Fractal features of oscillatory convection in the half-floating zone

Unsteady and two-dimensional numerical simulation is applied to study the transition process from steady convection to turbulence via subharmonic bifurcation in thermocapillary convection of a liquid bridge in the half-floating zone. The results of numerical tests show clearly the fractal structure of period-doubling bifurcations, and frequency-locking at f/4, f/8, f/16 with basic frequency f is observed with increasing temperature difference. The Feigenbaum universal constant is given by the present paper as delta(4) = 4.853, which can be compared with the theoretical value 4.6642016.

Transition from steady to oscillatory convection with chaotic feature in thermocapillary convection

The transition process from steady to turbulent convection via subharmonic bifurcation in thermocapillary convection of half floating zone was studied by numerical simulation and experimental test. Both approaches gave structure of period doubling bifurcations in the present paper, and the Feigenbaum universal law was checked for the system of thermocapillary convection.

Hardware development and ground-based studies for drop shaft experiment on oscillatory convection in half floating-zone

Coordinated measurement of temperature, velocity and free surface oscillation were obtained by using the drop shaft facility for microgravity experiments of half floating zone convection. The ground-based studies gave transition from steady to oscillatory convection for multi-quantities measurement.

Free surface vibration in oscillatory convection of half floating zone

Projecting an orthographical grating mask (20pl/mm) on the surface of a small liquid bridge and receiving the reflected distortion image, one can calculate out reversely the shape of free surface of a liquid bridge. In this way we measured the surface shape of a small floating zone and the two-dimensional deformation of its vibration. The mechanism of thermocapillary oscillatory convection and the three-dimensional variation of the free surface are revealed experimentally. The principle for space experiment has been studied in our laboratory.

Excitation mechanism of thermocapillary oscillatory convection

It is suggested that the oscillation of thermocapillary convection may be excited by the buoyancy instability. By means of numerical simulation of the finite-element method, the temperature distributions in the liquid bridge are qualitatively analyzed. The temperature gradient in a certain flow region of liquid bridge may turn to be parallel to the direction of gravity when the temperature difference △T between two boundary rods of liquid bridge is larger than the critical value. The buoyancy instability may be excited, and then the thermocapillary oscillatory convection appears, as the temperature difference increases further. The distribution of the critical Marangoni number in the micro-gravity environment is derived from the data on the ground experiments. The results show that the onset of thermocapillary oscillatory convection is delayed in the case of smaller typical scale of liquid bridge and lower gravity environment.

Effect of interfacial heat transfer on the onset of oscillatory convection in liquid bridge

In present study, effect of interfacial heat transfer with ambient gas on the onset of oscillatory convection in a liquid bridge of large Prandtl number on the ground is systematically investigated by the method of linear stability analyses. With both the constant and linear ambient air temperature distributions, the numerical results show that the interfacial heat transfer modifies the free-surface temperature distribution directly and then induces a steeper temperature gradient on the middle part of the free surface, which may destabilize the convection. On the other hand, the interfacial heat transfer restrains the temperature disturbances on the free surface, which may stabilize the convection. The two coupling effects result in a complex dependence of the stability property on the Biot number. Effects of melt free-surface deformation on the critical conditions of the oscillatory convection were also investigated. Moreover, to better understand the mechanism of the instabilities, rates of kinetic energy change and "thermal" energy change of the critical disturbances were investigated (C) 2009 Elsevier Ltd. All rights reserved.

Study on Flow Patterns of Oscillatory Thermocapillary Convection In Floating Half Zone by PIV

The velocity fields of oscillatory convection have been measured using the techniques of Particle Image Velocimetry (PIV) in a liquid bridge of half floating zone with small typical scales of a few millimeters for emphasizing the thermocapillary effect in comparison with the effect of buoyancy. The flow patterns of the oscillatory flow have been studied experimentally in a liquid bridge. The flow patterns in the liquid bridge are classified with mode numbers according to oscillatory flow characteristics. Results of the experiment show that the mode depends on the aspect ratio as well as the volume ratio of the liquid bridge. The experimental results are helpful for studying the structure of flow at the onset of oscillatory thermocapillary convection in a liquid bridge.

Oscillatory instability of Rayleigh-Marangoni-Bénard convection in two-layer liquid systems

The oscillatory behaviour of the Rayleigh-Marangoni-Bénard convective instability (R-M-B instability) regarding two combinations of two-layer fluid systems has been investigated theoretically and numerically. For the two-layer system of Silicone oil (10cSt) over Fluorinert (FC70), both linear instability analysis and 2D numerical simulation show that the instability of the system depends strongly on the depth ratio Hr = H1/H2 of the two-layer liquid. The oscillatory regime at the onset of R-M-B convection enlarges with reducing Γ = Ra/Ma values. In the two-layer system of Silicone oil (2cSt) over water, it loses its stability and onsets to steady convection at first, then the steady convection bifurcates to oscillatory convection with increasing Rayleigh number Ra. This behaviour was found through numerical simulation above the onset of steady convection in the case of r = 2.9, ε=(Ra-Ruc)/Rac = 1.0, and Hr = 0.5. Our findings are different from the previous study of the Rayleigh-Benard instability and show the strong effects of the thermocapillary force at the interface on the time-dependent oscillations at or after the onset of convection. We propose a secondary oscillatory instability mechanism to explain the experimental observation of Degen et al. [Phys. Rev. E, 57 (1998), 6647-6659].

