Three-dimensional numerical simulation of Marangoni flow instabilities in floating zones laterally heated by an equatorial ring

Instability of Marangoni convection in floating zones (full zone configuration) of a low Prandtl number fluid under microgravity conditions is investigated by parallel supercalculus and direct three-dimensional and time-dependent simulation of the problem. A parametric analysis (still absent in literature) of the influence of the aspect ratio of the liquid column on the features of the three-dimensional bifurcation of Marangoni flow is carried out. A novel distribution is introduced for the surface heat flux corresponding to the radiative flux generated by a ring heater positioned around the equatorial plane of the full zone at a distance h from the free interface. Axisymmetric computations are used to obtain the steady basic state, then the three-dimensional Navier–Stokes equations are solved to investigate the evolution of azimuthal disturbances. These disturbances always exhibit antisymmetric behavior with respect to the equatorial plane. The mirror symmetry with respect to this plane is broken. Strong...

[1]  B. Roux,et al.  Instability of thermocapillary convection in floating zones , 1992 .

[2]  C. Chun.  Experiments on steady and oscillatory temperature distribution in a floating zone due to the Marangoni convection , 1980 .

[3]  Vishwanath Prasad,et al.  Effect of liquid bridge volume on the instability in small-Prandtl-number half zones , 1999 .

[4]  J. Iwan D. Alexander,et al.  Surface tension and buoyancy-driven flow in a non-isothermal liquid bridge , 1992 .

[5]  G. Amberg,et al.  Experimental and numerical studies of thermocapillary convection in a floating zone like configuration , 1996 .

[6]  M. Wanschura,et al.  Instability of thermocapillary flow in symmetrically heated full liquid zones , 1998 .

[7]  Jyh-Chen Chen,et al.  Numerical computation of fluid flow of floating-zone crystal growth of molybdenum , 1995 .

[8]  G. Labrosse,et al.  Stability of the axisymmetric buoyant-capillary flows in a laterally heated liquid bridge , 1999 .

[9]  A. Batoul,et al.  Up to the unsteadiness of axisymmetric thermocapillary flows in a laterally heated liquid bridge , 2000 .

[10]  Interface shape in Czochralski grown crystals: Effect of conduction and radiation , 1985 .

[11]  M. Lappa,et al.  Three-dimensional numerical simulation of Marangoni instabilities in non-cylindrical liquid bridges in microgravity , 2001 .

[12]  R. Savino,et al.  3D Analysis of crystal/melt interface shape and Marangoni flow instability in solidifying liquid bridges , 2002 .

[13]  Jyh-Chen Chen,et al.  Linear stability analysis of thermocapillary convection in the floating zone , 1995 .

[14]  B. Roux,et al.  An analytical study of thermocapillary flow and surface deformations in floating zone , 1991 .

[15]  A. Danilewsky,et al.  Floating-zone and floating-solution-zone growth of GaSb under microgravity , 1998 .

[16]  J. M. Floryan,et al.  Thermocapillary effects in liquid bridges. I - Thermocapillary convection. II - Deformation of the interface and capillary instability , 1987 .

[17]  M. Lappa,et al.  PARALLEL SOLUTION OF THREE-DIMENSIONAL MARANGONI FLOW IN LIQUID BRIDGES , 1999 .

[18]  Sindo Kou,et al.  Thermocapillary flow and melt/solid interfaces in floating-zone crystal growth under microgravity , 1990 .

[19]  Jyh-Chen Chen,et al.  Numerical computation of heat flow, fluid flow and interface shapes in the float zone of lithium niobate during a melting process , 1996 .

[20]  Jyh-Chen Chen,et al.  Thermocapillary convection and melt-solid interface in the floating zone , 1994 .

[21]  Gustav Amberg,et al.  Hydrodynamical instabilities of thermocapillary flow in a half-zone , 1995, Journal of Fluid Mechanics.

[22]  Hans J. Rath,et al.  Three-dimensional numerical simulation of thermocapillary flows in cylindrical liquid bridges , 2000, Journal of Fluid Mechanics.