Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Volume 67, Number 19
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session U15: Magnetohydrodynamics |
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Chair: Arpan Sircar, Oak Ridge National Lab Room: 142 |
Tuesday, November 22, 2022 8:00AM - 8:13AM |
U15.00001: The influence of thermal convection on the MHD flow in a toroidal duct Ruben Avila, Mónica Orozco The non-steady, three-dimensional thermal convection in a laminar MHD flow that is confined in a toroidal duct with square cross-section, in the presence of a constant axial magnetic field is studied. The temperature difference between the liquid metal flow and the walls of the toroidal duct is generated by a homogeneous internal heat source. The transition from the steady state pure forced convection, at subcritical Rayleigh number, to time dependent mixed convection at supercritical Rayleigh number is investigated. The dimensionless equations governing the flow of the incompressible liquid metal under the Boussinesq and quasi-static (induction-less) approximations are solved by using the spectral-element method. The parameters governing the system are the Hartmann, the Reynolds, the Prandtl and the Rayleigh numbers. The walls of the toroidal duct are no-slip for velocity, while the side walls are electrically perfectly conducting and the top and bottom walls are electrically perfectly insulating. The four walls of the duct have the same constant dimensionless temperature. A three dimensional map where the Hartmann, Reynolds and Rayleigh numbers are involved (considering only one Prandtl number) is generated to identify the critical Rayleigh number at which the onset of thermal convection appears. The effect of the thermal convection on the flow patterns is presented. Additionally, the influence of the governing parameters on the temperature distribution and the heat transfer rate at the walls of the toroidal duct is reported. |
Tuesday, November 22, 2022 8:13AM - 8:26AM |
U15.00002: A magnetorotational instability in the solar near-surface shear layer. Kyle Augustson, Daniel Lecoanet, Geoffrey Vasil, Keaton J Burns, Jeff S Oishi, Benjamin P Brown The Sun rotates differentially in both latitude and depth. There is a region of near-surface shear, the outer 5\% by radius, where the rotation rate decreases with radius. This shear is sufficient to trigger the classical magneto-rotational instability. The linear instability is assessed in spherical shell geometry with a dipolar magnetic field and two shear profiles, while ignoring the dynamical influence of convection and buoyancy. The spherical eigenproblem and local Cartesian eigenproblem are shown to have some similarities, but geometry impacts the eigenfunctions and hence the growth rates. The influence of density stratification is also investigated, showing that it raises the effective magnetic energy of the system and can quench the instability if the stratification is large enough. For solar-like values of a density described by an adiabatic polytrope, it can enhance the growth depending on the assumed strength of the magnetic field at the upper boundary. The nonlinear problem is then considered in the sphere shell, using the eigenfunctions as an initial condition. |
Tuesday, November 22, 2022 8:26AM - 8:39AM |
U15.00003: Solidification of a water-based sessile magnetic drop under the effect of a vertical magnetic field Abrar Ahmed, Prashant R Waghmare The study, presented here, investigates the solidification time and height of water-based magnetic fluid, which is responsive to the magnetic field. Liquid solidification via freezing is ubiquitous in nature and affects several aspects of our daily lives and many industrial applications. However, little is known about a comprehensive model that can predict the freezing or solidification rate of a colloidal droplet while the freezing occurs under the influence of external body forces. In this study, we develop a mathematical model to describe a magnetic drop freezing on a solid substrate under the effect of a vertically oriented magnetic field. This model accounts for the strength of the actuating field, and the physical properties of liquid and ice (solid), in addition to the associated interfacial and surface energies and curvature of the droplet. The mathematical model formulated here is based on the mass, momentum, and energy conservation equation, which is eventually deduced to an equation similar to the lubrication equation accounting for the phase change and solidification height as a function of magnetic field strength. The solution of the governing equation will offer us a mechanism to control the solidification rate of the colloidal droplet, infused with metal nanoparticles, by tuning the magnetic field strength, which we also observed experimentally. In this study, We also proposed a magnetically influenced freezing time scale. Apart from academic interest, this study is essential to freeze casting and additive manufacturing of metallic and organic objects consisting of magnetic nanoparticles. In such processes, the solidification rate of a colloidal droplet dictates the pore morphology as well as the strength of the green body. |
