Session MY: Magnetohydrodynamics

Instabilities of conducting fluid flows in cylindrical shells under external forcing

Flows created in neutral conducting flows remain one of the less studied topics of fluid dynamics, in spite of their relevance both in fundamental research (dynamo action, turbulence suppression) and applications (continuous casting, aluminium production, biophysics). Here we present the effect of a time-dependent magnetic field parallel to the axis of circular cavities. Due to the Lenz's law, the time-dependent magnetic field generates an azymuthal current, that produces a radial force. This force produces the destabilization of the static fluid layer, and a flow is created. The geommetry of the experimental cell is a disc layer with external diameter smaller than 94 mm, with or without internal hole. The layer is up to 20mm depth, and we use as conducting fluid an In-Ga-Sn alloy. There is no external current applied on the problem, only an external magnetic field. This field evolves harmonically with a frequency up to 10Hz, small enough to not to observe skin depth effects. The magnitude ranges from 0 to 0.1 T. With a threshold of 0.01T a dynamical behaviour is observed, and the main characteristics of this flow have been determined: different temporal resonances and spatial patterns with differents symmetries (squares, hexagonal, triangles,...).   

An all-speed projection method for magneto-hydrodynamics

We present an all-speed algorithm for magneto-hydrodynamics (MHD) similar to the work of Colella \& Pao (J. Comput. Phys. 1999) for low speed hydrodynamics. The method is based on an asymptotic ordering of scales relevant for tokamak MHD physics. The central idea is to Hodge decompose the velocity, and a splitting of the magnetic guide field analogous to the pressure splitting in low Mach number hydrodynamics into a thermodynamic and an incompressible part. We present the derivation of the ideal MHD equations into slow (advective), intermediate and fast scales. The algorithm treats the slow advective scales using a Godunov-procedure while the intermediate and fast scales are treated implicitly using backward Euler. Results from numerical tests such as the MHD Kelvin-Helmholtz instability, magnetic reconnection and others will be presented. We will highlight the challenges of designing solvers for the intermediate scales.   

Direct Numerical Simulation for the MHD Homogeneous Shear Turbulence with the Uniform Magnetic Field

The MHD homogeneous shear turbulent flows with the streamwise or span uniform magnetic field are investigated by means of the direct numerical simulation. The kinetic and magnetic energy in the streamwise uniform magnetic field cases are slightly small in comparison with the zero mean magnetic field case. The energy transformation term between the kinetic and magnetic energy, which is related with only fluctuating-field quantities, is balanced with that of the mean magnetic field. Under the spanwise magnetic field, the kinetic and magnetic energy is strongly suppressed and the Reynolds and Maxwell stresses become isotropic. The negative production term of the kinetic energy plays an important role in the energy suppression. The contribution of the energy transformation term of the fluctuating field is small unlike the streamwise magnetic field cases. From the energy-spectral viewpoints, the additional spanwise magnetic field has an influence on the large-scale factors.   

Transition in MHD duct flow

A magnetic field applied to a flow of an electrically conducting fluid (e.g., a liquid metal) suppresses turbulence and can transform the flow into a weakly turbulent or laminar state. This situation is common in technological applications, such as metallurgy, materials processing, and liquid metal cooling for fusion reactors. The understanding and prediction of transition in MHD flows is therefore not only of interest from a theoretical perspective. We investigate the transition in the flow in a rectangular duct with electrically insulating walls and uniform transverse magnetic field. The essential features of the flow are the sidewall and Hartmann boundary layers on the walls parallel and perpendicular to the applied field. The transition mechanism based on the transient finite-amplitude growth is analyzed using numerical simulations with a highly conservative finite-difference scheme. The presented results include the identification and parametric study of optimal modes, which are found to be three-dimensional and localized in the sidewall layers. We also investigate, using the DNS approach, the growth and breakdown of the optimal modes leading to turbulence. Financial support is by the DFG (Bo 1668/2-4, 1668/5-1) and NSF (CBET 096557).   

Direct numerical simulations of turbulent MHD flow in a 2:1 aspect ratio rectangular duct subjected to transverse and span-wise magnetic fields

Magnetic fields are used to control flows in a variety of applications, notably in materials processing. One such process is continuous casting of steel which uses different types of magnetic fields to alter the flow, inclusion transport and multiphase flow in order to reduce defects in cast steel. Under a strong magnetic field, a turbulent flow can be altered significantly to the point that turbulence is completely suppressed and the flow is laminarized In the present study, we have considered a periodic duct with an aspect ratio of 2:1 and subjected to a magnetic field either on the broad side or on the narrower side. We have conducted DNS of five different cases, with two magnetic field intensities in either direction and compared them with the case of no magnetic field. Calculations have been performed for Hartmann numbers of 0, 6.0 and 8.5 at a Reynolds number (based on bulk velocity) of 5000. The grid used consisted of 512 x 120 x 224 control volumes with grid stretching in the cross-stream directions. Various turbulence and mean flow statistics have been computed to characterize the effects of the magnetic field. We believe these results can be valuable additions to the databases that can be used for turbulence model development.   

