Melt Flow Instability and Turbulence in Electro-Magnetically Levitated Droplets

Abstract

This article addresses fluid flow instabilities and flow transition to turbulent chaotic motions through numerical analysis and turbulence in electro-magnetically levitated droplets through direct numerical simulations. Numerical implementation and computed results are presented for flow instability and turbulence flows in magnetically levitated droplets under terrestrial and microgravity conditions. The linear melt flow stability is based on the solution of the Orr-Sommerfeld linearized equations with the base flows obtained numerically using high order numerical schemes. The resulting eigenvalue problems are solved using the linear transformation or Arnold's method. Melt flow instability in a free droplet is different from that bounded by solid walls and flow transits to an unstable motion at a smaller Reynolds number and at a higher wave number in a free droplet. Also, flow instability depends strongly on the base flow structure. Numerical experiments suggest that the transition to the unstable region becomes easier or occurs at a smaller Reynolds number when the flow structures change from two loops to four loops, both of which are found in typical levitation systems used for micro-gravity applications. Direct numerical simulations (DNS) are carried out for an electro-magnetically levitated droplet in a low to mild turbulence regime. The DNS results indicate that both turbulent kinetic energy and dissipations attain finite values along the free surface, which can be used to derive necessary boundary conditions for calculations employing engineering k--ε models.