Tuesday, November 22, 2022 8:39AM - 8:52AM |
U15.00004: Edge states in MHD duct flows with electrically insulating walls Mattias Brynjell-Rahkola, Yohann Duguet, Thomas Boeck The study of laminar-turbulent transition from a dynamical systems perspective has significantly advanced our understanding of subcritical transition in hydrodynamic (HD) shear flows. In spite of this, little attention has been paid to these developments in the magnetohydrodynamic (MHD) community, where subcritical transition occurs in wall-bounded flows relevant for liquid metal applications. In a duct subject to a transverse magnetic field, Hartmann and Shercliff layers form on the walls orthogonal and parallel to the field direction, respectively. Traditionally, transition to turbulence in such flows has been characterized by a critical Reynolds number based on the Hartmann layer thickness, whereas modern direct numerical simulations (DNS) suggest that transition first takes place in the Shercliff layers. Motivated by this contradiction, the MHD duct flow is revisited using the quasi-static MHD approximation, by means of DNS and dynamical system concepts developed in the HD community. Emphasis is placed on the periodic square duct for which different transition routes and edge states, which correspond to relative attractors on the basin boundary of the laminar flow, are studied. |
Tuesday, November 22, 2022 8:52AM - 9:05AM |
U15.00005: Solutions to ideal magnetohydrodynamics equations by deep learning neural networks Fang Chen, Ravi Samtaney We investigate solutions to ideal magnetohydrodynamic (MHD) equations using the idea of Physics-Informed Neural Networks (PINNs). The loss function is formulated into two parts: first, labeled training data such as the initial/boundary conditions; and the second, unlabelled data (inside the domain) monitored by the ideal MHD equations. We also provide additional labeled data from probes to the neural networks, which successfully reconstruct spatial-time solutions to classical one-dimensional shock tube problems, such as Brio-Wu and Sod shock tubes. We extend this to more complex two-dimensional (2D) problems that permit self-similar solutions, such as the MHD shock refraction problem. We inform the 2D self-similar MHD equations to the neural network. Some preliminary results indicate that the neural network is able to obtain self-similar solutions to some complex 2D shock refraction problems in MHD. |
Tuesday, November 22, 2022 9:05AM - 9:18AM |
U15.00006: Nambu brackets and induced Lie-Poisson brackets for ideal fluid and MHD equations Yasuhide Fukumoto, Rong Zou 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 straightforwardly 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 with constant coefficients, using the three topological invariants other than the total mass 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. With this form, the iso-magneto-vortical perturbations are explicitly written out in terms of the Casimirs. |
Tuesday, November 22, 2022 9:18AM - 9:31AM |
U15.00007: Numerical simulation of two-fluid magnetohydrodynamic flows in channels with deformities Avick Sinha, Shivasubramanian Gopalakrishnan, Upendra Bhandarkar, Kowsik Bodi The study of liquid metal magnetohydrodynamic (MHD) flows is of significant interest, especially in the test blanket module of the International Thermonuclear Experimental Reactor. The situation involves the flow of lead-lithium eutectic fluid in the presence of a strong magnetic fluid. Especially important are accident scenarios which involve the possible ingress of gaseous helium into the liquid metal flow. In our previous work (Unni et al., 2018) numerical investigation involving two fluids of different viscosities and electrical conductivities was presented. In the present study, two-dimensional numerical investigations are carried out for MHD flows in channels with possible deformities at various operating conditions. The deformities are modelled as rectangular cavities or protrusions with different aspect ratios. We use the coupled Navier-Stokes, energy and Maxwell’s equations to specifically look at the heat transfer characteristics and the effect of magnetic fields on the rate of heat transfer. The relation of the local Nusselt’s number with the Hartmann number in different flow configurations is also presented. This work is among the first numerical efforts to investigate MHD flows and the heat transfer characteristics associated with non-smooth channels. |
