Numerical simulation of free surface behaviour of a molten liquid metal droplet with and without electromagnetic induction

Electromagnetic levitation of electrically conductive droplets by alternating magnetic fields is a technique used to measure the physical properties of liquid metallic alloys such as surface tension or viscosity. Experiments can be conducted under terrestrial conditions or in microgravity, to reduce electromagnetic stirring and shaping of the droplet. Under such conditions, the time-dependent behaviour of a point of the free surface is recorded. Then the signal is analysed considering the droplet as a harmonic damped oscillator. We use a spectral code, for fluid flow and free surface descriptions, to check the validity of this assumption for two cases. First when the motion inside the droplet is generated by its initial distortion only and second, when the droplet is located in a uniform magnetic field originating far from the droplet. It is found that some deviations exist which can lead to an overestimate of the value of viscosity.

The study of flow and temperature fields in conducting droplets suspended in a DC/AC combination field

Electromagnetic Levitation (EML) is a valuable method for measuring the thermo-physical properties of metals - surface tensions, viscosity, thermal/electrical conductivity, specific heat, hemispherical emissivity, etc. – beyond their melting temperature. In EML, a small amount of the test specimen is melted by Joule heating in a suspended AC coil. Once in liquid state, a small perturbation causes the liquid envelope to oscillate and the frequency of oscillation is then used to compute its surface tension by the well know Rayleigh formula. Similarly, the rate at which the oscillation is dampened relates to the viscosity. To measure thermal conductivity, a sinusoidally varying laser source may be used to heat the polar axis of the droplet and the temperature response measured at the polar opposite – the resulting phase shift yields thermal conductivity. All these theoretical methods assume that convective effects due to flow within the droplet are negligible compared to conduction, and similarly that the flow conditions are laminar; a situation that can only be realised under microgravity conditions. Hence the EML experiment is the method favoured for Spacelab experiments (viz. TEMPUS). Under terrestrial conditions, the full gravity force has to be countered by a much larger induced magnetic field. The magnetic field generates strong flow within the droplet, which for droplets of practical size becomes irrotational and turbulent. At the same time the droplet oscillation envelope is no longer ellipsoidal. Both these conditions invalidate simple theoretical models and prevent widespread EML use in terrestrial laboratories. The authors have shown in earlier publications that it is possible to suppress most of the turbulent convection generated in the droplet skin layer, through use of a static magnetic field. Using a pseudo-spectral discretisation method it is possible compute very accurately the dynamic variation in the suspended fluid envelope and simultaneously compute the time-varying electromagnetic, flow and thermal fields. The use of a DC field as a dampening agent was also demonstrated in cold crucible melting, where suppression of turbulence was achieved in a much larger liquid metal volume and led to increased superheat in the melt and reduction of heat losses to the water-cooled walls. In this paper, the authors describe the pseudo-spectral technique as applied to EML to compute the combined effects of AC and DC fields, accounting for all the flow-induced forces acting on the liquid volume (Lorentz, Maragoni, surface tension, gravity) and show example simulations.

Magnetic damping of levitated liquid droplets in AC and DC field

The intense AC magnetic field required to produce levitation in terrestrial conditions, along with the buoyancy and thermo-capillary forces, results in turbulent convective flow within the droplet. The use of a homogenous DC magnetic field allows the convective flow to be damped. However the turbulence properties are affected at the same time, leading to a possibility that the effective turbulent damping is considerably reduced. The MHD modified K-Omega turbulence model allows the investigation of the effect of magnetic field on the turbulence. The model incorporates free surface deformation, the temperature dependent surface tension, turbulent momentum transport, electromagnetic and gravity forces. The model is adapted to incorporate a periodic laser heating at the top of the droplet, which have been used to measure the thermal conductivity of the material by calculating the phase lag between the frequency of the laser heating and the temperature response at the bottom. The numerical simulations show that with the gradual increase of the DC field the fluid flow within the droplet is initially increasing in intensity. Only after a certain threshold magnitude of the field the flow intensity starts to decrease. In order to achieve the flow conditions close to the ‘laminar’ a D.C. magnetic field >4 Tesla is required to measure the thermal conductivity accurately. The reduction in the AC field driven flow in the main body of the drop leads to a noticeable thermo-capillary convection at the edge of the droplet. The uniform vertical DC magnetic field does not stop a translational oscillation of the droplet along the field, which is caused by the variation in total levitation force due to the time-dependent surface deformation.