD turbulence. The higher Reynolds number flow shows a delay in the maximum dissipation with increased transfer of energy toward small scales, resulting in a −5/3 Kolmogorov inertial sub-range scaling. In addition, the effect of Reynolds number on the alignment between velocity and magnetic field, and the energy transfer between kinetic and magnetic energy, is studied. With the ABC flow having strong helicity and zero cross-helicity at low and high Reynolds numbers, a strong dynamo effect is also observed using the LES models, which is consistent with previous DNS.

MHD grid-turbulence in a closed decaying flow of liquid sodium

Grid-induced turbulent flows of liquid sodium in a toroidal channel at high Reynolds numbers and moderate magnetic Reynolds numbers are studied experimentally. Grids with a pitch of 15 mm and 31 mm were used, and one or two grids were installed in the channel. It is shown that the dynamics of the pulsed turbulent flow in the channel with grids differs significantly from that observed in a free channel, where the turbulence develops on the scale of the channel cross-section. Measurements of the characteristics of velocity and magnetic field pulsations have shown that induction effects in the unsteady pulse flow have time to manifest themselves in full. The spectra of velocity and magnetic field pulsations are obtained.

Interactions between vortex and magnetic rings at high kinetic and magnetic Reynolds numbers

Interactions between magnetic and vortex rings are studied over a wide interval of interaction parameter values ranging from negligible magnetic effects on vorticity structure, to very strong effects. The employed interaction parameter measures the strength of the Lorentz force in units of the inertial force. At small interaction parameters, the vortex ring shapes part of the magnetic ring into a dissipative, curved, magnetic sheet structure. At high interaction parameters, the Lorentz force acts as an agent of proliferation of vortex rings, since it generates two vortex rings adjacent to the original magnetic structure, one of which is pulled (together with the advected magnetic field) into the wake of the original vortex ring, while the other escapes, ready to interact with another magnetic ring. Once within the initial vortex ring wake, both magnetic and vorticity structures are stretched into spirals, whilst the Lorentz force continuously generates new, intense vorticity at high magnetic field sites.

Combined effects of variable thermal conductivity and induced magnetic field on convective Jeffrey fluid flow with nth order chemical reaction

AbstractThis study addresses the impact of variable thermal conductivity and induced magnetic field on an unsteady two‐dimensional channel flow of an incompressible laminar mixed convective and chemically reacted Jeffrey fluid embedded in a non‐Darcy porous medium with an appropriate convective type boundary conditions. The suction/injection velocity distribution has been assumed to be in an exponential form. The set of transport equations is reduced into coupled ordinary differential equations by using appropriate similar variables, which are solved by shooting technique with Runge‐Kutta fourth‐order algorithm. The investigation is carried out for various emerging nondimensional parameters on the axial, radial velocities, temperature distribution, concentration, and induced magnetic fields and also with skin friction coefficient are discussed through graphs. The value of the local Sherwood and Nusselt numbers are analyzed numerically. We noticed that the effect of the induced magnetic field is increased with Strommer's number while it decreases for high magnetic Reynolds number.

Dynamo Effect and Turbulence in Hydrodynamic Weyl Metals.

The dynamo effect is a class of macroscopic phenomena responsible for generating and maintaining magnetic fields in astrophysical bodies. It hinges on the hydrodynamic three-dimensional motion of conducting gases and plasmas that achieve high hydrodynamic and/or magnetic Reynolds numbers due to the large length scales involved. The existing laboratory experiments modeling dynamos are challenging and involve large apparatuses containing conducting fluids subject to fast helical flows. Here we propose that electronic solid-state materials-in particular, hydrodynamic metals-may serve as an alternative platform to observe some aspects of the dynamo effect. Motivated by recent experimental developments, this Letter focuses on hydrodynamic Weyl semimetals, where the dominant scattering mechanism is due to interactions. We derive Navier-Stokes equations along with equations of magnetohydrodynamics that describe the transport of a Weyl electron-hole plasma appropriate in this regime. We estimate the hydrodynamic and magnetic Reynolds numbers for this system. The latter is a key figure of merit of the dynamo mechanism. We show that it can be relatively large to enable observation of the dynamo-induced magnetic field bootstrap in an experiment. Finally, we generalize the simplest dynamo instability model-the Ponomarenko dynamo-to the case of a hydrodynamic Weyl semimetal and show that the chiral anomaly term reduces the threshold magnetic Reynolds number for the dynamo instability.

Minimal perturbation flows that trigger mean field dynamos in shear flows

Using a variational optimization method we find the smallest flow perturbations that can trigger kinematic dynamo action in Kolmogorov flow. In comparison to previous work, a second-order mean field dynamo model is used to track down the optimal dynamos in the high magnetic Reynolds number limit ($Rm$). The magnitude of minimal perturbation flows decays inversely proportional to the magnetic Reynolds number. We reveal the asymptotic high-$Rm$ structure of the optimal flow perturbation and the magnetic eigenmode. We identify the optimal dynamo as of $\unicode[STIX]{x1D6FC}{-}\unicode[STIX]{x1D6FA}$ type, with magnetic fluctuations that localize on a critical layer.

