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.

Transition to Chaos in the Floating Half Zone Convection

The transition process from steady convection to chaos is experimentally studied in thermocapillary convections of floating half zone. The onset of temperature oscillations in the liquid bridge of floating half zone and further transitions of the temporal convective behaviour are detected by measuring the temperature in the liquid bridge. The fast Fourier transform reveals the frequency and amplitude characteristics of the flow transition. The experimental results indicate the existence of a sequence of period-doubling bifurcations that culminate in chaos. The measured Feigenbaum numbers are delta(2) = 4.69 and delta(4) = 4.6, which are comparable with the theoretical asymptotic value delta = 4.669.

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.

A new model of thermocapillary convection in floating half zone

A new model of thermocapillary convection in floating half zone was suggested in the present paper. The liquid bridge floats between two co-axis rods, the lower rod consists of metal with constant temperature and the upper rod consists of thermal insulating materials, where the normal gradient of temperature is nearly zero. In this case, the new model is relatively closer to simulate a half part of floating full zone in microgravity environment in comparison with the usual model of floating half zone. Basic features of the new model were studied by both numerical simulation and experiments, and the comparisons with the usual model were also discussed.

Weak Zone Related Seismic Cycles in Progressive Failure Leading to Collapse in Brittle Crust

Until quite recently our understanding of the basic mechanical process responsible for earthquakes and faulting was not well known. It can be argued that this was partly a consequence of the complex nature of fracture in crust and in part because evidence of brittle phenomena in the natural laboratory of the earth is often obliterated or obscured by other geological processes. While it is well understood that the spatial and temporal complexity of earthquakes and the fault structures emerge from geometrical and material built-in heterogeneities, one important open question is how the shearing becomes localized into a band of intense fractures. Here the authors address these questions through a numerical approach of a tectonic plate by considering rockmass heterogeneity both in microscopic scale and in mesoscopic scale. Numerical simulations of the progressive failure leading to collapse under long-range slow driving forces in the far-field show earthquake-like rupture behavior. $En Echelon$ crack-arrays are reproduced in the numerical simulation. It is demonstrated that the underlying fracturing induced acoustic emissions (or seismic events) display self-organized criticality------from disorder to order. The seismic cycles and the geometric structures of the fracture faces, which are found greatly depending on the material heterogeneity (especially on the macroscopic scale), agree with that observed experimentally in real brittle materials. It is concluded that in order to predict a main shock, one must have extremely detailed knowledge on very minor features of the earth's crust far from the place where the earthquake originated. If correct, the model proposed here seemingly provides an explanation as to why earthquakes to date are not predicted so successfully. The reason is not that the authors do not understand earthquake mechanisms very well but that they still know little about our earth's crust.

Instability from steady and axisymmetric to steady and asymmetric floating half zone convection in a fat liquid bridge of larger Prandtl number

The linear instability analysis of the present paper shows that the thermocapillary convection in a half floating zone of larger Prandtl number has a steady instability mode w(i) = 0 and m = 1 for a fat liquid bridge V = 1.2 with small geometrical aspect ratio A = 0.6. This conclusion is different from the usual idea of hydrothermal instability, and implies that the instability of the system may excite a steady and axial asymmetric state before the onset of oscillation in the ease of large Prandtl number.

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.

Influence of liquid bridge volume on instability of floating half zone convection

Thermocapillary instabilities on floating half zone convection in microgravity environment were investigated by linear instability analysis method. The critical Marangoni numbers were obtained and compared with the experimental ones. The influences of the liquid bridge volume and the aspect ratio on the critical Marangoni number were analyzed. It is found that the liquid bridge volume and the aspect ratio have great influence on the critical Marangoni number. There was a gap region where the oscillatory convection will not be observed in present analyses and in experiments in the curve of the critical Marangoni number vs the liquid bridge volume for the case of large Prandtl number and small aspect ratio.

