Session J04: Magnetohydrodynamics (8:00am - 8:45am CST)

Physics-constrained data-driven methods in MHD

Accurate and efficient plasma models are essential to understand and control experimental devices. Data-driven techniques recently developed in fluid dynamics can be leveraged to develop interpretable reduced-order models of plasmas that strike a balance between accuracy and efficiency. The dynamic mode decomposition, POD-Galerkin methods, and other reduced order models are applied to experimental and simulation data, and suggest possible uses in real-time control and modeling for fusion devices.   

Energy Budget in Decaying Compressible MHD Turbulence

We study the decay of compressible magnetohydrodynamic (MHD) turbulence emphasizing exchanges of energy between compressive and incompressive flows, magnetic field energy, and thermal energy. A three dimensional compressible MHD code is employed that has been shown to be suitable for both incompressible and compressible flows. Varying the nature of initial conditions and initial Mach numbers permits examination of various dynamical regimes characterized here by the changes between different energy reservoirs. Acoustic waves are responsible to the oscillatory exchange between compressive kinetic and thermal energy through the pressure dilatation term. The results indicate that exchange between flow and magnetic energy is dominated by interactions involving the solenoidal velocity. Several systematic rapid adjustments are found to be reproducible with simple scalings derived form the empirical data.   

Numerical modeling of metal pad instability in liquid metal batteries

The rolling pad instability caused by electromagnetic coupling of interfacial waves in a three-layer system is analyzed for a simplified model of a liquid metal battery - a promising device for large-scale stationary energy storage. Simulations are performed using OpenFOAM. The stability characteristics and selection between symmetrically and antisymmetrically coupled waves are found to be determined by system's parameters, in particular by the ratio of the density differences across the two interfaces. Various scenarios possible in the battery system: stability, instability leading to sloshing, and instability leading to short-circuit are presented.   

Bounds on inertial transfer in saturated small-scale dynamos

The dimensionless dissipation coefficient $\beta_u = \varepsilon_u L_f/U^3$ is an important quantity in non-conducting turbulent flows as it relates the viscous dissipation rate $\varepsilon_u$ to the scale $L_f$ at which kinetic energy is injected into the flow and the root-mean-square velocity $U$. As $\beta_u$ expresses a relation between small-scale and large-scale dynamics, it can be interpreted as a measure of the inertial flux across scales in a turbulent flow. Here we investigate the same quantity for a saturated small-scale dynamo in order to assess the influence of a fluctuating magnetic field on the interscale inertial transfer. We obtain upper bounds on $\beta_u$ for a saturated nonhelical dynamo as a function of Reynolds and magnetic Prandtl numbers.   

Electro-vortex flow in a liquid metal battery electrode with annular current collector

Electro-vortex flow (EVF) develops when electric current lines converge or diverge inside a conducting fluid, when the curl of the Lorentz force is non-zero. In a three-layered liquid metal battery (LMB), the EVF occurs near the current collectors and drives a flow away from the wall. In a recent study [1] on an Mg-Sb LMB with circular current collector, it was observed that even in a moderate size LMB, the EVF could be strong enough to pinch the thin electrolyte layer and cause short-circuit. In this study, we conduct numerical simulations of the flow in the top LMB electrode using electric potential based solver incorporated in the code OpenFOAM. With the same value of the imposed current as in [1], we find that the choice of annular current collector geometry mitigates the pinching of the electrode-electrolyte interface. With this geometry, instead of a strong central EVF jet, the flow consists of two weaker jets which curl upwards resulting in much lower velocity near the interface. This result is valid even in the presence of an imposed temperature gradient, with hot (cold) bottom (top) boundary, at a large Rayleigh number. These results can be of relevance in a practical LMB to avoid short-circuiting. [1] Herreman et al. (2019) Phys. Rev. Fluids 4, 113702.   

Convection and electrovortex flow in liquid metal batteries

As renewable power sources like wind and solar energy become increasingly relevant, so too does the challenge of energy storage. Liquid metal batteries (LMBs) - galvanic cells composed of multiple fluid layers - are a promising technology to this end. Two major flow forcings interact within LMBs: thermal convection, due to the presence of internal heating, and electrovortex flow (EVF), driven by diverging current densities. Though these flows have potential to both help and hinder the batteries' operation, their properties remain largely unknown. Here, we study convection and EVF in a new liquid gallium laboratory experiment. Using ultrasonic Doppler velocimetry measurements, we construct phase diagrams for the dominant flow modes and flow speed scalings over broad ranges of convective forcing, EVF forcing, and container shape. Internal heating in LMBs also enforces stable density stratification, which interacts with EVF in largely unknown ways. We address this interaction experimentally for the first time in this work. Results are compared to linear theory predictions for the onset modes of each forcing. Combined with previous theoretical arguments and experimental/numerical results, this study lays the groundwork for future LMB design.   

Magneto-convective Heat Transfer Measurements in Liquid Gallium

We conduct heat transfer measurement of a liquid gallium Rayleigh-B\'enard system with a vertical magnetic field. The experiment is carried out in two cylindrical containers with diameter-to-height aspect ratio $\Gamma = 1$ and $2$ for $10^6 < Ra < 10^8$ and $0< Ch < 3\times 10^5$. Combined the results from the previous studies, our experiment shows a more complete picture of near-onset to supercritical behaviors of heat transfer in liquid metal magnetoconvection (MC) over a large range of parameter space ($10^3 < Ra < 10^9$). Moreover, we tested different critical $Ra$ predictions from Chandrasekhar(1961), Busse(2008), and Houchens et al.(2002). Our study shows that convection onsets below the predicted critical $Ra$ for an infinite fluid layer (Chandrasekhar, 1961) and MC in our finite cylindrical tanks onsets via stationary wall-attached modes. This result is in agreement with recent experiment (Z\"urner et al., 2020) where the wall-mode was found experimentally near onset. The heat transfer data also suggest that asymptotic critical $Ra$ from Busse(2008) is likely the best to describes the onset of magnetoconvection in a cylindrical confinement regardless of the different aspect ratios.