Vladimir Galindo

Contactless inductive flow tomography for a model of continuous steel casting

The contactless inductive flow tomography (CIFT) aims at reconstructing the velocity field in electrically conducting melts from externally measured induced magnetic fields. One of its possible applications is the velocity reconstruction in the continuous casting process. In this paper, we apply this method to the flow field in a small model (containing approximately 1.4 l of the eutectic alloy GaInSn) of a mould for thin slab casting. It is shown that the flow structure, in general, and the jet position and intensity, in particular, can be reliably determined from magnetic field data using only a modest number (in the order of 5) of sensors.

Numerical simulation of the Tayler instability in liquid metals

The electrical current through an incompressible, viscous and resistive liquid conductor produces an azimuthal magnetic field that becomes unstable when the corresponding Hartmann number exceeds a critical value of the order of 20. This Tayler instability (TI), which is not only discussed as a key ingredient of a nonlinear stellar dynamo model (Tayler-Spruit dynamo), but also as a limiting factor for the maximum size of large liquid metal batteries, was recently observed experimentally in a column of a liquid metal (Seilmayer et al 2012 Phys. Rev. Lett. 108 244501). On the basis of an integro-differential equation approach, we have developed a fully three-dimensional numerical code, and have utilized it for the simulation of the Tayler instability at typical viscosities and resistivities of liquid metals. The resulting growth rates are in good agreement with the experimental data. We illustrate the capabilities of the code for the detailed simulation of liquid metal battery problems in realistic geometries.

The Tayler instability at low magnetic Prandtl numbers: between chiral symmetry breaking and helicity oscillations

The Tayler instability is a kink-type, current driven instability that plays an important role in plasma physics but might also be relevant in liquid metal applications with high electrical currents. In the framework of the Tayler-Spruit dynamo model of stellar magnetic field generation, the question of spontaneous helical (chiral) symmetry breaking during the saturation of the Tayler instability has received considerable interest. Focusing on fluids with low magnetic Prandtl numbers, for which the quasistatic approximation can be applied, we utilize an integro-differential equation approach in order to investigate the saturation mechanism of the Tayler instability. Both the exponential growth phase and the saturated phase are analyzed in terms of the action of the alpha and beta effects of mean-field magnetohydrodynamics. In the exponential growth phase we always find a spontaneous chiral symmetry breaking which, however, disappears in the saturated phase. For higher degrees of supercriticality, we observe helicity oscillations in the saturated regime. For Lundquist numbers in the order of one we also obtain chiral symmetry breaking of the saturated magnetic field.

The influence of current collectors on Tayler instability and electro-vortex flows in liquid metal batteries

The Tayler instability is a kink-type flow instability which occurs when the electrical current through a conducting fluid exceeds a certain critical value. Originally studied in the astrophysical context, the instability was recently shown to be also a limiting factor for the upward scalability of liquid metal batteries. In this paper, we continue our efforts to simulate this instability for liquid metals within the framework of an integro-differential equation approach. The original solver is enhanced by multi-domain support with Dirichlet-Neumann partitioning for the static boundaries. Particular focus is laid on the detailed influence of the axial electrical boundary conditions on the characteristic features of the Tayler instability, and, secondly, on the occurrence of electro-vortex flows and their relevance for liquid metal batteries.

Phased Array Ultrasound System for Planar Flow Mapping in Liquid Metals

Controllable magnetic fields can be used to optimize flows in technical and industrial processes involving liquid metals in order to improve quality and yield. However, experimental studies in magnetohydrodynamics often involve complex, turbulent flows and require planar, two-component (2c) velocity measurements through only one acoustical access. We present the phased array ultrasound Doppler velocimeter as a modular research platform for flow mapping in liquid metals. It combines the pulse wave Doppler method with the phased array technique to adaptively focus the ultrasound beam. This makes it possible to resolve smaller flow structures in planar measurements compared with fixed-beam sensors and enables 2c flow mapping with only one acoustical access via the cross beam technique. From simultaneously measured 2-D velocity fields, quantities for turbulence characterization can be derived. The capabilities of this measurement system are demonstrated through measurements in the alloy gallium-indium–tin at room temperature. The 2-D, 2c velocity measurements of a flow in a cubic vessel driven by a rotating magnetic field (RMF) with a spatial resolution of up to 2.2 mm are presented. The measurement results are in good agreement with a semianalytical simulation. As a highlight, two-point correlation functions of the velocity field for different magnitudes of the RMF are presented.