Interactions between vortex tubes and magnetic-flux rings at high kinetic and magnetic Reynolds numbers

Calculations of interactions between vortex tubes and magnetic rings at high kinetic and magnetic Reynolds numbers indicate that when the Lorentz force dominates plasma inertia there is significant new structure generation that results in similar vorticity and magnetic structure morphologies.

Numerical Analysis of MHD Mixed Convection Flow in a Parallelogramic Porous Enclosure Filled with Nano Fluid and in Presence of Magnetic Field Induction

In the present study, the mixed convection Flow of nano Fluid in a lid-driven parallelogramic porous enclosure subjected to a magnetic Fi eld is investigated numerically. Induced magnetic Fi eld is also considered, in terms of the magnetic potential, in solving the magnetohydrodynamic (MHD) Flow and temperature equations. The Darcy-Brinkman-Forchheimer model with the Boussinesq approximation is adopted and the Finite volume method based on SIMPLE algorithm is utilized to solve the governing equations with the appropriate boundary conditions in an orthogonal computational domain. The governing equations in a non-orthogonal physical domain are transformed into a computational domain in an orthogonal co-ordinate by co-ordinate transformations. It has been shown that the Flow Fi eld and heat transfer are sensible greatly to the skew angle variation. Magnetic potential circulates through the parallelogramic porous enclosure with either high either magnetic Reynolds number or magnetic permeability of the nano Fluid. Results also indicate that the influence of external magnetic Fi eld on Fluid characteristics and heat transfer manifests variety fashions mainly depends on the e ffective area of the parallelogramic enclosure. Besides, the variation in rates of heat transfer while adding nanoparticles or applying magnetic Field are aff ected to some extent by porous medium permeability and Richardson number.

Characteristics of MHD instabilities for high beta plasmas in inward shifted LHD configurations

Characteristics of the MHD instabilities for high beta LHD (large helical device) plasmas in the inward shifted configurations have been investigated by numerical simulations. On the condition that the magnetic Reynolds number is lower than the experimental value, the time evolution of the MHD instabilities is as follows: (1) resistive ballooning modes, the toroidal mode number of which is higher than the LHD’s toroidal pitch (), are destabilized in the plasma peripheral region; (2) low toroidal modes typified by are destabilized by the nonlinear mode coupling of the resistive ballooning modes the toroidal mode number of which is adjacent to each other where n is the toroidal mode number. In particular, the velocity of the mode is finite at the magnetic axis so that there is a large velocity directed to the magnetic axis; and (3) when the high n modes are saturated, the destabilized low n modes, which have a global mode structure and shift the magnetic axis, also begin to be saturated. The self mode coupling of the low n modes induces the core crush and transports the plasma from the core region to the peripheral region. Since the nonlinear MHD phenomena are dominated by the resistive modes, the MHD phenomena for the experimental high magnetic Reynolds number are considered to be milder than our numerical results. Thus, when the experimental high magnetic Reynolds number is taken in the simulation, the core crush may be suppressed so that the numerical results are expected to become close to the experimental results where the stable high beta plasmas are obtained.

Active stabilization of error field penetration via control field and bifurcation of its stable frequency range

An active stabilization effect of a rotating control field against an error field penetration is numerically studied. We have developed a resistive magnetohydrodynamic code ‘AEOLUS-IT’, which can simulate plasma responses to rotating/static external magnetic field. Adopting non-uniform flux coordinates system, the AEOLUS-IT simulation can employ high magnetic Reynolds number condition relevant to present tokamaks. By AEOLUS-IT, we successfully clarified the stabilization mechanism of the control field against the error field penetration. Physical processes of a plasma rotation drive via the control field are demonstrated by the nonlinear simulation, which reveals that the rotation amplitude at a resonant surface is not a monotonic function of the control field frequency, but has an extremum. Consequently, two ‘bifurcated’ frequency ranges of the control field are found for the stabilization of the error field penetration.

Triad interactions and the bidirectional turbulent cascade of magnetic helicity

Using direct numerical simulations we demonstrate that magnetic helicity exhibits a bidirectional turbulent cascade at high but finite magnetic Reynolds numbers. Despite the injection of positive magnetic helicity in the flow, we observe that magnetic helicity of opposite signs is generated between large and small scales. We explain these observations by carrying out an analysis of the magnetohydrodynamic equations reduced to triad interactions using the Fourier helical decomposition. Within this framework, the direct cascade of positive magnetic helicity arises through triad interactions that are associated with small scale dynamo action, while the occurrence of negative magnetic helicity at large scales is explained through triad interactions that are related to stretch-twist-fold dynamics and small scale dynamo action, which compete with the inverse cascade of positive magnetic helicity. Our analytical and numerical results suggest that the direct cascade of magnetic helicity is a finite magnetic Reynolds number $Rm$ effect that will vanish in the limit $Rm \to \infty$.