Numerical Study on Flow Field and Temperature Distribution in Growth Process of 200 mm Czochralski Silicon Crystals

The melt flow and temperature distribution in a 200 mm silicon Czochralski furnace with a cusp magnetic field was modeled and simulated by using a finite-volume based FLUTRAPP ( Fluid Flow and Transport Phenomena Program) code. The melt flow in the crucible was focused, which is a result of the competition of buoyancy, the centrifugal forces caused by the rotations of the crucible and crystal, the thermocapillary force on the free surfaces and the Lorentz force induced by the cusp magnetic field. The zonal method for radiative heat transfer was used in the growth chamber, which was confined by the crystal surface, melt surface, crucible, heat shield, and pull chamber. It was found that the cusp magnetic field could strength the dominant counter-rotating swirling flow cell in the crucible and reduce the flow oscillation and the pulling-rate fluctuation. The fluctuation of dopant and oxygen concentration in the growing crystal could thus be smoothed.

Ocean currents-induced pipeline lateral stability on sandy seabed

Unlike previous mechanical actuator loading methods, in this study, a hydrodynamic loading method was employed in a flow flume for simulating ocean currents induced submarine pipeline stability on a sandy seabed. It has been observed that, in the process of pipeline losing lateral stability in currents, there usually exist three characteristic times: (1) onset of sand scour; (2) slight lateral displacement of pipeline; and (3) breakout of pipeline. An empirical linear relationship is established between the dimensionless submerged weight of pipeline and Froude number for describing pipeline lateral stability in currents, in which the current-pipe-soil coupling effects are reflected. Scale effects are examined with the method of "modeling of models," and the sand particle size effects on pipeline stability are also discussed. Moreover, the pipeline stability in currents is compared with that in waves, which indicates that the pipeline laid directly upon the sandy seabed is more laterally stable in currents than in waves.

Centrifuge modeling of suction bucket foundations for platforms under ice-sheet-induced cyclic lateral loadings

This paper presents the results of a series of centrifuge model tests performed to study the behavior of suction bucket foundations for a tension leg platform in the Bohai Bay, China. The target lateral loadings were from ice-sheet-induced structural vibrations at a frequency of 0.8-1.0 Hz. The results indicate that excess pore water pressures reach the highest values within a depth of 1.0-1.5 in below the mud line. The pore pressures and the induced settlement and lateral displacement increase with the amplitude of the cyclic loading. Two failure modes were observed: liquefaction in early excitations and settlement-induced problems after long-term excitations. (c) 2006 Elsevier Ltd. All rights reserved.

Experimental investigation on bubble coalescence under nonuniform temperature distribution in reduced gravity

Results on bubble coalescences from the space experiment of thermocapillary bubble migration conducted on board the Chinese 22nd recoverable satellite are presented in this paper. Some coalescences of large spherical bubbles under microgravity are observed through bubbles staying at the upper side of the test cell. The data of bubble coalescence time are recorded and compared with theoretical predictions, which is based on a theory to describe the tendency of coalescence connected to chemical potential difference. It is implied that the theory is applicable for the experimental data of bubble coalescence. Moreover, the angle between the line of two bubble centers and temperature gradient falled mostly in the range 20 degrees-40 degrees. (C) 2007 Elsevier Inc. All rights reserved.

Self-consistent kinetic modeling of electron distribution function in a low-pressure inductively coupled plasma

Based upon the spatially inhomogeneous Boltzmann equation in two-term approximation coupled with electromagnetic and fluid model analysis for the recently developed inductively coupled plasma sources, a self-consistent electron kinetic model is developed. The electron distribution function, spatial distributions of the electron density and ionization rate are calculated and discussed.

Concentration distribution in crystallization from solution under microgravity

Concentration distribution in crystallization from solution under microgravity is numerically studied. A quasi-steady state growth and dissolution in a 2D rectangular enclosure filled with sodium chlorate (NaClO3) aqueous solution, in which one wall is the growth surface of the crystal and the opposite one is the dissolution surface, is considered. The solute transport process at the growth surface is described by the diffusion-reaction theory with finite interface kinetics coefficient. The results show that the concentration at the growth surface is supersaturated and the supersaturation distribution is of non-uniformity, i.e. the supersaturation in a region facing an incoming flow is high. On the other hand, the non-uniformity of supersaturation at the growth surface is closely related to the gravity level even under microgravity, it exponentially increases as the thermal Rayleigh number on behalf of the gravity level rises.

The effects of coil current distribution in a cylindrical electron-cyclotron-resonance reactor

Using a 2-D hybrid model, the authors have found that external currents play an important role in the plasma parameters in the reactor. The plasma density, temperature and electrostatic potential would be significantly influenced by the applied external currents.

