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.

Effects of high-frequency vibration on critical marangoni number

The influence of vibration on thermocapillary convection and critical Marangoni number in liquid bridge of half floating zone was discussed for the low frequency range 0.4-1.5 Hz and the intermediate frequency range 2.5-15 Hz in our previous papers. This paper extends the study to high frequency range 15-100Hz. This ground based experiment was completed on the deck of an electromagnetic vibration machine. The results of our experiment shows when the frequency of the applied acceleration is high enough, the amplitude of the time varying part of the temperature response is disappear and the shape of the free surface of the liquid bridge exhibits no fluctuations due to inertia. The critical Marangoni number which is defined to describe the transitions from a peroidical convection in response to vibration to an oscillatory convection due to internal instability is nearly the same as the critical Marangoni number for oscillatory flow in the absence of vibration.

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.

Influence of liquid bridge volume on the onset of oscillation in floating-zone convection .1. Experiments

The onset of oscillation in the floating zone convection driven by the gradient of surface tension was experimentally studied, and discussions were concentrated on the influence of liquid bridge volume on the onset of oscillation. Distributions of critical applied temperature difference and frequency depending on the volume of the liquid bridge were obtained, and there was a gap range of liquid volume which separated the curve of marginal stability into two parts for fixed rod diameter and aspect ratio. The results imply that the volume of the liquid bridge is a sensitive critical parameter for the onset of oscillation. The implication on the instability is also discussed in the present paper.

Influence of liquid bridge volume on the onset of oscillation in floating-zone convection .2. Numerical-simulation

The onset of oscillation in the floating zone convection driven by the gradient of surface tension was studied numerically for an unsteady and two-dimensional model, and studies were concentrated on the influence of liquid bridge volume on the onset of oscillation in comparison with the experimental results in the Paper I. The numerical results agree with the experimental ones presented in the previous paper, in which the distributions of critical applied temperature difference depending on the volume of liquid bridge and a gap range of liquid volume in marginal stability curve were obtained.

Influence of convections on dopant segregation in floating-zone crystal-growth system

The steady and axisymmetric crystal growth process of floating zone model was studied numerically to concern with the influence of convection and phase change on effective segregation. An iteration method of numerical simulation considering both thermocapillary and buoyancy effects for GaAs crystal growth gave the effective segregation coefficient, which was compared with the space experiment of GaAs on board the Chinese recoverable satellite. The calculated segregation coefficient of a two-dimensional model was found to be smaller than the one suggested by space experiment with the simplified assumption of an one-dimensional model.

Influence of buoyancy on floating-zone convection of small bond number

Gravity may influence the velocity and temperature distributions, bouyancy may induce Rayleigh instability and the instability may be excited due to the change of free surface shape associating with gravity in the thermocapillary convection. These effects have been studied in the present paper. The results show that gravity may have an important effect in thermocapillary oscillatory convection even for the cases of small Bond number experiments either on the ground or in space.

Effect of phase-transformation on mechanical-behavior of dual-phase steel plate

The mechanical behavior of dual phase steel plates is affected by internal stresses created during martensite transformation. Analytical modelling of this effect is made by considering a unit cell made of martensite inclusion in a ferrite matrix. A large strain finite element analysis is then performed to obtain the plane stress deformation state. Displayed numerically are the development of the plastic zone and distribution of local state of stress and strain. Studied also are the shape configuration of the martensite (hard-phase) that influences the interfacial condition as related to stress transmission and damage. Internal stresses are found to enhance the global flow stress after yield initiation in the ferrite matrix. Good agreement is obtained between the analytical results and experimental observations.

Influence of low-gravity level on crystal-growth in floating-zone

The influence of low gravity level on crystal growth in the floating zone, which involves thermocapillary convection, phase change convection, thermal and solutal diffusion, is investigated numerically by a finite element method for the silicon crystal growth process. The velocity, temperature, concentration fields and phase change interfaces depending on heating temperature and growth rates are analyzed. The influence of low gravity level on the concentration is studied especially. The results show that the non-uniformities of concentration are about 10(-3) for growth rate nu(p) = 5.12 x 10(-8) m/s, 10(-2) for nu(p) = 5.12 x 10(-7) m/s and relatively larger for larger growth rate in the gravity level g = 0-9.8 m/s2. The thermocapillary effect is strong in comparison with the Bridgman system, and the level of low gravity is relatively insensitive for lower growth rates.

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.

Crystal-growth in floating zone with phase-change and thermosolutal convections

Floating zone crystal growth in microgravity environment is investigated numerically by a finite element method for semiconductor growth processing, which involves thermocapillary convection, phase change convection, thermal diffusion and solutal diffusion. The configurations of phase change interfaces and distributions of velocity, temperature and concentration fields are analyzed for typical conditions of pulling rates and segregation coefficients. The influence of phase change convection on the distribution of concentration is studied in detail. The results show that the thermocapillary convection plays an important role in mixing up the melt with dopant. The deformations of phase change interfaces by thermal convection-diffusion and pulling rods make larger variation of concentration field in comparison with the case of plane interfaces.

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.

Complex stress functions and plastic zone sizes for notch cracks subjected to various loading conditions

In this paper, the conformal mapping method is used to solve the plane problem of an infinite plate containing a central lip-shaped notch subjected to biaxial loading at a remote boundary or a surface uniform pressure on the notch. The stress intensity factors KI and KII are obtained by the derived complex stress functions. The simple analytical expressions can be applied to the situation of cracks originating from a circular or an elliptical notch. The plastic zone sizes for such notch cracks are subsequently evaluated in light of the Dugdale strip yield concept. The results are consistent with available numerical data.

The effect of variable currents on internal solitary waves

The effect of variable currents on internal solitary waves is described within the context of a variable coefficient Korteweg-de Vries (KdV) equation, and the approximate slowly varying, solitary-wave solution of this equation. The general theory which leads to the variable coefficient KdV equation is described; a derivation for the special case when the solitary wave and the current are aligned in the same direction is given in the Appendix. Using further simplifications and approximations, a number of analytical expressions are obtained for the variation in the solitary wave amplitude resulting from variable shear in the basic current or from when the basic current is a depth-independent flow which is a simple representation of a geostrophic current, tidal flow or inertial wave.