Free surface oscillation of thermocapillary convection in liquid bridge of half-floating-zone

Free surface deformations of thermocapillary convection in a small liquid bridge of half floating-zone are studied in the present paper. The relative displacement and phase difference of free surface oscillation are experimentally studied, and the features of free surface oscillation for various applied temperature differences are obtained. It is discovered that there is a sort of surface waves having the character of small perturbation, and having a wave mode of unusually large amplitude in one corner region of the liquid bridge.

Coupling of melting-solidification phase-change convection with floating-zone convection under microgravity

A finite element algorithm is used to analyze the process of floating zone crystal growth under microgravity. The effect of phase change convection coupled with surface tension convection is considered. The results show that the rate of crystal growth is very important. The single-crystal-melt interface is steeper than the feed-melt interface during the process of crystal growth. When the rate exceeds a critical value, the Marangoni vortex near the feed-melt interface will become so large that a secondary vortex will exist.

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.

Floating zone convection

der="0" alt="" hspace="8" width="141" height="200" align="left" />The microgravity research, as a branch of the advanced sciences and a spe- cialized field of high technology, has been made in China since the late 1980's. The research group investigating microgravity fluid physics consisted of our col- leagues and the authors in the Institute of Mechanics of the Chinese Academy of Sciences (CAS), and we pay special attention to the floating zone convection as our first research priority. Now, the research group has expanded and is a part of the National Microgravity Laboratory of the CAS, and the research fields have been extended to include more subjects related to microgravity science. Howev- er, the floating zone convection is still an important topic that greatly holds our research interests.

Period-doubling bifurcations of the thermocapillary convection in a floating half zone

This study experimentally explored the fine structures of the successive period-doubling bifurcations of the time-dependent thermocapillary convection in a floating half zone of 10 cSt silicone oil with the diameter d (0)=3.00 mm and the aspect ratio A=l/d (0)=0.72 in terrestrial conditions. The onset of time-dependent thermocapillary convection predominated in this experimental configuration and its subsequent evolution were experimentally detected through the local temperature measurements. The experimental results revealed a sequence of period-doubling bifurcations of the time-dependent thermocapillary convection, similar in some way to one of the routes to chaos for buoyant natural convection. The critical frequencies and the corresponding fractal frequencies were extracted through the real-time analysis of the frequency spectra by Fast-Fourier-Transformation (FFT). The projections of the trajectory onto the reconstructed phase-space were also provided. Furthermore, the experimentally predicted Feigenbaum constants were quite close to the theoretical asymptotic value of 4.669 [Feigenbaum M J. Phys Lett A, 1979, 74: 375-378].

Modelling the diurnal cycle of tropical convection across the "Grey Zone"

We present the results of simulations carried out with the Met Office Unified Model at 12km, 4km and 1.5km resolution for a large region centred on West Africa using several different representations of the convection processes. These span the range of resolutions from much coarser than the size of the convection processes to the cloud-system resolving and thus encompass the intermediate "grey-zone". The diurnal cycle in the extent of convective regions in the models is tested against observations from the Geostationary Earth Radiation Budget instrument on Meteosat-8. By this measure, the two best-performing simulations are a 12km model without convective parametrization, using Smagorinsky style sub-grid scale mixing in all three dimensions and a 1.5km simulations with two-dimensional Smagorinsky mixing. Of these, the 12km model produces a better match to the magnitude of the total cloud fraction but the 1.5km results in better timing for its peak value. The results suggest that the previously-reported improvement in the representation of the diurnal cycle of convective organisation in the 4km model compared to the standard 12km configuration is principally a result of the convection scheme employed rather than the improved resolution per se. The details of and implications for high-resolution model simulations are discussed.

Reynolds stress and heat flux in spherical shell convection

Context. Turbulent fluxes of angular momentum and heat due to rotationally affected convection play a key role in determining differential rotation of stars. Aims. We compute turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime in order to study whether restricted geometry introduces artefacts into the results. Methods. We employ direct numerical simulations of turbulent convection in spherical and Cartesian geometries. In order to alleviate the computational cost in the spherical runs and to reach as high spatial resolution as possible, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number or inverse Rossby number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes. Results. For slow rotation we find that the radial and latitudinal turbulent angular momentum fluxes are directed inward and equatorward, respectively. In the rapid rotation regime the radial flux changes sign in accordance with earlier numerical results, but in contradiction with theory. The latitudinal flux remains mostly equatorward and develops a maximum close to the equator. In Cartesian simulations this peak can be explained by the strong 'banana cells'. Their effect in the spherical case does not appear to be as large. The latitudinal heat flux is mostly equatorward for slow rotation but changes sign for rapid rotation. Longitudinal heat flux is always in the retrograde direction. The rotation profiles vary from anti-solar (slow equator) for slow and intermediate rotation to solar-like (fast equator) for rapid rotation. The solar-like profiles are dominated by the Taylor-Proudman balance.

3D MHD simulations of subsurface convection in OB stars

During their main sequence evolution, massive stars can develop convective regions very close to their surface. These regions are caused by an opacity peak associated with iron ionization. Cantiello et al. (2009) found a possible connection between the presence of sub-photospheric convective motions and small scale stochastic velocities in the photosphere of early-type stars. This supports a physical mechanism where microturbulence is caused by waves that are triggered by subsurface convection zones. They further suggest that clumping in the inner parts of the winds of OB stars could be related to subsurface convection, and that the convective layers may also be responsible for stochastic excitation of non-radial pulsations. Furthermore, magnetic fields produced in the iron convection zone could appear at the surface of such massive stars. Therefore subsurface convection could be responsible for the occurrence of observable phenomena such as line profile variability and discrete absorption components. These phenomena have been observed for decades, but still evade a clear theoretical explanation. Here we present preliminary results from 3D MHD simulations of such subsurface convection.

