Session R9: Magnetohydrodynamics

Turbulent transfer and secondary flow patterns in transitional MHD duct flows under the non-uniform magnetic field

Large-eddy simulation (LES) of transitional turbulent duct flows is carried out in a liquid metal MHD power generator, and the influence of the non-uniform magnetic field on the turbulent flows is examined. As increasing the magnetic flux density (or Hartmann number), the turbulence is suppressed downstream of electrodes. The higher Hartmann number modulates the mean velocity profile to the M-shaped velocity one (the so-called sidewall jet) in the plane parallel to the external magnetic field. The velocity profiles are modulated more strongly with the magnetic flux density. In the higher Hartmann number, the wall-shear stress in the sidewall layer becomes large and the sidewall jets transit to turbulence. The sidewall jets in the MHD turbulent duct flows have a similar mean velocity profile of the non-MHD wall jets with outer scaling as well as the profiles of Reynolds shear stress with the opposite sign and two maxima for the turbulent intensities in a sidewall jet. The Lorentz force suppresses the vortices of the secondary mean flow near the Hartmann layer for low Hartmann number, whereas the secondary vortices remain near the Hartmann layer for high Hartmann number.   

Experimental Investigation on Liquid Metal Flow Distribution in Insulating Manifold under Uniform Magnetic Field

Magnetohydrodynamics (MHD) problem which is caused by interaction between electrical conducting fluid flow and the magnetic field is one of the biggest problem in the liquid metal blanket of the fusion reactor. In the liquid metal blanket concept, it is necessary to distribute liquid metal flows uniformly in the manifold because imbalance of flow rates should affect the heat transfer performance directly, which leads to safety problem. While the manifold is insulated electrically as well as the flow duct, the 3D-MHD effect on the flowing liquid metal in the manifold is more apparent than that in straight duct. With reference to the flow distribution in this concept, the liquid metal flow in the electrical insulating manifold under the uniform transverse magnetic field is investigated experimentally. In this study, GaInSn is selected as working fluid. The experimental system includes the electrical magnet and the manifold test section which is made of acrylic resin for perfectly electrical insulation. The liquid metal flows in a non-symmetric 180$^{\circ}$-turn with manifold, which consists of one upward channel and two downward channels. The flow rates in each channel are measured by electromagnetic flow meters for several combinations Reynolds number and Hartman number. The effects of magnetic field on the uniformity of flow distribution are cleared.   

Numerical investigation of the turbulent MHD flow in a circular pipe with transverse magnetic field

In modern industrial metallurgical processes, external magnetic fields are often applied to control the motion of liquid metals by a non-intrusive means. The desired results are for example the damping of unwanted motions or the homogenization of a liquid zone in a partially solidified ingot. Because of the commonly appearing parameters in these processes, one can assume the quasi-static assumption for the magnetohydrodynamic equations. Here we are interested in the numerical study of the turbulent flow of a liquid metal inside an electrically insulated pipe with a transverse uniform magnetic field. For this purpose, we will use a hybrid spectral/finite element solver, which allows to study complex flows in Cartesian and axisymmetric geometries. For the case of interest, we consider a bulk Reynolds number of 8200 and a Hartmann number ranging between 5 and 30. Here, the main points of interest are the evolution of the skin friction coefficient as a function of the ratio of the Hartmann number Ha over the Reynolds number Re (with 0 $<$ Ha/Re $<$ 75x10$^{-4})$ as well as the energy budget (viscous, Joule and numerical dissipations, kinetic energy production) in a cross-section. These results will determine the transition point between laminar and turbulent flows.   

Instabilities in Turbulent Magnetized Spherical Couette Flow

We present experimental studies of the turbulent shear flow of a conducting fluid in a spherical-Couette device in the presence of a magnetic field. Our experimental apparatus consists of an outer spherical shell concentric with an inner sphere, which both rotate independently. The geometry of the experiment makes these studies applicable to geophysical and astrophysical bodies. Liquid sodium fills the gap between the inner sphere and the shell. We apply an axial magnetic field of varying strength to study the influence of the applied field on the dynamics of the flow. Instrumentation includes an array of hall probes to measure the induced magnetic field, providing information about the global fluid flow. We also measure the torque required to drive the inner and outer spheres at their respective rotation rates, and take direct fluid pressure measurements. We use these to study instabilities that appear as the applied field is increased, for the case of a stationary outer sphere, and for both spheres rotating independently, and compare with theory and numerical predictions.   

