M. Kassemi¹, Y. Wang², S. Barsi^1,3, B.T.F. Chung²

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.1, pp. 27-46, 2006, DOI:10.3970/fdmp.2006.002.027

Abstract Microgravity experiments, especially materials processing experiments, have often been hampered by presence of unwanted bubbles. In this work, the effect of thermocapillary convection generated by a bubble on the Bridgman growth of a dilute binary alloy in microgravity is investigated numerically. The model is based on the quasi-steady Navier-Stokes equations for the fluid flow in the melt coupled with the conservation equations for transport of energy and species in the growth ampoule. Numerical results indicate three different growth regimes based on the distance between the bubble and the growth interface: a diffusion dominated regime that is separated from a well-mixed… More >

M. Sekhon¹, N. Armour¹, S. Dost^1,2

FDMP-Fluid Dynamics & Materials Processing, Vol.9, No.4, pp. 331-351, 2013, DOI:10.3970/fdmp.2013.009.331

Abstract Liquid Phase Diffusion (LPD) growth of Si_xGe_1-x single crystals has been numerically simulated under zero gravity. The objective was to examine growth rate and silicon concentration distribution in the LPD grown crystals under diffusion dominated mass transport prior to the planned LPD space experiments on the International Space Station (ISS). Since we are interested in predicting growth rate and crystal composition, the gravitational fluctuation of the ISS (g-jitter) was neglected and the gravity level was taken as zero for simplicity.
A fixed grid approach has been utilized for the simulation. An integrated top-level solver was developed in OpenFOAM to carry… More >

V. Haslavsky, E. Miroshnichenko, E. Kit, A. Yu. Gelfgat

FDMP-Fluid Dynamics & Materials Processing, Vol.9, No.3, pp. 209-234, 2013, DOI:10.3970/fdmp.2013.009.209

Abstract Experimental and numerical observations of oscillatory instability of melt flow in a Czochralski model are compared, and a disagreement observed at small crystal dummy rotation rates is addressed. To exclude uncertainties connected with flow along the free surface, the latter is covered by a no-slip thermally insulating ring. Experiments reveal an appearance of oscillations at temperature differences smaller than the numerically predicted critical ones. At the same time, a steep increase of the oscillations amplitude is observed just beyond the computed threshold values. By increasing the dummy rotation gradually, we are able to qualitatively confirm the numerically predicted flow destabilization.… More >

M. M. Shemirani¹, M. Z. Saghir²

FDMP-Fluid Dynamics & Materials Processing, Vol.9, No.1, pp. 11-21, 2013, DOI:10.3970/fdmp.2013.009.011

Abstract Producing homogeneous single bulk crystals requires a good understanding of the thermo-solutal behavior in the solvent region. This study explores simulation of the growth of large diameter single bulk crystals of silicon and germanium alloy from its melt utilizing Bridgman method. Both thermal and solutal diffusion of silicon and germanium in the molten SiGe alloy are of interest. It was observed that the diffusion dominates the transport phenomenon in the solvent region especially in the first 25 mm of the model due to having a Pe_T <<1. It was also found that the control of both radial and axial applied… More >

Akira Hirata¹

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.3, pp. 203-230, 2007, DOI:10.3970/fdmp.2007.003.203

Abstract This article is a summary of author's typical research works (over the last four decades) on interphase transport phenomena in the presence of interfacial fluid motion and surface tension gradients on liquid-fluid interfaces, and related applications to single crystal growth and microgravity sciences. A unified theory for momentum, heat and mass transfer on liquid-fluid and solid-fluid interfaces is proposed, which takes into account interface mobility. It is shown that interface contamination and turbulence can be well explained, respectively, by suppression and enhancement of the interfacial velocity induced by surface tension gradients. Transport phenomena on solid spheres, liquid drops and gas… More >

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 effective and allows to perform… More >

N.I. Wakayama¹, D.C. Yin², J.W. Qi³

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.2, pp. 153-170, 2005, DOI:10.3970/fdmp.2005.001.153

Abstract The production of crystals of adequate size and high quality is the "bottleneck'' for three-dimensional structure analysis of protein crystals. In this work, in order to shed additional light on the (still controversial) beneficial effect of microgravity on crystal growth, we focus on recent advanced experimental and theoretical research about the effects of buoyancy-driven convection on protein crystallization. In the light of the numerical studies the following major outcomes can be highlighted: (1) when the crystal size exceeds several dozens of µm, buoyancy-driven convection dominates solute transport near the growing crystal and the crystal growth rate becomes larger than that… More >

Cosmina S. Hogea¹, Bruce T. Murray¹, James A. Sethian^2,3

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.2, pp. 109-130, 2005, DOI:10.3970/fdmp.2005.001.109

Abstract A computational framework for simulating growth and transport in biological materials based on continuum models is proposed. The advantages of the finite difference methodology employed are generality and relative simplicity of implementation. The Cartesian mesh/level set method developed here provides a computational tool for the investigation of a host of transport-based tissue/tumor growth models, that are posed as free or moving boundary problems and may exhibit complicated boundary evolution including topological changes. The methodology is tested here on a widely studied "incompressible flow" type tumor growth model with a numerical implementation in two dimensions; comparisons with results obtained from a… More >

T. Tsukada¹, M. Kobayashi², C. J. Jing³, N. Imaishi⁴

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.1, pp. 45-62, 2005, DOI:10.3970/fdmp.2005.001.045

Abstract In this paper, our recent numerical studies on the Czochralski (CZ) crystal growth of oxide are surveyed. In the first part of the analysis, a "global" heat transfer model for an inductively heated CZ furnace is introduced and depicted in detail. It is emphasized that accounting for the internal radiation within the crystal and/or melt is of crucial importance since they are often semitransparent to infrared radiation. Results coming from such a "global" approach suggest that the melt/crystal interface shape is strongly affected by the optical properties of the crystal, of the melt and by the melt convection. The second… More >

C. W. Lan¹, B. C. Yeh

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.1, pp. 33-44, 2005, DOI:10.3970/fdmp.2005.001.033

Abstract The suppression of unstable Marangoni convection in floating-zone crystal growth by magnetic fields has enjoyed over recent years a widespread use as a reliable and useful strategy. A transversal direction of the field is particularly efficient, but asymmetric zone shapes and thus segregation are induced. Counter-rotation of the feed and of the crystal rods is a common way to improve dopant homogeneity. However, its effects under magnetic fields are complex and have not yet been studied in detail. In the present analysis, three-dimensional (3D) simulations based on a finite-volume/multigrid method are used to illustrate the effects of rotation on the… More >