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This work comprises accurate computational analysis of levitated liquid droplet oscillations in AC and DC magnetic fields. The AC magnetic field interacting with the induced electric current within the liquid metal droplet generates intense fluid flow and the coupled free surface oscillations. The pseudo-spectral technique is used to solve the turbulent fluid flow equations for the continuously dynamically transformed axisymmetric fluid volume. The volume electromagnetic force distribution is updated with the shape and position change. We start with the ideal fluid test case for undamped Rayleigh frequency oscillations in the absence of gravity, and then add the viscous and the DC magnetic field damping. The oscillation frequency spectra are further analysed for droplets levitated against gravity in AC and DC magnetic fields at various combinations. In the extreme case electrically poorly conducting, diamagnetic droplet (water) levitation dynamics are simulated. Applications are aimed at pure electromagnetic material processing techniques and the material properties measurements in uncontaminated conditions. KEY WORDS: electromagnetic material processing; magnetic levitation; free surface dynamics; turbulent fluid flow.results demonstrate the correspondence to analytical Rayleigh frequencies without numerical damping in the case of an ideal fluid droplet. For the case of realistic AC field levitation with normal gravity the internal fluid flow is turbulent, and an appropriate model for the time dependent turbulence is applied to obtain the oscillation frequencies in this complex nonlinear case. For the electrically conducting droplet both DC and AC magnetic fields exert a damping effect included in the numerical model. Finally, diamagnetic water droplet levitation is simulated in a high gradient DC magnetic field. The predicted oscillations are strongly affected by the droplet surface motion within the steep gradient force field. Mathematical Model Momentum and Temperature EquationsThe present modelling approach is based on the turbulent momentum and heat transfer equations for an incompressible fluid:where v is the velocity vector, p -the pressure, r -the density, n e ϭn T ϩn (summ of turbulent and laminar viscosity) is the effective viscosity which is variable in time and position, f is the electromagnetic force, g -the gravity vector, T -the temperature, a e ϭa T ϩa (summ of turbulent and laminar) is the effective thermal diffusivity, C p -the specific heat, C p * -the solid fraction modified specific heat function which accounts for latent heat effects (see Ref. 19)) for details), and | J| 2 /s is the Joule heat. The momentum Eq. (1) contains the nonlinear term in the convective (in difference to the rotational) form which, according to our tests, gives greater stability for the long time development problems. We will consider the flow representation for an axisymmetric fluid droplet in the spherical co-ordinates (R, q, f). The momentum and the continuity Eqs. (1), (2) in the absence of the azimuthal velocit...

The aim of this paper is to develop a stability theory and a numerical model for three density-stratified electrically conductive liquid layers. Using regular perturbation methods to reduce the full three-dimensional problem to the shallow layer model, the coupled wave and electric current equations are derived. The problem set-up allows for weakly nonlinear velocity field action and an arbitrary vertical magnetic field. Further linearisation of the coupled equations is used for the linear stability analysis in the case of a uniform vertical magnetic field. New analytical stability criteria accounting for the viscous damping are derived for particular cases of practical interest and compared to the numerical solutions for a variety of materials used in batteries. These new criteria are equally applicable to the aluminium electrolysis cell magnetohydrodynamic (MHD) stability estimates.

Induction skull melting (ISM) is a widely used process for melting certain alloys that are very reactive in the molten condition, such as those based on Ti, TiAl, and Zr, prior to casting components such as turbine blades, engine valves, turbocharger rotors, and medical prostheses. A major research project has been undertaken with the specific target of developing improved techniques for casting TiAl components. The aims include increasing the superheat in the molten metal to allow thin section components to be cast, improving the quality of the cast components and increasing the energy efficiency of the process. As part of this, the University of Greenwich (United Kingdom) has developed a dynamic, spectral-method-based computer model of the ISM process in close collaboration with the University of Birmingham (United Kingdom), where extensive melting trials have been undertaken. This article describes in detail the numerical model that encompasses the coupled influences of turbulent flow, heat transfer with phase change, and AC and DC magneto-hydrodynamics (MHD) in a time-varying liquid metal envelope. Associated experimental measurements on Al, Ni, and TiAl alloys have been used to obtain data to validate the model. Measured data include the true root-meansquare (RMS) current applied to the induction coil, the heat transfer from the molten metal to the crucible cooling water, and the shape of the semi-levitated molten metal. Examples are given of the use of the model in optimizing the design of ISM furnaces by investigating the effects of geometric and operational parameter changes.

In semilevitation melting, a cylindrical metal ingot is melted by a coaxial a.c. induction coil. A watercooled solid base supports the ingot, while the top and side free surface is confined by the magnetic forces as the melting front progresses. The dynamic interplay between gravity, hydrodynamic stress, and the Lorentz force in the fluid determines the instantaneous free surface shape. The coupled nonstationary equations for turbulent flow, heat with phase change, and high-frequency electromagnetic field are solved numerically for the axisymmetric time-dependent domain by a continuous mesh transformation, using a pseudospectral method. Results are obtained for the two actually existing coil configurations and several validation cases.