Numerical Study for the MHD Homogeneous Decaying Turbulence under the System Rotation

In this study the MHD homogeneous decaying turbulence under the system rotation is directly simulated by means of the pseudo-spectral method. The decaying rates of the kinetic and magnetic energy are suppressed due to the rotation effect like that of the HD turbulence. The small-scale anisotropy of the velocity and magnetic fields is reversed in comparison with the weak anisotropy of the Reynolds and Maxwell stresses. The weak transformation of the energy and stress from the velocity field to the magnetic one occurs under the system rotation, but in the small-scale region the magnetic energy is converted into the kinetic energy. In the strong rotation case, the slope of the energy spectrum is steeper than Kolmogorov one. In the strong rotation case, the vortex structures are aligned with the rotation axis.   

Coherent vorticity and current density simulation of three-dimensional magnetohydrodynamic turbulence using orthogonal wavelets

A simulation method to track the time evolution of coherent vorticity and current density, called coherent vorticity and current density simulation (CVCS), is developed for three-dimensional (3D) incompressible magnetohydrodynamic (MHD) turbulence. The vorticity and current density fields are, respectively, decomposed at each time step into two orthogonal components, the coherent and incoherent fields, using an orthogonal wavelet representation. Each of the coherent fields is reconstructed from the wavelet coefficients whose modulus is larger than a threshold, while their incoherent counterparts are obtained from the remaining coefficients. The two threshold values depend on the instantaneous kinetic and magnetic enstrophies. In order to compute the flow evolution, one should retain not only the coherent wavelet coefficients but also their neighbors in wavelet space, and the set of those additional coefficients is called the safety zone. CVCS is performed for 3D forced incompressible homogeneous MHD turbulence without mean magnetic field for a magnetic Prandtl number equal to unity and with $256^3$ grid points. The quality of CVCS is assessed by comparing the results with a direct numerical simulation. It is found that CVCS with the safety zone well preserves the statistical pred   

Intrinsic rotation of toroidally confined magnetohydrodynamics

Time-dependent three-dimensional toroidal visco-resistive MHD pseudo-spectral computations are performed, using the recently developed penalization method for enforcing the boundary conditions. An imposed toroidal magnetic field is present and the current is driven by an imposed toroidal electric field. Both poloidal and toroidal rotation result, and depend strongly on the shape of the toroidal cross section and the value of the Hartmann number. Net toroidal rotation results from a departure from up/down symmetry in the cross-sectional boundary shape. By increasing the Hartmann number, the plasma seeks out a characteristic configuration in which the velocity aligns approximately with the magnetic field lines. The resulting flow is characterized by both toroidal and poloidal rotation, starting from initial conditions in which such flows are absent. Ideal MHD equilibrium considerations appear not to play an important role.   

Experimental investigation of heat transfer in free-surface MHD flow

The presence of a strong external magnetic field can significantly alter the dynamics of large and small scale features within the flow. In particular, turbulent eddies with vorticity non-parallel to the magnetic field are strongly damped. This anisotropization of the turbulence may be critically important for heat transport in flowing liquid metal walls in a fusion reactor. Experiments have been conducted in the Liquid Metal Experiment (LMX) using a GaInSn eutectic alloy as a working fluid to investigate these effects. These experiments considered free-surface, wide aspect-ratio flows up to 20 cm/s through a channel situated in a magnetic field up to 2 kG, corresponding to a Reynolds number up to $\textrm{Re} \approx 10^4$ and a Hartmann number up to $\textrm{Ha} \approx 50$. Resistive heaters were placed on the free surface and the fluid temperature downstream was monitored by an array of thermocouples and an infrared camera. The relationship between Nusselt number and Hartmann number will be presented.   

Falling-Ball Rheometry of Magnetized Ferrofluids in the Presence of Magnetic Particle Threads

To probe the rheology of magnetized ferrofluid on a millimeter scale, we examine the paths of glass spheres (500 micrometer diameter) falling in a bulk ferrofluid under a uniform magnetic field, applied at a fixed angle with respect to the horizontal. Visualization of the ball trajectories is accomplished by the capture of high-resolution, X-ray phase-contrast images on high-speed, digital video. The drag on each sphere is determined by measurement of its terminal velocity. The effective viscosity of the ferrofluid is observed to be anisotropic: the terminal velocity of a sphere depends on the angle of the applied magnetic field. Specifically, the drag is greater when the applied field is normal to the vertical path of the falling sphere than when parallel. We propose that this effect is due the field-induced formation of magnetic particle ``threads'' having diameter of a few microns ($\sim$1000 nanoparticles) and lengths that span the container (a few millimeters). These threads form a dense parallel array aligned with the applied magnetic field and are visible in phase-contrast images of the bulk ferrofluid. We model the drag experienced by the falling ball as originating from the falling-ball Stokes flow through a fixed array of rigid threads with an inter-penetrating fluid.