|
Organizers |
Stress problems in liquid bridge thermocapillary convection: a numerical approach
by
Guillaume Kasperski
LIMSI-CNRS, UPR 3251, Université Paris-Sud XI, BP 133, 91402 Orsay Cedex France
Coauthors: Gérard Labrosse (LIMSI-CNRS, UPR 3251, Université Paris-Sud XI, BP 133, 91402 Orsay Cedex France)
Axisymmetric thermocapillary convection is computed in a liquid bridge, held between two cylindrical isothermal rods and laterally heated. Geometrical simplifications lead to a rectangular computationnal domain. Flow fields and spatial derivatives are estimated by a Chebyshev collocation method and the conservation equations are solved by a projection-diffusion algorithm. To avoid mathematical singularities on the axial velocity boundary conditions, the thermocapillary stress is weighted by a regularising function, which cancels at the junctions of the free surface and the solid rods. The shape of this function, particularly the caracteristic length scale of the filtering, can be controlled by the experimentalist and may depend on the temperature profile at the free surface. The role of the Prandtl number, caracteristic of the considered fluid, on the flow regimes has been studdied for a particular, smooth, filtering of the thermocapillary stress. Increasing the control parameter of the convection, the Marangoni number, high-Pr flows keep a diffusive nature, as low-Pr flows become rapidely convective. They respectively undergo hydrothermal and hydrodynamical transitions to unsteadiness. The discussion will be lead on the role of the filter shape, on which thermally convective flows seem to be very dependent, leading to expensive computationnal investigations. The results could be partly relevant for fluid phenomena occuring in floating zone crystal growth processes.
Stress problems in liquid bridge thermocapillary convection
Date received: March 10, 1999
Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caco-19.