Effects on Dense-phase Zone Temperature of Fluidized Bed with Uneven Air Distribution

由于采用非均匀布风,内旋流流化床的移动区空气量不足,导致燃烧不充分,温度较低。当移动区未流化时,密相区内存在较明显的温度不均匀性。随着移动区流速的提高,温度差迅速减小。当移动区流速超过2.0#mu#m后,密相区温度基本均匀一致。流动区流速对密相区温度均匀有一定的影响,流速越高,温度越均匀。

Influence of liquid bridge volume on the onset of oscillation in floating-zone convection III. Three-dimensional model

An unsteady and three-dimensional model of the floating-half-zone convection on the ground is studied by the direct numerical simulation for the medium of 10 cSt silicon oil, and the influence of the liquid bridge volume on the critical applied temperature difference is especially discussed. The marginal curves for the onset of oscillation are separated into two branches related, respectively, to the slender liquid bridge and the fat liquid bridge. The oscillatory features of the floating-half-zone convection are also discussed.

Influence of Liquid Bridge Volume on the Floating Zone Convection

The liquid bridge volume is a critical geometrical parameter in addition to the aspect ratio for onset of oscillation in the floating zone convection. The oscillatory features are generally divided into two characteristic regions: slender liquid bridge region and fat liquid bridge region. The oscillatory modes in two regions are discussed in the present paper.

Crack propagation in the power-law nonlinear viscoelastic material

An analysis on crack creep propagation problem of power-law nonlinear viscoelastic materials is presented. The creep incompressilility assumption is used. To simulate fracture behavior of craze region, it is assumed that in the fracture process zone near the crack tip, the cohesive stress sigma(f) acts upon the crack surfaces and resists crack opening. Through a perturbation method, i. e., by superposing the Mode-I applied force onto a referential uniform stress state, which has a trivial solution and gives no effect on the solution of the original problem, the nonlinear viscoelastic problem is reduced to linear problem. For weak nonlinear materials, for which the power-law index n similar or equal to 1, the expressions of stress and crack surface displacement are derived. Then, the fracture process zone local energy criterion is proposed and based on which the formulas of cracking incubation time t

Statistical analysis of synthetic earthquake catalogs generated by models with various levels of fault zone disorder

The stress release model, a stochastic version of the elastic rebound theory, is applied to the large events from four synthetic earthquake catalogs generated by models with various levels of disorder in distribution of fault zone strength (Ben-Zion, 1996) They include models with uniform properties (U), a Parkfield-type asperity (A), fractal brittle properties (F), and multi-size-scale heterogeneities (M). The results show that the degree of regularity or predictability in the assumed fault properties, based on both the Akaike information criterion and simulations, follows the order U, F, A, and M, which is in good agreement with that obtained by pattern recognition techniques applied to the full set of synthetic data. Data simulated from the best fitting stress release models reproduce, both visually and in distributional terms, the main features of the original catalogs. The differences in character and the quality of prediction between the four cases are shown to be dependent on two main aspects: the parameter controlling the sensitivity to departures from the mean stress level and the frequency-magnitude distribution, which differs substantially between the four cases. In particular, it is shown that the predictability of the data is strongly affected by the form of frequency-magnitude distribution, being greatly reduced if a pure Gutenburg-Richter form is assumed to hold out to high magnitudes.

Investigation on mechanical properties and size effect of nanocrystalline twin copper

The stress-strain relations of nanocrystalline twin copper with variously sized grains and twins are studied by using FEM simulations based on the conventional theory of mechanism-based strain gradient plasticity (CMSG). A model of twin lamellae strengthening zone is proposed and a cohesive interface model is used to simulate grain-boundary sliding and separation. Effects of material parameters on stress-strain curves of polycrystalline twin copper are studied in detail. Furthermore, the effects of both twin lamellar spacing and twin lamellar distribution on the stress-strain relations are investigated under tension loading. The numerical simulations show that both the strain gradient effect and the material hardening increase with decreasing the grain size and twin lamellar spacing. The distribution of twin lamellae has a significant influence on the overall mechanical properties, and the effect is reduced as both the grain size and twin lamellar spacing decrease. Finally, the FEM prediction results are compared with the experimental data.