Jacek Narski^1,2, Marco Picasso¹

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 49-64, 2007, DOI:10.3970/fdmp.2007.003.049

Abstract An adaptive phase field model for the solidification of binary alloys in three space dimensions is presented. The fluid flow in the liquid due to different liquid/solid densities is taken into account. The unknowns are the phase field, the alloy concentration and the velocity/pressure in the liquid. Continuous, piecewise linear finite elements are used for the space discretization, a semi-implicit scheme is used for time discretization. An adaptive method allows the number of degrees of freedom to be reduced, the mesh tetrahedrons having high aspect ratio whenever needed. Numerical results show that our method is More >

Frédéric Gibou¹, Chohong Min², Hector D. Ceniceros³

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 37-48, 2007, DOI:10.3970/fdmp.2007.003.037

Abstract We describe two finite difference schemes for simulating incompressible flows on nonuniform meshes using quadtree/octree data structures. The first one uses a cell-centered Poisson solver that yields first-order accurate solutions, while producing symmetric linear systems. The second uses a node-based Poisson solver that produces second-order accurate solutions and second-order accurate gradients, while producing nonsymmetric linear systems as the basis for a second-order accurate Navier-Stokes solver. The grids considered can be non-graded, i.e. the difference of level between two adjacent cells can be arbitrary. In both cases semi-Lagrangian methods are used to update the intermediate fluid More >

Mark Sussman¹, Mitsuhiro Ohta²

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 21-36, 2007, DOI:10.3970/fdmp.2007.003.021

Abstract In this paper, we describe new techniques for numerically approximating two-phase flows. Specifically, we present new techniques for treating the viscosity and surface tension terms that appear in the Navier-Stokes equations for incompressible two-phase flow. Our resulting numerical method has the property that results computed using our two-phase algorithm approach the corresponding "one-phase'' algorithm in the limit of zero gas density/viscosity; i.e. the two-phase results approach the one-phase free-boundary results in the limit that the gas is assumed to become a uniform pressure void. By grid convergence checks and comparison with previous experimental data, we More >

J.S. Lowengrub¹, J-J. Xu², A. Voigt³

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 1-20, 2007, DOI:10.3970/fdmp.2007.003.001

Abstract We introduce and investigate numerically a thermodynamically consistent simple model of a drop or vesicle in which the interfacial surface contains multiple constitutive components (e.g. amphiphilic molecules). The model describes the nonlinear coupling among the flow, drop/vesicle morphology and the evolution of the surface phases. We consider a highly simplified version of the Helfrich model for fluid-like vesicle membranes in which we neglect the effects of bending forces and spontaneous curvature but keep the effects of inhomogeneous surface tension forces. Thus, this model may also describe liquid drops. To solve the highly nonlinear, coupled system More >

E. A. Semma¹, M. El Ganaoui², V. Timchenko³, E. Leonardi³

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.3, pp. 191-202, 2006, DOI:10.3970/fdmp.2006.002.191

Abstract This paper deals with the investigation of thermovibrational convection induced by harmonic oscillations of the temperature boundary conditions related to the hot wall in a Bridgman-like (VB) geometrical configurations. Two different models of the VB configuration are considered (a simplified version referred to as "restricted" model and a more realistic and complete model with phase change allowed). The effects of temperature modulation are considered for both models and with regard to several possible initial (basic) states (stationary and oscillatory). In the restricted fluid cavity, we identify the existence of a critical frequency minimizing the flow More >

T. J. Jaber¹, M. Z. Saghir¹

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.3, pp. 175-190, 2006, DOI:10.3970/fdmp.2006.002.175

Abstract The study deals with three-dimensional numerical simulations of fluid flow and heat transfer under the effect of a rotating magnetic field (RMF) during the growth of Ge_0.98Si_0.02 by the traveling solvent method (TSM). By using a RMF, an attempt is made to suppress buoyancy convection in the Ge_0.98Si_0.02 solution zone in order to get high quality and homogeneity with a flat growth interface. The full steady-state Navier-Stokes equations, as well as the energy, mass transport and continuity equations, are solved numerically using the finite element method. Different magnetic field intensities (B=2, 4, 10, 15 and 22 More >

E. Abhilash¹, M.A. Joseph¹, Prasad Krishna¹

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.3, pp. 211-220, 2006, DOI:10.3970/fdmp.2006.002.211

Abstract Aluminium-Silicon alloys are in high de-mand as an engineering material for automotive,aerospace and other engineering applications. Mechanical properties of Al-Si alloys depend not only on chemical composition but also more importantly on microstructural features such as dendritic alpha-aluminiumphase and eutectic silicon particles. As an additive to Al-Si alloys, sodium improves mechanical properties byforming finer and fewer needles like microstructures.Thus, prediction of the macro and microstructures obtained at the end of the solidification is of great interest for the manufacturer of aluminium alloys. Neuralnetworks are sophisticated nonlinear regression routinesthat, when properly “trained”, allow for the identificationof More >

V.G. Kozlov^1,2, A.A. Ivanova³, P. Evesque¹

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.3, pp. 203-210, 2006, DOI:10.3970/fdmp.2006.002.203

Abstract Sedimentation of granular matter in a vertical channel filled with a viscous liquid and subject to longitudinal translational vibration is studied, starting froma compact suspension. A new vibrational effect is foundexperimentally and described theoretically; it is the formation of blocks (with a relatively high density) of sedimenting granular matter with stable lower and upper horizontal demarcations and a sharp density discontinuity. Owing to this phenomenon the sedimentation velocity of such granular matter is reduced. A new theoreticalmodel based on viscous vibrational particle interactionin the limit of concentrated suspensions is elaborated, assuming particle-particle attraction in direction More >

Koichi Kakimoto, Lijun Liu

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.3, pp. 167-174, 2006, DOI:10.3970/fdmp.2006.002.167

Abstract This paper deals with the investigation of the flow instability of molten silicon in a magnetic field during crystal growth by means of the Czochralski method. The flow exhibits a three-dimensional structure due to a transverse non-axisymmetric pattern of the magnetic field. The melt-crystal interface is found to be nearly two-dimensional. The azimuthal non-uniformity of the temperature field is much weaker on the crystal and crucible sidewalls in the case of high rotation rates of crucible and crystal than in the case of non-rotating crucible and crystal. More >

Y.R. Li¹, L. Peng¹, W.Y. Shi¹, N. Imaishi²

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.3, pp. 153-166, 2006, DOI:10.3970/fdmp.2006.002.153

Abstract The convective instabilities in semiconduc-tor or oxide melts, significantly affect the quality oflarge crystals grown from the melts by the Czochralskimethod. This paper reviewsour recent numerical stud-ies of thermal convection in annular pools of low-Pr sili-con melt and moderate-Pr silicone oil. The mechanismsof the convective instability are discussed and the criticalconditions for the onset of three-dimensional flow are de-termined. The results show that the hydrothermal wave,characterized by curved spokes, is dominant in a shallowthin pool. In a thick pool of the low-Pr silicon melt, thereappears a standing wave type of oscillatory longitudinalrolls, which moves in the azimuthal More >