Session Q19: Magnetohydrodynamics

Magnetorotational instability breaks rotational symmetry in the laboratory

The standard magnetorotational instability (SMRI) has been regarded as the sole viable instability responsible for the turbulence required to explain the fast accretion observed across the Universe. Nonetheless, SMRI remains unconfirmed even for its existence long after its proposal, despite its widespread applications in modeling including recent black hole imaging. Its direct detection has been hindered in observations due to its microscopic nature atastronomical distances, and in the laboratory due to stringent requirements and interferences from other processes. Here we report the first direct evidence showing that SMRI indeed exists in a novel laboratory setup where a uniform magnetic field is imposed along the axis of a differentially rotating flow of liquid metal confined radially between concentric cylinders and axially by copper endrings. As predicted the observed SMRI exists only at sufficiently large rotation rates and moderate field strengths, but surprisingly with its symmetry broken about the rotation axis. The nonaxisymmetric nature of SMRI is important in generating large-scale magnetic fields, as detected recently. Our results show that the axisymmetric presumption is oversimplified in past studies on SMRI, which calls for future investigations.   

Magnetoconvection in a horizontal duct flow at very high Hartmann and Grashof numbers

Direct numerical simulations and linear stability analysis are carried out to study mixed convection in a horizontal duct with constant-rate heating applied at the bottom and imposed transverse horizontal magnetic field. A two-dimensional approximation corresponding to the asymptotic limit of very strong magnetic field effect is validated and applied, together with full three-dimensional analysis, to investigate the flow's behavior in the previously unexplored range of control parameters corresponding to typical conditions of a liquid metal blanket of a nuclear fusion reactor (the Hartmann numbers up to 10⁴ and the Grashof numbers up to 10¹⁰). It is found that the instability to quasi-two-dimensional rolls parallel to the magnetic field discovered at smaller Hartmann and Grashof numbers in earlier studies also occurs in this parameter range. Transport of the rolls by the mean flow leads to magnetoconvective temperature fluctuations of exceptionally high amplitudes. The fluctuations are not suppressed or even significantly reduced in amplitude by the very strong magnetic field. It is also demonstrated that the quasi-two-dimensional structure of flows at very high Hartmann numbers does not guarantee the accuracy of the classical two-dimensional approximation. The accuracy deteriorates at the highest Grashof numbers considered in the study.   

NUMERICAL STUDY OF NATURAL CONVECTION UNDER AN IMPOSED ALTERNATING MAGNETIC FIELD IN CYLINDRICAL VESSEL

3D magneto-hydrodynamic DNS inside a cylindered vessel filled with a liquid metal under an alternating magnetic (AM) field and bounded by a vertical temperature gradient were performed. The numerical setup aims to explore a wide range of Hartman number (Ha) and shielding parameter (Sw) to interrogate the average Nusselt number and the flow patterns. When only a temperature gradient is applied to the fluid, it is well known that above a critical Rayleigh number (Ra), the fluid becomes unstable, and this situation is referred to as Rayleigh-Bénard Convection (RBC). A large amount of research has been dealing with this kind of instability to understand the flow patterns. Our study is dedicated to this configuration when an AM field is added. The vessel is placed inside an inductor supplied with an alternating electrical current. The power distribution within the conducting liquid metal is non-uniform and depends on the frequency through Sw, and the AC amplitude through Ha. Playing on both parameters, the Lorentzs force field and the Joule heating field can be controlled. The conjugation of both effects (Joule heating and Lorentz force) on the fluid motion leads to various regimes depending on Sw and Ha. In a first step RBC has been simulatedat moderate Ra. In a second step, DNS have been computed including Maxwell’s equations in the regime of low magnetic Reynolds number (Rm<<1). When Sw>=1, It has been found that the LSC is cancelled by the Lorentz force’s stirring effect and  two horizontal tori are generated in the upper half and the lower half of the vessel. The time and volume average temperatures of the tori are different, and their values depend on the intensity of Joule heating and Lorentz force. The heat and mass transfer between the tori is negligible when averaged in time, but bursts of fluid through the mid plane occur intermittently. In addition, it was observed that the AM field enhances the total heat exchange compare to classical RBC.   

