Oscillatory thermocapillary convection in liquid bridges with highly deformed free surfaces: Experiments and energy-stability analysis

2001 ◽  
Vol 13 (1) ◽  
pp. 107-120 ◽  
Author(s):  
L. B. S. Sumner ◽  
G. P. Neitzel ◽  
J.-P. Fontaine ◽  
P. Dell’Aversana
Keyword(s):  
Stability Analysis ◽  
Thermocapillary Convection ◽  
Energy Stability ◽  
Liquid Bridges ◽  
Free Surfaces

Thermocapillary Convection With Undeformable Curved Surfaces in Open Cylinders

2001 ◽  
Author(s):  
Bok-Cheol Sim ◽  
Abdelfattah Zebib
Keyword(s):  
Free Surface ◽  
Critical Frequency ◽  
Thermocapillary Convection ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Fluid Volume ◽  
Uniform Heat Flux ◽  
Free Surfaces ◽  
Space Experiments ◽  
Steady Convection

Abstract Thermocapillary convection driven by a uniform heat flux in an open cylindrical container of unit aspect ratio is investigated by two- and three-dimensional numerical simulations. The undeformable free surface is either flat or curved as determined by the fluid volume (V ≤ 1) and the Young-Laplace equation. Convection is steady and axisymmetric at sufficiently low values of the Reynolds number (Re) with either flat or curved interfaces. Only steady convection is possible in strictly axisymmetric computations. Transition to oscillatory three-dimensional motions occurs as Re increases beyond a critical value dependent on Pr and V. With a flat free surface (V = 1), two-lobed pulsating waves are found on the free surface and prevail with increasing Re. While the critical Re increases with increasing Pr, the critical frequency decreases. In the case of a concave surface, four azimuthal waves are found rotating clockwise on the surface. The critical Re decreases with increasing fluid volume, and the critical frequency is found to increase. The numerical results with either flat or curved free surfaces are in good quantitative agreement with space experiments.

Stability Analysis of Thermocapillary Convection of B2O3/Sapphire Melt in an Annular Pool

2021 ◽  
Vol 1036 ◽  
pp. 175-184
Author(s):  
Dong Ming Mo
Keyword(s):  
Stability Analysis ◽  
Temperature Distribution ◽  
Thermocapillary Convection ◽  
Silicone Oil ◽  
Liquid Interface ◽  
Sapphire Crystal ◽  
Neutral Stability ◽  
Unstable Flow ◽  
Fluid Layers ◽  
Lower Fluid

Aiming at the thermocapillary convection stability of sapphire crystal grown by liquid-encapsulated Czochralski method, by non-linear numerical simulation, obtained the flow function and temperature distribution of R-Z cross section, as well as the velocity and temperature distribution at liquid-liquid interface and monitoring point of B2O3/sapphire melt in annular two liquid system, covered with solid upper wall and in microgravity. By means of linear stability analysis, obtained the neutral stability curve and critical stability parameters of the system, and revealed the temperature fluctuation of the liquid-liquid interface. The calculated results of B2O3/sapphire melt were compared with 5cSt silicone oil/HT-70. The results show that under the same geometrical conditions, the flow of B2O3/sapphire melt system is more unstable than 5cSt silicone oil/HT-70, there are two unstable flow patterns, radial three-dimensional steady flow cell and hydrothermal waves near the hot wall. The larger the ratio of Pr number of upper and lower fluid layers is, the better the effect of restraining the flow of lower fluid layers is.

Energy stability of thermocapillary convection in a model of the float-zone crystal-growth process

1990 ◽  
Vol 217 ◽  
pp. 639-660 ◽  
Author(s):  
Y. Shen ◽  
G. P. Neitzel ◽  
D. F. Jankowski ◽  
H. D. Mittelmann
Keyword(s):  
Finite Length ◽  
Marangoni Number ◽  
Growth Process ◽  
Thermocapillary Convection ◽  
Energy Stability ◽  
Stability Criteria ◽  
Lagrange Equations ◽  
Float Zone ◽  
Crystal Growth Process ◽  
Axisymmetric Disturbances

Energy stability theory has been applied to a basic state of thermocapillary convection occurring in a cylindrical half-zone of finite length to determine conditions under which the flow will be stable. Because of the finite length of the zone, the basic state must be determined numerically. Instead of obtaining stability criteria by solving the related Euler–Lagrange equations, the variational problem is attacked directly by discretization of the integrals in the energy identity using finite differences. Results of the analysis are values of the Marangoni number, MaE, below which axisymmetric disturbances to the basic state will decay, for various values of the other parameters governing the problem.

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