Stress-distribution at the rigid circular-arc inclusion end

The elastic plane problem of a rigid co-circular arc inclusion under arbitrary loads is dealt with. Applying Schwarz's reflection principle integrated with the analysis of the singularity of complex stress functions, the general solution of the problem is found and several closed-form solutions to some problems of practical importance are given. Finally, the stress distribution at the arc inclusion end is examined and a comparison is made with that of the rigid line inclusion end to show the effect of curvature.

The strength distribution of brittle materials with a high-concentration of cavities

The maximum stress concentration factor in brittle materials with a high concentration of cavities is obtained. The interaction between the nearest cavities, in addition to the far field interactions, is taken into account to evaluate the strength distribution based on the statistical analysis of the nearest distance distribution. Through this investigation, it is found that the interaction between the nearest neighbors is much more important than the far field interactions, and one has to consider it in calculating the strength of brittle materials even if the volume fraction of cavities it contains is small. The other important conclusion is that the maximum stress concentration factor has a wide scattered distribution.

Distribution, stability, bifurcations and catastrophe of steady rotation of a symmetrical heavy gyroscope with viscous-liquid-filled cavity

The number, the angles of orientation and the stability in Rumyantsev Movchan's sense of oblique steady rotations of a symmetric heavy gyroscope with a cavity completely filled with a uniform viscous liquid, possessing a fixed point 0 on its symmetric axis. are given for various values of the parameters. By taking the square of the upright component of the angular momentum M2 as a control parameter, three types of bifurcation diagrams of the steady rotations, two types of jumps and two kinds of local catastrophes, one being the symmetric reduced cusp type and the other being of the symmetric reduced butterfly type, are obtained. By taking account of the M2-damping owing to the moment of unavoidable faint friction, two different modes for the gyroscope, initially in a stable quasi-steady upright rotation with a nutation angle theta(s) equal to zero, to topple over are found.

Stress-distribution around a rigid line in dissimilar media

The elastic plane problem of a rigid line inclusion between two dissimilar media was considered. By solving the Riemann-Hilbert problem, the closed-form solution was obtained and the stress distribution around the rigid line was investigated. It was found that the modulus of the singular behavior of the stress remains proportional to the inverse square root of the distance from the rigid line end, but the stresses possess a pronounced oscillatory character as in the case of an interfacial crack tip.

Vertical sediment distribution

So far, various calculation models for the vertical distribution of suspended sediment concentration have been produced by several investigators from different theories. The limitations of all these models imply that it is possible to find a more reasonable model, for which each previous model can be included as special case. The formulation of a reasonable general model is the purpose of this paper.

Kinetic theory for particle concentration distribution in two phase flow

The results of experiments in open channels and closed pipelines show two kinds of patterns for the vertical distribution of particle concentration (i.e., pattern I and pattern II). The former shows a pattern of maximum concentration at some location above the bottom and the downward decay of the concentration below the location. The latter always shows an increase of the particle concentration downward over the whole vertical, with the maximum value at the bottom. Many investigations were made on the pattern II, but few were made on pattern I. In this paper, a particle velocity distribution function is first obtained in the equilibrium state or in dilute steady state for the particle in two-phase flows, then a theoretical model for the particle concentration distribution is derived from the kinetic theory. More attention is paid to the predictions of the concentration distribution of pattern I and comparisons of the present model are made with the data measured by means of laser doppler anemometry (LDA). Very good agreements are obtained between the measured and calculated results.

The thermal and mechanical structure of a two-dimensional plume in the earths mantle

On the condition that the distribution of velocity and temperature at the mid-plane of a mantle plume has been obtained (pages 213–218, this issue), the problem of determining the lateral structure of the plume at a given depth is reduced to solving an eigenvalue problem of a set of ordinary differential equations with five unknown functions, with an eigenvalue being related to the thermal thickness of the plume at this depth. The lateral profiles of upward velocity, temperature and viscosity in the plume and the thickness of the plume at various depths are calculated for two sets of Newtonian rheological parameters. The calculations show that the precondition for the existence of the plume, δT/L 1 (L = the height of the plume, δT = lateral distance from the mid-plane), can be satisfied, except for the starting region of the plume or near the base of the lithosphere. At the lateral distance, δT, the upward velocity decreases to 0.1 – 50% of its maximum value at different depths. It is believed that this model may provide an approach for a quantitative description of the detailed structure of a mantle plume.

Transient Temperature Distribution in a Sheet Metal by Low-Energy Laser Scanning

Low-energy laser-heating techniques are widely used in engineering applications such as, thinfilm deposition, surface treatment, metal forming and micro-structural pattern formation. In this paper,under the conditions of ignoring the thermo-mechanical coupling, a numerical simulation on the spatialand temporal temperature distribution in a sheet metal produced by the laser beam scanning in virtue of thefinite element method is presented. Both the three-dimensional transient temperature field and thetemperature evolution as a function of heat penetrating depth in the metal sheet are calculated. Thetemperature dependence of material properties was taken into account. It was shown that, after taking thetemperature dependence of the material absorbance effect into consideration, the temperature change ratealong the scanning direction and the temperature maximum were both increased.