Numerical simulation of magnetic field design for damping thermocapillary convection in a floating half-zone

The magnetic fields produced by electrical coils are designed for damping the the thermocapillary convection in a floating half-zone in microgravity. The fields are designed specially to reduce the flow near the free surface and then in the melt zone by adjusting the longitudinal coil positions close to the melt zone. The effects of the designed magnetic fields on reducing the flow velocity and temperature distribution non-uniformity in the melt zone are stronger than those of the case of an uniform longitudinal magnetic field obtained by numerical simulation, particularly at the melt-rod interface. It brings fundamental insights into the heat and mass transfer control at the solidification interface by the magnetic field design for crystal growth by the floating full-zone method.

液层厚度对浮力-热毛细对流面型的影响

将Michelson光学干涉测量系统与图像处理技术相结合,发展形成一种实时诊断热毛细对流和浮力对流流体表面形貌的实验测量系统.采用光学干涉测量方法研究了两端带有温差的矩形池内薄层流体的对流、表面变形、以及表面波的基本问题.应用Fourier变换方法对实验结果进行计算和分析,得到了流体表面变形和表面波的定量的实验结果.实验结果表明了在浮力-热毛细对流的发展过程中,首先出现流体的表面变形,之后在该变形的基础上,叠加了一个表面波的信息,该表面变形和表面波与流体的温度梯度、表面张力、以及浮力有直接的关系;表面波隐藏在表面变形内.

Influence of the thickness ratio of air layer to liquid layer on the onset of Benard-Marangoni convection

An experimental investigation of the onset of Benard-Marangoni convection has been performed in a liquid layer of rectangular configuration. The critical temperature difference was measured via the detections of both temperature field pattern (IR-imaging) on the free surface and fluid convection (PIV) in the liquid layer. The critical temperature difference or the critical Marangoni number was given. The experiments were performed for a fixed depth of air layer and a changeable depth of the liquid layer, and then the influence of the thickness ratio of the air layer to liquid layer on the Marangoni instability was studied.

Thermocapillary Effect in a Thermal Rheological Jet

The process of die swell in polymer jets is an important feature within polymer processing and can be explained through a study of its rheological effects. The existence of a thermocapillary effect, driven by the gradient of its surface tension, should be considered when examining a thermal jet that has a non-uniform temperature distribution on its free surface, as in various polymer processings. Both the rheological effect and thermocapillary effect on die swell can be studied numerically through a finite element method as used on a two-dimensional and unsteady model, in which a Coleman-Noll second-order fluid model is employed. The results show that the expanding angle depends on both the rheological property of the fluid and the pressure at the vessel exit. Although both the thermocapillary and the rheological effects contribute to the cross-section expansion of the fluid jet, the latter is more important in determining the expansion.

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.

Governing Equations and Numerical Solutions of Tension Leg Platform with Finite Amplitude Motion

It is demonstrated that when tension leg platform (TLP) moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP. The tensions of the tethers are also nonlinear functions of the displacement of TLP. Then the displacement, the velocity and the acceleration of TLP should be taken into account when loads are calculated. In addition, equations of motions should be set up on the instantaneous position. A theoretical model for analyzing the nonlinear behavior of a TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e., finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Based on the theoretical model, the comprehensive nonlinear differential equations are deduced. Then the nonlinear dynamic analysis of ISSC TLP in regular waves is performed in the time domain. The degenerative linear solution of the proposed nonlinear model is verified with existing published one. Furthermore, numerical results are presented, which illustrate that nonlinearities exert a significant influence on the dynamic responses of the TLP.

Seismic Responses of a Hemispherical Alluvial Valley to SV Waves: A Three-Dimensional Analytical Approximation

An analytical solution to the three-dimensional scattering and diffraction of plane SV-waves by a saturated hemispherical alluvial valley in elastic half-space is obtained by using Fourier-Bessel series expansion technique. The hemispherical alluvial valley with saturated soil deposits is simulated with Biot's dynamic theory for saturated porous media. The following conclusions based on numerical results can be drawn: (1) there are a significant differences in the seismic response simulation between the previous single-phase models and the present two-phase model; (2) the normalized displacements on the free surface of the alluvial valley depend mainly on the incident wave angles, the dimensionless frequency of the incident SV waves and the porosity of sediments; (3) with the increase of the incident angle, the displacement distributions become more complicated; and the displacements on the free surface of the alluvial valley increase as the porosity of sediments increases.

Mesofracture mechanics: a necessary link

Classical fracture mechanics is based on the premise that small scale features could be averaged to give a larger scale property such that the assumption of material homogeneity would hold. Involvement of the material microstructure, however, necessitates different characteristic lengths for describing different geometric features. Macroscopic parameters could not be freely exchanged with those at the microscopic scale level. Such a practice could cause misinterpretation of test data. Ambiguities arising from the lack of a more precise range of limitations for the definitions of physical parameters are discussed in connection with material length scales. Physical events overlooked between the macroscopic and microscopic scale could be the link that is needed to bridge the gap. The classical models for the creation of free surface for a liquid and solid are oversimplified. They consider only the translational motion of individual atoms. Movements of groups or clusters of molecules deserve attention. Multiscale cracking behavior also requires the distinction of material damage involving at least two different scales in a single simulation. In this connection, special attention should be given to the use of asymptotic solution in contrast to the full field solution when applying fracture criteria. The former may leave out detail features that would have otherwise been included by the latter. Illustrations are provided for predicting the crack initiation sites of piezoceramics. No definite conclusions can be drawn from the atomistic simulation models such as those used in molecular dynamics until the non-equilibrium boundary conditions can be better understood. The specification of strain rates and temperatures should be synchronized as the specimen size is reduced to microns. Many of the results obtained at the atomic scale should be first identified with those at the mesoscale before they are assumed to be connected with macroscopic observations. Hopefully, "mesofracture mechanics" could serve as the link to bring macrofracture mechanics closer to microfracture mechanics.