Numerical simulation of quasi-static magnetohydrodynamic flow in a right-angle bend

We discuss simulation results of magnetohydrodynamic flows in a right-angle bend in the limit of vanishing magnetic Reynolds number. Both the Hartmann number and the interaction parameter are much larger then one (these are nondimensional estimates of the magnitude of the electromagnetic interaction with respect to the vicous term, respectively to the inertial term). Such a configuration is of interest in the context of the design of self-cooled blankets for future fusion devices. We consider the situation in which the magnetic field is perfectly aligned with the outflow direction, as well as a so-called backward elbow, in which the magnetic field lines make a positive angle with the to the outflow direction. Both cases are characterized by a thin, intense shear layer, aligned with the magnetic field, in the vicinty of the inner corner. We present results for steady as well as non-steady cases and various values of the Hartmann number. These results will be compared to existing asymptotic analysis and experimental data.   

Gyroviscous effects in channel flow with Braginskii magnetohydrodynamics

We study the pressure-driven flow across a magnetic field of a fluid obeying magnetohydrodynamics with the full Braginskii stress tensor. Momentum transport across magnetic field lines is strongly suppressed by the spiralling of charged particles around the field lines. This spiralling also creates gyroviscous stresses perpendicular to both the strain rate and the magnetic field. These stresses are negligible in the bulk of the flow, but they alleviate the singularities in current and shear that otherwise occur at the channel walls. They create boundary layers whose width scales as the three-quarters power of the ratio $\epsilon=\mu_\times/\mu_\parallel$ of the gyro to parallel viscosities. The maximum current and velocity scale as $\epsilon^{-1/4}$. The gyroviscous stresses generate a leading-order flow perpendicular to the plane defined by the pressure gradient and imposed magnetic field, so the maximum velocity is tilted close to $40^\circ$ out of this plane. The related out of plane magnetic field scales as $\epsilon^{1/2}$ in the boundary layers, and as $\epsilon$ elsewhere. Regularisation by gyroviscous stresses alone is sufficient. Perpendicular viscosity makes only a further regular perturbation.   

Measuring and analyzing the magnetic field in (SERAJ system) theta pinch device using the Magnetic probes

Using the internal and the external magnetic probes in different positions inside and outside plasma discharge chamber of Seraj's Theta-pinch system (L = 150cm, D = 8.4cm), the generated magnetic field on the coil of Seraj's system has been calculated. When the plasma is discharged (by discharging the four capacitors bank connected on parallel, the capacity of each is (12.5$\mu$F) in the system coil (12nH)) the characteristics of plasma can be defined as how much magnetic field is affected. Comparing the magnetic field in the absence or presence of plasma, trapped magnetic field and Diamagnetic effect could be determined in the Theta pinch system. In the present study, one could determine the appropriate operating circumstances to produce suitable plasma with specific features (density \& electron temperature) as an advantage for different application.   

Magneto-Hydrodynamic Flow of a Binary Electrolyte in a Concentric Annulus

We study theoretically the motion of an electrolyte solution confined between two concentric, metallic cylinders subjected to an electrical potential difference in the presence of an axial magnetic field. When the annulus is infinitely long, the Navier-Stokes and Nernst Planck equations admit one-dimensional, azimuthal motion. We study the stability of this azimuthal motion in the limiting case of a narrow gap. Under certain circumstances, as the potential difference between the electrodes increases, the azimuthal flow loses stability and cellular, two dimensional convection, similar to Dean's vortices, ensues. The lose of stability occurs at Dean's numbers that differ greatly from the classical values of pressure-driven flow, and the critical Dean number at the onset of instability depends on the direction of the electrical current. The results of the linear stability analysis are compared and favorably agree with finite element simulations of the nonlinear equations. When the length of the annulus is finite, secondary flows exist for all Dean's numbers. In this case, we solve numerically for the fluid motion.   

Stability of mixed convection flows in poloidal ducts of DCLL blanket

In the Dual-Cooled Lead-Lithium (DCLL) blanket, which is considered in the US for testing in ITER and for using in DEMO, the eutectic alloy PbLi circulates slowly (at $\sim $ 10 cm/s) for power conversion and tritium production. The flows in the poloidal ducts are strongly affected by buoyancy effects associated with volumetric heating, the forced flow is combined with the buoyant flow resulting in a mixed regime. Under strong reactor magnetic field, the convective flows are seen to be essentially quasi-two-dimensional (Q2D), with 3-D effects localized in the Hartmann layers. This striking feature allows for using the Q2D flow model. Two-dimensional linear stability analysis of both upward and downward flows with Q2D base flow considering only thermal shear instability revealed that the internal shear layer in the base velocity profile results in a shear layer instability (primary instability), these primary vortices are found to trigger an instability in the boundary layers causing the side layers to become unstable (secondary instability). The study shows that upward flows under blanket conditions are stable considering the effects of mixed convection whereas downward flows can be unstable.