The instability analysis and direct numerical simulation of turbulent flows in electromagnetically levitated droplets

The electromagnetic levitation has found a wide range of application in materials processing community. The melt flow, which is driven by the induced Lorentz forces, is one of the important phenomena associated with the system. Experimental observations and some numerical approximations have shown that melt flows in electromagnetically levitated droplets are at least in a mildly turbulent regime. So far, little information on the instability and turbulence phenomena in melt flows has been provided. Therefore, the studies of the flow instability and turbulent flows inside the droplet generate information that is critical for both fundamental understanding and quantitative assessment of this system. The main objective of this research work is twofold. One is to present a linear stability analyses of melt flows in the magnetically levitated droplet, and the other is to predict the turbulent flows in the droplet by direct numerical simulation.; Based on the high order finite difference scheme, we develop a parallel computing methodology for numerical simulation of two or three-dimensional laminar/turbulent flows. This algorithm has been verified with the spectral-like accuracy with superior computational efficiency and is used for the linear stability analysis and direct numerical simulation in this work.; The stability analysis is based on the solution of linearized Navier-Stokes equations in a spherical coordinate system. The perturbation equations are discretized by the high order finite difference method, and the resulting eigenvalue problem is solved by the linear fractional transformation with a full account of band matrix structure. Results suggest that the critical Reynolds number is below 100 and the most dangerous mode is k = 3. The discussion of physical mechanism of flow instability is presented.; The flow transition and turbulent flows in electromagnetically levitated droplets are studied by the direct numerical simulation. The typical Taylor-Gortler instability is identified in the flow transition. Detailed information of turbulent flows in the droplet is provided. Based on the database from direct numerical simulation, characteristic eddies on the free surface and inside the droplet, which are well agreed with experimental observations, are determined by using an orthogonal decomposition technique.