Contactless Inductive Bubble Detection in a Liquid Metal Flow

The detection of bubbles in liquid metals is important for many technical applications. The opaqueness and the high temperature of liquid metals set high demands on the measurement system. The high electrical conductivity of the liquid metal can be exploited for contactless methods based on electromagnetic induction. We will present a measurement system which consists of one excitation coil and a pickup coil system on the opposite sides of the pipe. With this sensor we were able to detect bubbles in a sodium flow inside a stainless steel pipe and bubbles in a column filled with a liquid Gallium alloy.

Measurement of the spatio-temporal distribution of harmonic and transient eddy currents in a liquid metal

Harmonic and transient eddy currents in the eutectic liquid metal alloy GaInSn positioned above an excitation coil are determined by measuring the corresponding voltage drop in an electric potential probe. The resulting spatio-temporal eddy current field is compared with the corresponding analytical expressions for a conducting half-space. Further, a deformation of the eddy current distribution due to a non-conducting torus immersed into the liquid metal is measured and compared with numerical results. The method can be generalized to arbitrary geometries, and might help us to validate numerical models for non-destructive testing and magnetic inductance tomography.

Electro-vortex flow simulation using coupled meshes

Abstract A numerical model for simulating electro-vortical flows in OpenFOAM is developed. Electric potential and current are solved in coupled solid-liquid conductors by a parent-child mesh technique. The magnetic field is computed using a combination of Biot–Savart’s law and induction equation. Further, a PCG solver with special regularisation for the electric potential is derived and implemented. Finally, a performance analysis is presented and the solver is validated against several test cases.

Instabilities and spin-up behaviour of a rotating magnetic field driven flow in a rectangular cavity

This study presents numerical simulations and experiments considering the flow of an electrically conducting fluid inside a cube driven by a rotating magnetic field (RMF). The investigations are focused on the spin-up, where a liquid metal (GaInSn) is suddenly exposed to an azimuthal body force generated by the RMF and the subsequent flow development. The numerical simulations rely on a semi-analytical expression for the induced electromagnetic force density in an electrically conducting medium inside a cuboid container with insulating walls. Velocity distributions in two perpendicular planes are measured using a novel dual-plane, two-component ultrasound array Doppler velocimeter with continuous data streaming, enabling long term measurements for investigating transient flows. This approach allows identifying the main emerging flow modes during the transition from stable to unstable flow regimes with exponentially growing velocity oscillations using the Proper Orthogonal Decomposition method. Characteris...

Efficient solution of 3D electromagnetic eddy-current problems within the finite volume framework of OpenFOAM

Eddy-current problems occur in a wide range of industrial and metallurgical applications where conducting material is processed inductively. Motivated by realising coupled multi-physics simulations, we present a new method for the solution of such problems in the finite volume framework of foam-extend, an extended version of the very popular OpenFOAM software. The numerical procedure involves a semi-coupled multi-mesh approach to solve Maxwells equations for non-magnetic materials by means of the Coulomb gauged magnetic vector potential A and the electric scalar potential ϕ. The concept is further extended on the basis of the impressed and reduced magnetic vector potential and its usage in accordance with Biot–Savarts law to achieve a very efficient overall modelling even for complex three-dimensional geometries. Moreover, we present a special discretisation scheme to account for possible discontinuities in the electrical conductivity. To complement our numerical method, an extensive validation is completing the paper, which provides insight into the behaviour and the potential of our approach.