Bulletin of the American Physical Society
73rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 65, Number 13
Sunday–Tuesday, November 22–24, 2020; Virtual, CT (Chicago time)
Session J04: Magnetohydrodynamics (8:00am  8:45am CST)Interactive On Demand

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J04.00001: Physicsconstrained datadriven methods in MHD Alan Kaptanoglu, Kyle Morgan, Christopher Hansen, Steven Brunton Accurate and efficient plasma models are essential to understand and control experimental devices. Datadriven techniques recently developed in fluid dynamics can be leveraged to develop interpretable reducedorder models of plasmas that strike a balance between accuracy and efficiency. The dynamic mode decomposition, PODGalerkin methods, and other reduced order models are applied to experimental and simulation data, and suggest possible uses in realtime control and modeling for fusion devices. [Preview Abstract] 

J04.00002: Energy Budget in Decaying Compressible MHD Turbulence Yan Yang, Minping Wan, William Matthaeus 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. [Preview Abstract] 

J04.00003: Numerical modeling of metal pad instability in liquid metal batteries Linyan Xiang, Oleg Zikanov The rolling pad instability caused by electromagnetic coupling of interfacial waves in a threelayer system is analyzed for a simplified model of a liquid metal battery  a promising device for largescale 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 shortcircuit are presented. [Preview Abstract] 

J04.00004: Bounds on inertial transfer in saturated smallscale dynamos Moritz Linkmann The dimensionless dissipation coefficient $\beta_u = \varepsilon_u L_f/U^3$ is an important quantity in nonconducting 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 rootmeansquare velocity $U$. As $\beta_u$ expresses a relation between smallscale and largescale 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 smallscale 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. [Preview Abstract] 

J04.00005: Electrovortex flow in a liquid metal battery electrode with annular current collector Avishek Ranjan, Saksham Jindal Electrovortex flow (EVF) develops when electric current lines converge or diverge inside a conducting fluid, when the curl of the Lorentz force is nonzero. In a threelayered 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 MgSb 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 shortcircuit. 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 electrodeelectrolyte 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 shortcircuiting. [1] Herreman et al. (2019) Phys. Rev. Fluids 4, 113702. [Preview Abstract] 

J04.00006: Convection and electrovortex flow in liquid metal batteries Jonathan Cheng, Ibrahim Mohammed, Bitong Wang, Gerrit Horstmann, Douglas Kelley 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. [Preview Abstract] 

J04.00007: Magnetoconvective Heat Transfer Measurements in Liquid Gallium Yufan Xu, Susanne Horn, Jonathan Aurnou We conduct heat transfer measurement of a liquid gallium RayleighB\'enard system with a vertical magnetic field. The experiment is carried out in two cylindrical containers with diametertoheight 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 nearonset 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 wallattached modes. This result is in agreement with recent experiment (Z\"urner et al., 2020) where the wallmode 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. [Preview Abstract] 
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