Space-Time Scales of Northward Propagation of Convection during Boreal Summer

This study uses precipitation estimates from the Tropical Rainfall Measuring Mission to quantify the spatial and temporal scales of northward propagation of convection over the Indian monsoon region during boreal summer. Propagating modes of convective systems in the intraseasonal time scales such as the Madden-Julian oscillation can interact with the intertropical convergence zone and bring active and break spells of the Indian summer monsoon. Wavelet analysis was used to quantify the spatial extent (scale) and center of these propagating convective bands, as well as the time period associated with different spatial scales. Results presented here suggest that during a good monsoon year the spatial scale of this oscillation is about 30 degrees centered around 10 degrees N. During weak monsoon years, the scale of propagation decreases and the center shifts farther south closer to the equator. A strong linear relationship is obtained between the center/scale of convective wave bands and intensity of monsoon precipitation over Indian land on the interannual time scale. Moreover, the spatial scale and its center during the break monsoon were found to be similar to an overall weak monsoon year. Based on this analysis, a new index is proposed to quantify the spatial scales associated with propagating convective bands. This automated wavelet-based technique developed here can be used to study meridional propagation of convection in a large volume of datasets from observations and model simulations. The information so obtained can be related to the interannual and intraseasonal variation of Indian monsoon precipitation.

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.

A simulation model of a floating half zone

A simulation model of a floating half zone was suggested by steady numerical simulation and experiment respectively, in the previous papers [Q.S. Chen, W.R. Hu, Int. J. Mass Heat Transfer 40 (1997) 757; J.H. Han, Y. Ar, R. Zhou, W.R. Hue, Int. J. Mass Heat Transfer 40 (1997) 2671]. In the present paper, the simulation model is studied by using the method of unsteady and three-dimensional numerical simulation, and the transient process from steady convection to oscillatory convection is especially analyzed. Comparison of onsets of oscillation for both simulation model and the usual model were obtained, and the results show that the critical Marangoni number of the simulation model is obviously smaller than that of the usual model for the same slender liquid bridge. This implies that the usual model of a floating half zone gives a lower estimation on the onset of oscillation for floating zone convection.

Magnetic field design for floating zone crystal growth

The magnetic fields produced by electrical coils are designed for P-doped Si crystal growth in a floating full zone in microgravity environment. The fields are designed specially to reduce the how near the free surface and then in the melt zone by adjusting the coil positions near the melt zone. The effects of the designed magnetic fields on reducing the Row velocity and the non-uniformity of the concentration distribution in the melt zone are better than those of the case of a uniform longitudinal magnetic field, obtained by numerical simulation. It is expected to improve the radial macro-segregation and reduce the convection in the crystal growth at the same time by using the designed magnetic field.

Influence of Forced Convection on Columnar Microstructure During Directional Solidification of Al-Ni Alloys

This paper presents a summary of cellular and dendritic morphologies resulting from the upward directional solidification of Al - Ni alloys in a cylindrical crucible. We analysed the coupling of solid-liquid interface morphology with natural and forced convection. The influence of natural convection was first analyzed as a function of growth parameters (solute concentration, growth rate and thermal gradient). In a second step, the influence of axial vibrations on solidification microstructure was investigated by varying vibration parameters (amplitude and frequency). Experimental results were compared to preliminary numerical simulations and a good agreement is found for natural convection. In this study, the critical role of the mushy zone in the interaction between fluid flow and solidification microstructure is pointed out.

Thermocapillary Convection in Floating Zones

This paper provides an overview of ongoing studies in the area of thermocapillary convection driven by a surface tension gradient parallel to the free surface in a floating zone. Here, research interests are focused around the onset of oscillatory thermocapillary convection, also known as the transition from quasisteady convection to oscillatory convection. The onset of oscillation depends on a set of critical parameters, and the margin relationship can be represented by a complex function of the critical parameters. The experimental results indicate that the velocity deviation of an oscillatory flow has the same order of magnitude as that of an average flow, and the deviations of other quantities, such as temperature and free surface radii fluctuations, are much smaller when compared with their normal counterparts. Therefore, the onset of oscillation should be a result of the dynamic process in a fluid, and the problem is a strongly nonlinear one. In the past few decades, several theoretical models have been introduced to tackle the problem using analytical methods, linear instability analysis methods, energy instability methods, and unsteady 3D numerical methods. The last of the above mentioned methods is known to be the most suitable for a thorough analysis of strong nonlinear processes, which generally leads to a better comparison with the experimental results. The transition from oscillatory thermocapillary convection to turbulence falls under the studies of chaotic behavior in a new system, which opens a fascinating new frontier in nonlinear science, a hot research area drawing many recent works. This paper reviews theoretical models and analysis, and also experimental research, on thermocapillary connection in floating zones. It cites 93 references.

Hydrothermal Instability Of Thermocapillary Convection In Large-Prandtl-Number Liquid Bridges Under Microgravity

Linear stability analysis was performed to study the mechanism of transition of thermocapillary convection in liquid bridges with liquid volume ratios ranging from 0.4 to 1.2, aspect ratio of 0.75 and Prandtl number of 100. 2-D governing equations were solved to obtain the steady axi-symmetric basic flow and temperature distributions. 3-D perturbation equations were discretized at the collocation grid points using the Chebyshev-collocation method. Eigenvalues and eigenfunctions were obtained by using the Q-R. method. The predicted critical Marangoni numbers and critical frequencies were compared with data from space experiments. The disturbance of the temperature distribution on the free surface causes the onset of oscillatory convection. It is shown that the origin of instability is related to the hydrothermal origin for convections in large-Prandtl-number liquid bridges. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.