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Scientific paper
Jan 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002iaf..confe.536m&link_type=abstract
IAF abstracts, 34th COSPAR Scientific Assembly, The Second World Space Congress, held 10-19 October, 2002 in Houston, TX, USA.,
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Scientific paper
Floating zone method is a very attractive containerless technique for commercial growing the purest large- volume crystals. Liquid bridge is a configuration where a model liquid is held between two coaxial circular disks kept at different temperatures. Due to temperature-dependence of surface tension, convective flow appears. When the temperature difference between the disks exceeds the critical value, T>Tcr, the two- dimensional toroidal flow undergoes a transition to time-dependent three-dimensional one. For liquids with Pr>0.1, the resulting oscillatory flow is two hydrothermal waves, propagating azimuthaly in opposite directions. Depending on ratio of amplitudes of the two counter propagating waves, traveling or standing resulting waves are observed. A great number of numerical and experimental studies have been devoted to the oscillatory instabilities that occur at critical temperature difference between the two disks. But the real crystal growth processes deal with far-supercritical temperature differences T. At large temperature difference secondary instabilities leading to chaos take place. Actually, what route to chaos the system chooses depends on the many factors such as physical parameters of the liquid bridge, initial state of the system in phase-plane etc. Little information has been published regarding the temperature and flow fields in liquid bridge with increase T further to far-supercritical area up to chaotic regime. A real ground-based experiment with silicone oil of 1cSt (Pr18.76 at T=-20°C) is simulated in taking the real temperature-dependence of viscosity into consideration. As in the modeled experiment, the temperature of the cold disk is kept at T=-20°C. The transition process (also called the route) that leads the oscillatory thermoconvective flow in liquid bridge from a periodic behavior to chaos is under investigation. The simulations are done using finite volume method for solving the 3-D, time-dependent Navier-Stokes equations in the Boussinesq approximation in cylindrical coordinate system. In the studied case, T changed up to 6.3Tcr. The experimentally observed consequence of the flow regimes is recovered. The observed route to turbulence is quite unusual, as it does not involve such classical pre-chaotic flow organizations as quasi- periodical motion, entrainment, period doubling, three frequencies motion or intermittent noise. Starting as an m=1 standing wave, it rather quickly (at T1.04Tcr) undergoes transition to m=1 traveling one. When T3.06Tcr, the second bifurcation takes place and m=2 standing wave is the stable solution. The change of the azimuthal wave number m goes together with frequency skip, when fundamental frequency slightly lessens. Exactly as for the m=1 mode, standing wave undergoes transition to the traveling one (at T5.87Tcr), but the m=2 standing wave remains stable for a wide range of T. The transition to chaos takes place at T6.11Tcr. The onset of non-periodicity is preceded by second frequency skip, when observed stable flow organization is described by m=2 traveling wave.
Melnikov Denis E.
Shevtsova Valentina M.
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