A cellular automaton technique for modelling of a binary dendritic growth with convection

A two-dimensional model for the simulation of a binary dendritic growth with convection has been developed in order to investigate the effects of convection on dendritic morphologies. The model is based on a cellular automaton (CA) technique for the calculation of the evolution of solid/liquid (s/l) interface. The dynamics of the interface controlled by temperature, solute diffusion and Gibbs–Thomson effects, is coupled with the continuum model for energy, solute and momentum transfer with liquid convection. The solid fraction is calculated by a governing equation, instead of some approximate methods such as lever rule method [A. Jacot, M. Rappaz, Acta Mater. 50 (2002) 1909–1926.] or interface velocity method [L. Nastac, Acta Mater. 47 (1999) 4253; L. Beltran-Sanchez, D.M. Stefanescu, Mat. and Mat. Trans. A 26 (2003) 367.]. For the dendritic growth without convection, mesh independency of simulation results is achieved. The simulated steady-state tip velocity are compared with the predicted values of LGK theory [Lipton, M.E. Glicksmanm, W. Kurz, Metall. Trans. 18(A) (1987) 341.] as a function of melt undercooling, which shows good agreement. The growth of dendrite arms in a forced convection has been investigated. It was found that the dendritic growth in the upstream direction was amplified, due to larger solute gradient in the liquid ahead of the s/l interface caused by melt convection. In the isothermal environment, the calculated results under very fine mesh are in good agreement with the Oseen–Ivanstov solution for the concentration-driven growth in a forced flow.     

Non-linear approximations for natural convection in a horizontal annulus

Two different problems are proposed as approximations of the usual system modelling natural convection under the Oberbeck-Boussinesq assumptions. The error is evaluated by means of the norm of its gradient in the Hilbert space. The average Nusselt number is also estimated.     

一类Marangoni对流边界层方程的近似解析解

利用Adomain解析拆分和Padé逼近方法对由Marangoni对流诱发的层流边界层问题进行了研究, 提供了一种求解边界层方程的解析分析方法. 得到了问题的近似解析解并对相应的流动及传热特性进行了探讨. 本文所提出的思想方法可以用于解决其他科学和工程技术问题. 关键词： Marangoni对流 非线性 Adomain拆分法 近似解析解     

激光穿透焊的三维数值模拟

本文对激光穿透焊进行了三维数值模拟，除考虑焊接速度影响外，还研究了Ｍａｒａｎｇｏｎｉ对流对熔池流动与传热的影响。将三维数值模拟结果与相应的二维模拟结果进行了比较，结果表明，Ｍａｒａｎｇｏｎｉ对流对熔池的形成有很大的影响，因此不可忽略。本文还给出了估计激光穿透焊中蒸气孔尺寸与焊接热效率的方法。     

Equation of convective diffusion of a multicomponent mixture in a capillary for an arbitrary velocity field

It is shown that the convective transport in a binary mixture in the presence of vortex convection can be described in terms of Fick’s law with an effective diffusion coefficient independent of the concentration. The form of the effective diffusion coefficient is found for arbitrary convection in the mixture. A generalization of the Stefan-Maxwell diffusion equation is proposed to include an arbitrary rotational mixture velocity field. The characteristics of convective transport are considered with reference to a three-component mixture. A solution of the equation of three-component mixture transport through a long capillary in the presence of convection homogeneous along the capillary axis is presented. It is established that for sharply different component diffusion coefficients a mixture density extremum may appear inside the capillary and then change or disappear depending on the convective flow intensity.     

A fourth‐order compact finite difference scheme for the steady stream function–vorticity formulation of the Navier–Stokes/Boussinesq equations

A fourth‐order compact finite difference scheme on the nine‐point 2D stencil is formulated for solving the steady‐state Navier–Stokes/Boussinesq equations for two‐dimensional, incompressible fluid flow and heat transfer using the stream function–vorticity formulation. The main feature of the new fourth‐order compact scheme is that it allows point‐successive overrelaxation (SOR) or point‐successive underrelaxation iteration for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature. Copyright © 2003 John Wiley & Sons, Ltd.     

Spatially localized states in Marangoni convection in binary mixtures

Two-dimensional Marangoni convection in binary mixtures is studied in periodic domains with large spatial period in the horizontal. For negative Soret coefficients convection may set in via growing oscillations which evolve into standing waves. With increasing amplitude these waves undergo a transition to traveling waves, and then to more complex waveforms. Out of this state emerge stable stationary spatially localized structures embedded in a background of small amplitude standing waves. The relation of these states to the time-independent spatially localized states that characterize the so-called pinning region is investigated by exploring the stability properties of the latter, and the associated instabilities are studied using direct numerical simulation in time.     

Active control and a simple estimation method for the onset of Rayleigh-Bénard convection in temperature-dependent-viscosity liquids

Active feedback control for the onset of Rayleigh-Bénard Convection in temperature-dependent-viscosity liquids is investigated. In this paper, three major problems are addressed: (1) The results of Tang-Bau control are improved by considering the effects of temperature-dependent viscosity; (2) A more efficient two-plate control strategy is presented. A phenomenon of coalescence of the unstable modes is observed as the controller gain is large enough; (3) A simple way to estimate the critical Rayleigh number under the effects of temperature-dependent viscosity is described. Numerical results show that the effects of temperature-dependent viscosity on the critical Rayleigh number should be taken into account in some cases and the onset of Rayleigh-Bénard convection can be effectively delayed or advanced by the active feedback control strategies studied here.     

三层同轴液柱内的热毛细对流的近似解析解

1引言在微重力下用浮区法生长高质量、大体积单晶体是一种很有应用前景的方法，但热毛细对流所引起的诸如宏观不均匀性、生长条纹等缺陷严重限制了这一方法的应用。目前，人们试着用液封方法抑制热毛细对流。文献［1～3］分别对两层流体系统内的热毛细对流所作的研究表明：通过液封，被封层内的热毛细对流可以得到显著抑制。本文对圆柱三层流体系统内的热毛细对流进行研究，为热毛细对流规律的揭示以及进一步总结出其控制方法提供了理论数值依据。2控制方程和边界条件考虑长为L的互不溶混的三层轴对称同轴液柱，如图1所示，两端壁保持定温T…     

不同倾角的脉管制冷机内自然对流影响的研究

本文通过对脉管内自然对流的数值模拟，讨论了当脉管冷端处在不同方向时，脉管内的自然对流对脉管制冷机性能的影响．数值模拟结果表明，当冷端在下时获得的制冷温度最低；当热端在下并与重力方向成３０°时制冷温度最高．结论与实验测量结果定性一致．所做的理论分析对实现脉管制冷机的良好运行有指导意义。