Oscillatory Thermocapillary Flows in Simulated Floating-zones with Time-dependent Temperature Boundary Conditions

Abstract

This study deals with numerical simulations of the Maxus sounding rocket experiment on oscillatory Marangoni convection in liquid bridges. The problem is investigated through direct numerical solution of the non-linear, time-dependent, three-dimensional Navier–Stokes equations. In particular, a liquid bridge of silicon oil 2[cs] with a length L=20 [mm] and a diameter D=20 (mm) is considered. A temperature difference ΔT=30 [K] is imposed between the supporting disks, by heating the top disk and cooling the bottom one with different rates of ramping. The results show that the oscillatory flow starts as an ‘axially running wave', but after a transient time the instability is described by the dynamic model of a ‘standing wave', with an azimuthal spatial distribution corresponding to m=1 (where m is the critical wave number). After the transition, the disturbances become larger and the azimuthal velocity plays a more important role and the oscillatory field is characterized by a travelling wave. The characteristic times for the onset of the different flow regimes are computed for different rates of ramping.