The influence of thermal convection on the liquid metal flow in a rectangular duct in the presence of a magnetic obstacle

The nonsteady, three dimensional thermal convection in a  pressure driven liquid metal flow, that is confined  in a rectangular duct heated from below, in the presence of heterogenous vertical magnetic field  is studied. The transition from steady state pure forced convection to time dependent  mixed convection is investigated. The four  walls of the duct confining the flow  are no slip and electrically insulating. The dimensionless equations  governing the flow of the incompressible fluid, under the Boussinesq and  quasi-static (induction-less) approximations, are solved by using the  spectral  element method. The dimensionless  parameters of the system are the Hartmann, Reynolds, Prandtl and Rayleigh numbers, and the constrainment factor (defining the spanwise distribution of the magnetic field). Three dimensional maps, where the Hartmann, Reynolds and Rayleigh numbers are involved, are generated. The results show the critical  Rayleigh number at which the thermal convection is dominant. The influence of the thermal convection on the  flow patterns generated in the vicinity the  magnetic obstacle is presented. The influence of the Hartmann and Reynolds numbers on the temperature distribution and heat transfer rate in the region close to the magnetic obstacle is reported.   

Laboratory model of electro-vortex flow with thermal gradients, for liquid metal batteries

To facilitate the adoption of renewable sources of energy, grid-scale storage options are needed. One promising solution to this problem is the liquid metal battery (LMB). The fluid dynamics of LMBs can be paramount to their operation and efficiency. It is thus important to develop a broad understanding of how various flow drivers interact with one another in a reduced model, whose results can be scaled to full-size LMBs. We designed and constructed a novel laboratory device to explore the interactions between two prominent drivers — thermal gradients and electro-vortex flow (EVF) — over broad ranges of governing parameters. We apply these forces to a layer of liquid gallium to simulate a single layer of an LMB, collecting temperature data with thermocouples and velocity data with Ultrasonic Doppler Velocimetry (UDV) probes. Using this experimental setup, we demonstrate scaling relationships with the Reynolds number, for both thermal convection and EVF individually, that agree well with theory and previous experiments and simulations. Our setup will establish a launching point for further understanding of flow characteristics in LMBs, and introduce novel methods for studying these flows.   

MHD Shock Refraction at an Inclined Density Interface

Shock wave refraction at a sharp density interface is a classical problem in hydrodynamics. Presently, we investigate the refraction of magnetohydrodynamic (MHD) shock waves at an inclined density interface. For a chosen incident shock strength, and Atwood ratio, the MHD shock refraction transitions from regular (all nonlinear waves meeting at a single point) into irregular when the inclined density interface angle is less than a critical value. The MHD shock refraction process results in a pair of outer fast shocks (reflected and transmitted) and a set of inner nonlinear magneto-sonic waves. By varying magnetic field strength, the latter waves can be slow shocks, slow expansion fans, intermediate shocks or slow-mode compound waves. A Mach stem occurs in an irregular MHD shock refraction, resulting in a quadruple-point in which the Mach stem, shocked contact and a pair of transmitted waves meet, and a triple-point in which the incident shock, fast reflected shock and the Mach stem meet. Since the MHD shock refraction is self-similar, we further explore by converting the initial value problem (IVP) into a boundary value problem (BVP) by a self-similar coordinate transformation. The self-similar solution to the BVP is numerically solved using an iterative method, and implemented using the p4est adaptive mesh framework. Existing Riemann solvers (e.g., Roe, HLLD etc.) can be modified in a relatively straightforward manner and used in this method.   

