Transient behaviours of float zones in μ‐g and 1‐g environments

This work is concerned with the problem of the transient behaviours of the axisymmetric thermocapillary laminar flow occurring inside a half zone subjected to a variable thermal boundary condition during a heating process. The molten liquid with its deformable free surface is considered incompressible with constant physical properties except for its density in buoyancy forces where Boussinesq’s approximation has been applied. The system of governing equations has been successfully solved by using the modified‐SIMPLE method, while the instantaneous position of the free surface was determined by employing a special procedure. Numerical simulations have been carried out for both NaNO3 and Silicon float zones operating under 1‐g and μ‐g conditions. The transient behaviours as well as the influence of the Marangoni number and the aspect ratio have been investigated.

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

[2]  William R. Wilcox,et al.  Analysis of surface tension driven flow in floating zone melting , 1976 .

[3]  Robert Finn,et al.  Equilibrium Capillary Surfaces , 1985 .

[4]  D. Schwabe,et al.  Measurement of the critical Marangoni number in a floating zone under reduced gravity , 1983 .

[5]  N. Kazarinoff,et al.  Marangoni Flows in a Cylindrical Liquid Bridge of Silicon , 1990 .

[6]  C. T. Nguyen,et al.  TRANSIENT BEHAVIOR OF A NaNO3 FLOAT ZONE OPERATING AT HIGH MARANGONI NUMBER UNDER μg CONDITIONS , 1995 .

[7]  D. Schwabe,et al.  Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface , 1983, Journal of Fluid Mechanics.

[8]  D. Schwabe,et al.  Verification of the oscillatory state of thermocapillary convection in a floating zone under low gravity , 1982 .

[9]  A. Scharmann,et al.  Experiments on surface tension driven flow in floating zone melting , 1978 .

[10]  W. Wilcox.  Floating zone melting of electronic materials in space , 1991 .

[11]  D. Schwabe,et al.  Some evidence for the existence and magnitude of a critical marangoni number for the onset of oscillatory flow in crystal growth melts , 1979 .

[12]  C. T. Nguyen,et al.  Numerical investigation of the effects of rotation on a germanium float zone under microgravity conditions , 1995 .

[13]  Robert A. Brown,et al.  Thermal-capillary analysis of small-scale floating zones: Steady-state calculations , 1986 .

[14]  S. Kou,et al.  A half-zone study of Marangoni convection in floating-zone crystal growth under microgravity , 1990 .

[15]  Ch.-H. Chun,et al.  Suppression of temperature oscillations of thermal Marangoni convection in a floating zone by superimposing of rotating flows , 1981 .

[16]  Dietrich Schwabe,et al.  Surface-Tension-Driven Flow in Crystal Growth Melts , 1988 .

[17]  N. Kobayashi.  Steady Convection caused by the Temperature Inhomogeneity in a Cylindrical Floating Zone , 1988 .

[18]  A. Scharmann,et al.  The instability of surface tension driven flow in models for floating zones under normal and reduced gravity , 1990 .

[19]  R. Rupp,et al.  Three-dimensional time dependent modelling of the marangoni convection in zone melting configurations for GaAs , 1989 .

[20]  C. Chun.  Marangoni convection in a floating zone under reduced gravity , 1980 .

[21]  A. S. Jordan,et al.  A thermoelastic analysis of dislocation generation in pulled GaAs crystals , 1980, The Bell System Technical Journal.

[22]  W. Wilcox,et al.  Inhomogeneities due to thermocapillary flow in floating zone melting , 1975 .

[23]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[24]  C. Chun,et al.  Correlation of oscillations of flow and temperature in floating zone under microgravity , 1981 .

[25]  S. Slavchev,et al.  Computer simulation of the thermocapillary convection in a non-cylindrical floating zone , 1986 .

[26]  D. Schwabe,et al.  Microgravity experiments on the transition from laminar to oscillatory thermocapillary convection in floating zones , 1984 .

[27]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[28]  C. E. Chang.  Computer simulation of convection in floating zone melting. I. Pure rotation driven flows , 1978 .