Tuesday, November 22, 2022 9:31AM - 9:44AM |
U15.00008: Experimental and numerical study of the electrically driven flow of an electrolyte in a cylindrical cavity under axial current and magnetic field. María Dalia Marín Núñez, Sergio Cuevas, Alberto Beltrán We analyze experimentally the flow of a weak electrolyte in a small glass cylindrical cavity of radius R and aspect ratio of 1 through which an electrical current flows axially. The current is set by a potential difference between two parallel circular electrodes of radius r (r |
Tuesday, November 22, 2022 9:44AM - 9:57AM |
U15.00009: MHD turbulence models for fusion reactor blankets Arpan Sircar, Vittorio Badalassi Turbulence models, considering the effect of magnetohydrodynamics (MHD), were derived for canonical flows and can't predict complex engineering flows. For this reason, most researchers either consider the quasi-two-dimensional approximation when appropriate or perform high-resolution DNS and LES of MHD turbulence. However, with continued interest in fusion reactors, timely predictions of MHD turbulent heat transfer in fusion blankets and vacuum vessel cooling channels are crucial for design. In fact, the superconducting magnets used to confine the plasma affect the turbulent fluid flow through Lorentz forces. In this work, we implement MHD turbulence in the open-source code OpenFOAM. First, the laminar MHD solver is improved and benchmarked with existing data. Next, existing MHD RANS turbulence models are incorporated and compared against commercial codes such as HIMAG. The fidelity of these models is tested in simplified geometries of conceptual fusion reactor designs like the ARC reactor from Commonwealth Fusion Systems. It is found that MHD turbulence significantly hinders heat transfer in fusion blankets, and robust 3D models are required for accurate predictions and design improvements. |
Tuesday, November 22, 2022 9:57AM - 10:10AM |
U15.00010: Onset of instability and travelling wave states in MHD pipe flow subject to a transverse magnetic field Yelyzaveta Velizhanina, Bernard C Knaepen Linear stability theory suggests that all three-dimensional perturbations of small amplitude superposed on a flow of viscous incompressible fluid in a circular pipe decay exponentially in the asymptotic limit of large times. However, the experiments indicate that the flow undergoes laminar-turbulent transition at a Reynolds number Re=2000. There were numerous attempts to resolve this inconsistency. In particular, more recent studies focus on finding non-linear equilibrium solutions of the equations of motion. They correspond to the coherent states observed in a turbulent pipe flow and are labeled travelling waves. Despite significant advancement in understanding the instability mechanism in the Hagen-Poiseuille flow, little is known about the onset of turbulence in a liquid metal flow in a circular pipe subject to a transverse magnetic field. Since the classic experiments of Hartmann and Lazarus in 1937, it is well known that an applied magnetic field can stabilize otherwise unstable flow. However, it may as well introduce anisotropy and create velocity jets with inflection points. The present study consists in two parts and addresses the evolution of small disturbances and the formation of the travelling waves states in the MHD pipe flow subject to a transverse magnetic field. |
Tuesday, November 22, 2022 10:10AM - 10:23AM |
U15.00011: Large Eddy Simulation of magnetohydrodynamic inhomogeneous turbulent flow for high magnetic Reynolds number Kiran S Jadhav, Abhilash J Chandy Large eddy simulations (LES) of high magnetic Reynolds number (Rem) flow in the turbulent channel flow are performed. A hybrid formulation of spectral and finite difference methods is developed to carry out the simulations. The velocity and magnetic fields are initialized with laminar conditions. Validation of current code is carried out by comparing the turbulent flow results (without magnetic field) to previous published channel flow results. Quantities like evolution of kinetic and magnetic energy and variation of dissipation in the wall normal direction, magnetic and kinetic energy spectra are used to analyze the flow. The simulations are carried out at bulk Reynolds number, Reb, of 2200 and unity magnetic Prandtl number for increasing levels of interaction parameter. Turbulent state occurs in channel flow at Re=2200 and the energy spectra shows a -5/3 Kolmogorov inertial sub-range scaling. At high Rem, the Lorentz force term is added to the momentum equation. This paper aims to explore the interaction between kinetic and magnetic field in inhomogeneous environment. It is observed that higher interaction parameter inhibits the transition from laminar to turbulent transition which is visualized by the flow-direction magnetic field plots. |
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