Nambu brackets and induced Lie-Poisson brackets for fluid mechanics and magnetohydrodynamics

For the ideal magnetohydrodynamics (MHD), Noether's theorem states that the topological invariant associated with the particle relabeling symmetry is the cross helicity, the volume integral of the scalar product of the velocity field and a frozen-in field. This is also the case for the dynamics of an ideal fluid. A proof to it is given in terms of variation of the Lagrangian label as a function of the Eulerian position. In addition to the cross helicity, the total mass, the total entropy and the magnetic helicity are topological invariants. We construct the Nambu bracket for the ideal MHD, using all the four topological invariants as Hamiltonians, together with the total energy. The Lie-Poisson bracket induced from the Nambu bracket gives an extension of the known one and automatically guarantees the cross-helicity to be a Casimir invariant. A remark is given to Noether's second theorem.   

Oscillating currents stabilize aluminum cells for efficient, low carbon production

In an aluminum smelter, a large electrical current (∼105A) is passed vertically through an electrolyte layer, where aluminum oxide is dissolved, and a layer of molten Al that lies below the electrolyte. The current can amplify resonant motions on the Al-electrolyte interface, producing a circulating traveling wave that can grow out of control . Thick electrolyte layers prevent this metal pad instability (MPI) but sacrifice efficiency because the electrolyte is a poorconductor. We simulated a TRIMET 180 kA smelter using MHD-Valdis, a high-fidelity software package common in the Al industry. When the layer thickness (anode-cathode distance, ACD) was 4.0 cm and the current was 180 kA, the MPI occurred, as expected. Including an oscillating current component with half-amplitude 19.8 kA and frequency 0.045 Hz prevented the MPI and replaced it with stable standing waves. Their dynamics caused electromagnetic forces that opposed the MPI. Oscillations at other frequencies that drove standing waves could likewise prevent the MPI. We also found that an oscillating current component can halt the MPI in progress. Additional simulations showed that stable operation without the oscillating current required a 4.3 cm ACD, but with oscillation, required only a 3.8 cm ACD — reducing heat power by 12% and overall powerby 4%. Similar reductions worldwide might save 34 TWh/year and reduce greenhouse gas emissions by 13 Mton/year.   

Motion Dynamics of Magnetically Actuated Rod-Like Softrobots Swimming in Viscous Fluids

Soft and flexible structures made of hydrogel polymer have garnered a lot of excitement and promise in mesoscale (milli- and microscale) soft robotics, as they can be loaded with magnetic materials for actuation, biosensors for sensing, and are already commonly used in areas such as tissue engineering, drug delivery, and micromanipulation. Here, we present experimental and numerical investigations of the locomotion of magnetically actuated hollow, rod-like softrobots in Newtonian fluids. We report propulsion and boundary rolling in Newtonian fluids with different viscosities for soft rod-like swimmers actuated by an externally applied uniform rotating magnetic field. The propulsion is only observed in some Newtonian fluids, and we numerically test if that can be explained by time-dependent deformations, by simulating the dynamics of the deformed shape using Kirchhoff rod theory.   

Transition to turbulence and transport of angular momentum in electromagnetically driven Keplerian flows

The flow of an electrically conducting fluid in a thin disc under the action of an azimuthal Lorentz force is studied experimentally herein. Quasi-Keplerian velocity profiles occur when the forcing is small so the Lorentz force is balanced by either viscoity or inertia. At large current and moderate magnetic field, a new regime is observed which is characterized by a Keplerian mean rotation profile Ω∼(IB)^1/2r^-3/2.  In this turbulent regime, the dynamics is typical of thin layer turbulence. A direct cascade transports the energy from the vertical integral length scale h towards the small scales and for scales larger than h, an inverse cascade occurs. The transition from the viscous/inertial regime to the fully turbulent state is well understood as resulting from an instability of the B\"odewadt-Hartmann  layers at large Reynolds number. At very large forcing, the experiment then presents a configuration analogous to astrophysical disks, depicted by a fully turbulent flow, a Keplerian rotation rate and a volume injection of angular momentum. The angular momentum is then transported through an ultimate regime Nu∼Ta^1/2 independent of molecular viscosity. It is thus possible to make predictions for the accretion rates of astrophysical  accretion disks.