Search

In modern times, exposure to a liquid metal by a travelling magnetic field is widely applied. There are laboratory studies on the processes of stirring and crystallization under the action of a traveling magnetic field. However, in the majority of studies it is assumed that the inductor power supply of the linear induction machine is carried out by a symmetrical three-phase system of currents with an equal phase shift, which, in some cases, is not quite correct. To approximate the model to real operating conditions, a numerical simulation of the magnetic field and the flow of liquid metal was carried out when supplied from a power source of symmetric three-phase voltage. The distortion of magnetic field, which, in turn, causes an nonuniform distribution of forces and the flow of a liquid metal, is shown. Evaluation of asymmetrical effect on the liquid metal flow was carried out by means of finite element method. That effect is caused by different coefficients of mutual coils induction of the linear induction machine, which is confirmed by experimental data. © Published under licence by IOP Publishing Ltd. Russian Foundation for Basic Research, RFBR: 17-48-590539 r a Ural Federal University, UrFU The work of Institute of Continuous Media Mechanics team is supporting by the RFBR grant 17-48-590539 r a and the work of Ural Federal University team is supporting by Act 211 Government of the Russian Federation, contract 02.A03.21.0006.

This paper presents qualitative and quantitative characterization of two-phase liquid metal flows agitated by the stirrer on rotating permanent magnets. The stirrer was designed to fulfill various eddy flows, which may have different rates of solid particle entrapment from the liquid surface and their homogenization. The flow was characterized by visualization of the tailored tracer particles by means of dynamic neutron radiography, an experimental method well suited for liquid metal flows due to low opacity of some metals for neutrons. The rather high temporal resolution of the image acquisition (32 Hz image acquisition rate) allows for the quantitative investigation of the flows up to 30 cm/s using neutron particle image velocimetry. In situ visualization of the two-phase liquid metal flow is also demonstrated.

This paper presents a combined experimental and numerical study of the properties of a liquid metal flow inside a cylinder driven by the application of a strong electrical current. The interaction between the electric current running through the melt and the corresponding induced magnetic field produces so-called electro-vortex flows. We consider here a configuration of two parallel pencil electrodes immersed at the free surface. Velocity measurements were performed by means of the Ultrasound Doppler method. A linear array of 25 singular transducers was used to determine the two-dimensional pattern of the vertical flow component. Numerical simulations of the magnetohydrodynamic (MHD) problem were conducted to calculate the Lorentz force, the Joule heating and the induced melt flow. Experimental and numerical results reveal a complex three-dimensional flow structure of the liquid metal flow. In particular, two pronounced downward jets are formed below both electrodes. The flow structure appears to be symmetrical with respect to two vertical cross sections being perpendicular to each other and one of the two planes contains the electrodes. The comparison between the experimental data and the numerical results shows a very good agreement.

This review considers the stability of melt motion in two simplified models of semiconductor crystal growth by either vertical gradient freeze (VGF) or Czochralski (Cz) processes under the influence of various magnetic fields. In VGF the crystal is grown at the bottom of the crucible, resulting in a stable thermal stratification of the melt. The presence of a stabilizing temperature gradient surprisingly decreases the stability of the flow driven by a rotating magnetic field (RMF). The instability of the travelling magnetic field (TMF)-driven flow, in contrast, is significantly delayed by thermal stratification in VGF. The TMF may, thus, be used in VGF to control the shape of the solidification interface or the radial dopant distribution without causing undesirable flow oscillations. The crystal is pulled out from the melt in the Cz process, producing an unstable temperature gradient below the crystal. The RMF is able to force the resulting unstable buoyant flow into a state of small-scale, high-frequency turbulence that may be regarded as stable for practical purposes. This effect is experimentally observed over a wide range of Grashof numbers, up to 10^9, characteristic for a large Cz system.

This paper addresses liquid-metal flow under a strong, fringing, decreasing magnetic field in an insulating circular pipe by a full resolution of the magnetohydrodynamic (MHD) equations. The aims of the paper are first to provide a detailed description of the flow and second to perform a study of the restrictions related to the approximate numerical techniques commonly used in the nuclear fusion field, namely, the so-called core flow approximation based on asymptotic methods. Finally, a comparison between full MHD solutions obtained under conducting and insulating circular pipe walls, at similar MHD conditions, is provided. The current results show that the role of inertia is clearly more important under electrically insulating ducts because no net braking MHD forces are present in such configurations. This fact adversely affects the accuracy of asymptotic method results. From a phenomenological point of view, the effects of wall conductivity are found to be very important. For instance, when insulating walls are present, the intensity of the generated near-wall jets is three times larger than that found in conducting configurations. As a result, the shear effects and the triggering of turbulence in the downstream area are clearly enhanced. 61 1 10 1-10

The immersed boundary method (IB hereafter) is an efficient numerical methodology for treating purely hydrodynamic flows in geometrically complicated flow-domains. Recently Grigoriadis et als. [1] proposed an extension of the IB method that accounts for electromagnetic effects near non-conducting boundaries in magnetohydrodynamic (MHD) flows. The proposed extension (hereafter called MIB method) integrates naturally within the original IB concept and is suitable for magnetohydrodynamic (MHD) simulations of liquid metal flows. It is based on the proper definition of an externally applied current density field in order to satisfy the Maxwell equations in the presence of arbitrarily-shaped, non-conducting immersed boundaries. The efficiency of the proposed method is achieved by fast direct solutions of the two poisson equations for the hydrodynamic pressure and the electrostatic potential. The purpose of the present study is to establish the performance of the new MIB method in challenging configurations for which sufficient details are available in the literature. For this purpose, we have considered the classical MHD problem of a conducting fluid that is exposed to an external magnetic field while flowing across a circular cylinder with electrically insulated boundaries. Two- and three-dimensional, steady and unsteady, flow regimes were examined for Reynolds numbers Red ranging up to 200 based on the cylinder's diameter. The intensity of the external magnetic field, as characterized by the magnetic interaction parameter N, varied from N = 0 for the purely hydrodynamic cases up to N = 5 for the MHD cases. For each simulation, a sufficiently fine Cartesian computational mesh was selected to ensure adequate resolution of the thin boundary layers developing due to the magnetic field, the so called Hartmann and sidewall layers. Results for a wide range of flow and magnetic field strength parameters show that the MIB method is capable of accurately reproducing integral parameters, such as the lift and drag coefficients, as well as the geometrical details of the recirculation zones. The results of the present study suggest that the proposed MIB methodology provides a powerful numerical tool for accurate MHD simulations, and that it can extend the applicability of existing Cartesian flow solvers as well as the range of computable MHD flows. Moreover, the new MIB method has been used to carrry out a series of accurate simulations allowing the determination of asymptotic laws for the lift and drag coefficients and the extent of the recirculation length as a function of the amplitude of the magnetic field. These results are reported herein. © 2009 Elsevier Ltd. All rights reserved. 39 345 358 345-358

A physically consistent approach is considered for defining an external magnetic field as needed in computational fluid dynamics problems involving magnetohydrodynamics (MHD). The approach results in simple analytical formulae that can be used in numerical studies where an inhomogeneous magnetic field influences a liquid metal flow. The resulting magnetic field is divergence and curl-free, and contains two components and parameters to vary. As an illustration, the following examples are considered: peakwise, stepwise, shelfwise inhomogeneous magnetic fields, and the field induced by a solenoid. Finally, the impact of the streamwise magnetic field component is shown qualitatively to be significant for rapidly changing fields., Comment: 8 pages, 4 figures, accepted to TCFD