An Introduction to Magnetohydrodynamics

Hydrodynamic and hydromagnetic stability

An experimental study with respect to the influence of a rotating magnetic field (RMF) on the unidirectional solidification of Pb–Sn alloys is reported. The magnitude of the bulk flow in the melt generated by the RMF varies with the magnetic Taylor number Ta = σωB2R4/2ρν2. The forced convection causes distinct modifications of the temperature and concentration field such as a reduction of the temperature gradient ahead of the solidification front. Without electromagnetic stirring, the alloy solidifies solely in form of dendrites aligned parallel to the heat flow direction. In contrast, a transition from columnar-to-equiaxed growth (CET) is observed if the solidifying ingot is exposed to an RMF. The position of the CET is shifted towards the bottom of the casting by increasing the Ta number. The CET was found to occur for a cooling rate of about 0.4 K/s and temperature gradients in the range between 0.6 and 1.0 K/mm.

The columnar-to-equiaxed transition in Pb–Sn alloys affected by electromagnetically driven convection

Travelling magnetic fields applied to bulk crystal growth from the melt: The step from basic research to industrial scale

The present study considers the solidification of an Al-7 wt pct Si alloy under the influence of electromagnetic melt stirring using a rotating magnetic field (RMF). The effect of a continuously applied RMF is compared with an RMF pulse sequence of alternating direction (RMF-PSAD). The resulting flow structure in a cylindrical liquid metal column has been measured by isothermal experiments using the ternary alloy GaInSn. The solidification experiments performed with the Al-7 wt pct Si alloy confirm our numerical predictions concerning the temperature field during solidification and the distribution of primary crystals and eutectic phase in the solidified samples. The application of the RMF-PSAD regime at suitable frequencies of the reversals of the magnetic field direction fP delivers an equiaxed microstructure without macrosegregation.

Efficient Melt Stirring Using Pulse Sequences of a Rotating Magnetic Field: Part II. Application to Solidification of Al-Si Alloys

This paper deals with the stability analysis of an axially symmetric liquid metal flow driven by a rotating magnetic field in a cylinder of finite dimensions. The limit of linear stability with respect to axially symmetric perturbations is found for diameter-to-height ratios between 0.4 and 1. This oscillatory instability is shown to be different from the expected Taylor–Gortler vortices. Several linearly unstable steady solutions are found close to the stable basic state. It is shown that small finite-amplitude perturbations in the form of Taylor–Gortler vortices give rise to instability in the linearly stable regime.

Stability of axially symmetric flow driven by a rotating magnetic field in a cylindrical cavity

The instability of a rotating-magnetic-field-driven liquid metal flow in a finite cylinder with respect to infinitesimal azimuthally periodic perturbations is studied numerically This instability is observed to set in prior its axisymmetric counterpart with relatively low frequency at diameter-to-height ratios between 05 and 2 The axisymmetric and three-dimensional instabilities have similar characteristic features The instability originates in the cross-section of the horizontal and vertical rotating boundary layers and excites inertial waves in the inviscid core

I. Grants

Papers

Stability of axially symmetric flow driven by a rotating magnetic field in a cylindrical cavity

Linear three-dimensional instability of a magnetically driven rotating flow

Stability of melt flow due to a traveling magnetic field in a closed ampoule

Experimental and numerical results on the fluid flow driven by a traveling magnetic field

Vertical gradient freeze growth of GaAs with a rotating magnetic field