On three-dimensional flow structures and oscillatory instability due to free surface heat loss in half-floating zones under microgravity

Abstract

Present work describes a numerical investigation concerning the response of oscillatory thermo-capillary convection to free surface heat loss in a cylindrical half floating zone of high Prandtl number liquid (Pr=67) under microgravity conditions. Unsteady and three-dimensional computations have been carried out in the liquid domain using the finite volume method (FVM) to reveal the oscillatory thermo-fluid dynamic regimes at the onset of instability. The influence of different free surface heat loss conditions on the bifurcation from the basic steady axisymmetric state has been discussed in terms of critical azimuthal wavenumber, m. The dynamic evolution of the temperature disturbances at supercritical conditions are characterized by ‘pulsating’ and ‘rotating’ modes of spatio-temporal convection. The development of counter-propagating hydrothermal waves in azimuthal direction is found to be followed by an even mode of convection characterised by m = 2. The liquid bridge system exhibiting the well-known transition from periodic (m=2) to quasi-periodic behaviour (m=1) with an increase in Biot number, Bi has been analysed from both spatial and temporal points of view. The existence of both symmetric and asymmetric modes of the supercritical state for different Bi are presented. The dominant fluid dynamic information of 3D oscillatory state are extracted from a specific set of disturbance temperature data by employing a data-driven computational technique ‘dynamic mode decomposition’ (DMD). Various neutral, stable and unstable dynamic modes responsible for bifurcation to the 3D supercritical state are depicted with the help of DMD spectrum and the frequency spectrum.