Transition of oscillatory floating half zone convection from Earth's gravity to microgravity

Oscillatory features of floating half zone convection were experimentally studied by using the drop shaft facility of Japan Microgravity Center which supported microgravity period of 10 s. Coordinated measurements including free surface deformation and oscillation, temperature and flow pattern in both 1-g and micro-g environment were obtained. The oscillatory frequency and amplitude in micro-g condition were lower and larger than the ones in l-g condition, respectively. The results gave, at first time, the oscillatory features such as free surface wave in micro-g, coordinated measurements of more than two physical quantities in the micro-g, and transition of thermocapillary oscillatory convection from I-g to micro-g.

Experimental study on oscillatory thermocapillary convection

The transition processes from steady flow into oscillatory flow in a liquid bridge of the half floating zone are studied experimentally. Two methods of noncontacted diagnoses are developed to measure the distribution of critical Marangoni numbers described by the onset of the oscillation st the free surface of the liquid bridge.The experimental results obtained for both cases of the upper rod heated and the lower rod heated agree with the prediction by Rayleigh's instability theory.The sensitive relations between the relatively fat or slender liquid bridge and the onset of oscillatory convection are also discussed to reveal the insight of the pressure distribution near the free surface. The experiments have been performed in a small liquid bridge, where the Bond number is much smaller than 1, and the results can be used to simulate the experiment in the microgravity environment.

Two bifurcation processes for onset of oscillatory thermocapillary convection in a floating half zone

An overview on the onset of thermocapillary oscillatory convection in a floating half zone is provided, and it is a typical subject in the microgravity sciences related to the space materials science, especially the floating zone processing, and also to the microgravity fluid physics. The main interests are focused around the process for onset of oscillatory thermocapillary convection, which is known also as the bifurcation transition from quasi-steady convection to oscillatory convection. The onset of oscillation depends on a set of critical parameters, such as the Marangoni number, Prandtl number, geometrical parameters, and heat transfer parameters. Recent studies show that, there exists the bifurcation transition from steady and axial symmetric convection to the steady and axial non-symmetric convection before the onset of oscillation in cases of small Prandtl number fluids and in cases of larger Prandtl number fluids of fat liquid bridge with small aspect ratio. The transition process is a strong non-linear process because the velocity deviation has the same order of magnitude as that of an average flow after the onset of oscillation, and unsteady 3-D numerical simulation is suitable to do in depth analysis on strong non-linear process, and leads generally to a better comparison with the experimental results.

Experimental Study on the Transition Process to the Oscillatory Thermocapillary Convections in a Floating Half Zone

The transition process of the thermocapillary convection from a steady and axisymmetric mode to the oscillatory mode in a liquid bridge with a fixed aspect ratio and varied volume ratio was studied experimentally. To ensure the surface tension to play an important role in the ground-based experiment, the geometrical configuration of the liquid bridge was so designed that the associated dynamic Bond number Bd ≈ 1. The velocity fields were measured by Particle Image Velocimetry (PIV) technique to effectively distinguish the different flow modes during the transition period in the experiments. Our experiments showed that as the temperature difference increased the slender and fat bridges presented quite different features on the evolution in their flow feature: for the former the thermocapillary convection transformed from a steady and axisymmetric pattern directly into an oscillatory one; but for the latter a transition flow status, characterized by an axial asymmetric steady convection, appeared before reaching the oscillatory mode. Experimental observations agree with the results of numerical simulations and it is obvious that the volume of liquid bridge is a sensitive geometric parameter. In addition, at the initial stage of the oscillation, for the former a rotating oscillatory convection with azimuthal wave number m = 1 was observed while for the latter a pulsating oscillatory pattern with azimuthal wave number m = 2 emerged, and then with further increase of the temperature difference, the pulsating oscillatory convection with azimuthal wave number m = 2 evolved into a rotating oscillatory pattern with azimuthal wave number m = 2.

Two bifurcation transitions of the floating half zone convection in a fat liquid bridge of larger Pr

The transient process of the thermocapillary convection was obtained for the large Pu floating half zone by using the method of three-dimensional and unsteady numerical simulation. The convection transits directly from steady and axisymmetric state to oscillatory flow for slender liquid bridge, and transits first from steady and axisymmetric convection to the steady and non-axisymmetric convection, then, secondly to the oscillatory convection for the fatter liquid bridge. This result implies that the volume of liquid bridge is not only a sensitive critical parameter for the onset of oscillation, but also relates to the new mechanism for the onset of instability in the floating half zone convection even in case of large Prandtl number fluid.

Two Bifurcation Transition Processes in Floating Half Zone Convection of Larger Prandtl Number Fluid

Processes of the onset oscillation in the thermocapillaxy convection under the Earth's gravity are investigated by the numerical simulation and experiments in a floating half zone of large Prandtl number with different volume ratio. Both computational and experimental results show that the steady and axisymmetric convection turns to the oscillatory convection of m=1 for the slender liquid bridge, and to the oscillatory convection before a steady and 3D asymmetric state for the case of a fat liquid bridge. It implies that, there are two critical Marangoni numbers related, respectively, to these two bifurcation transitions for the fat liquid bridge. The computational results agree with the results of ground-based experiments.