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.

The Fluid Phenomena In the Crystallization Of the Protein Crystal

This paper reports that an optical diagnostic system consisting of Mach-Zehnder interferometer with a phase shift device and image processor has been used for study of the kinetics of protein crystal growing process. The crystallization process of protein crystal by vapour diffusion is investigated. The interference fringes are observed in real time. The present experiment demonstrates that the diffusion and the sedimentation influence the crystallization of protein crystal which grows in solution, and the concentration capillary convection associated with surface tension occurs at the vicinity of free surface of the protein mother liquor, and directly affects on the outcome of protein crystallization. So far the detailed analysis and the important role of the fluid phenomena in protein crystallization have been discussed a little in both space- and ground-based crystal growth experiments. It is also found that these fluid phenomena affect the outcome of protein crystallization, regular growth, and crystal quality. This may explain the fact that many results of space-based investigation do not show overall improvement.

Coupling Of Evaporation And Thermocapillary Convection In A Liquid Layer With Mass And Heat Exchanging Interface

We propose and analyse a new model of thermocapillary convection with evaporation in a cavity subjected to horizontal temperature gradient, rather than the previously studied model without evaporation. The pure liquid layer with a top free surface in contact with its own vapour is considered in microgravity condition. The computing programme developed for simulating this model integrates the two-dimensional, time-dependent Navier-Stokes equations and energy equation by a second-order accurate projection method. We focus on the coupling of evaporation and thermocapillary convection by investigating the influence of evaporation Biot number and Marangoni number on the interfacial mass and heat transfer. Three different regimes of the coupling mechanisms are found and explained from our numerical results.

Rheological effect on thermocapillary flow of a liquid film jet painted on a moving boundary

In the present paper, a liquid (or melt) film of relatively high temperature ejected from a vessel and painted on the-moving solid film is analyzed by using the second-order fluid model of the non-Newtonian fluid. The thermocapillary flow driven by the temperature gradient on the free surface of a Newtonian liquid film was discussed before. The effect of rheological fluid on thermocapillary flow is considered in the present paper. The analysis is based on the approximations of lubrication theory and perturbation theory. The equation of liquid height and the process of thermal hydrodynamics of the non-Newtonian liquid film are obtained, and the case of weak effect of the rheological fluid is solved in detail.

Rheological flow from a die and painting on a moving solid wall

Die swell is an important, phenomenon. in polymer processing, and is explained usually by rheological properties of the fluid. Because of the nonuniform of temperature distribution on the free surface of the liquid jet, the thermo capillary convection driven by surface tension gradient exists. The rheological fluid flowing out of a die and painting on a moving solid wall is studied by the numerical finite element method of a two-dimensional and unsteady model in the present paper, and both the rheological effect of a non-Newtonian fluid and the thermocapillary effect are considered. The results show that both,effects; will enlarge the cross-section of the fluid jet, and the rheological effect of non-Newtonian fluid dominates the process in general.

The motion of a small bubble in waves

The motion of a single spherical small bubble due to buoyancy in the ideal fluid with waves is investigated theoretically and experimentally in this article. Assuming that the bubble has no effect on the wave field, equations of a bubble motion are obtained and solved. It is found that the nonlinear effect increases with the increase of the bubble radius and the rising time. The rising time and the motion orbit are given by calculations and experiments. When the radius of a bubble is smaller than 0.5mm and the distance from the free surface is greater than the wave height, the results of the present theory are in close agreement with measurements.

On crack path stability in a layered material

Crack paths in an elastic layer on top of a substrate are considered. Crack growth is initiated from an edge crack in the layer. The plane of the initially straight crack forms an angle to the free surface. The load consists of a pair of forces applied at the crack mouth and parallel to the interface. Crack paths are calculated using a boundary element method. Crack growth is assumed to proceed along a path for which the mode II stress intensity factor vanishes. The inclination and the length of the initial crack are varied. The effect of two different substrates on the crack path evolution is demonstrated. A crack path initially leading perpendicularly to the interface is shown to be directionally unstable for a rigid substrate. Irrespective of its initial angle, the crack does not reach the interface, but reaches the free surface if the layer is infinitely long. At finite layer length the crack reaches the upper free surface if the initial crack inclination to the surface is small enough. For an inextendable flexible substrate, on the other hand, the crack reaches the interface if its initial inclination is large enough. For the flexible substrate an unstable path parallel with the sides of an infinitely long layer is identified. The results are compared with experimental results and discussed in view of characterisation of directionally unstable crack paths. The energy release rate for an inclined edge crack is determined analytically.