R. Prud’homme¹, M. El Ganaoui²

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.2, pp. 161-172, 2007, DOI:10.3970/fdmp.2007.003.161

Abstract Some problems related to solid/liquid phase change are presented. Attention is focused on interface modeling for numerical analysis and one-dimensional directional growing and melting. Microgravity relevance of some situations is emphasized. It is shown, in particular, that in some circumstances melting is not the simple reversal of crystal growth due to some (still poorly known) phenomena (nucleation and growth of liquid droplets in the bulk, solid and liquid dendrites due to a morphological instability of the phase boundary). Relevant mathematical models are discussed and described (to a certain extent) for analysis and/or characterization of these More >

Y. Kamotani¹, S. Matsumoto², S. Yoda²

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.2, pp. 147-160, 2007, DOI:10.3970/fdmp.2007.003.147

Abstract A Marangoni Convection Modeling Research group was formed in Japan in order to investigate oscillatory thermocapillary flow systematically over a wide range of Prandtl number (Pr). The research by the group represents the current status of the subject. The present article reports the work done by the group members. The work is divided into three Pr ranges (low, medium and high) because the cause of oscillations is different in each range. For the low-Pr case, the transition to oscillatory flow is preceded by a steady bifurcation to three-dimensional convection. For the first time an experimental More >

H. Tang¹, L.C. Wrobel², Z. Fan²

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.2, pp. 129-146, 2007, DOI:10.3970/fdmp.2007.003.129

Abstract This paper presents an overview of diverse extrusion techniques and, in particular, a focused discussion about the rheoextrusion process for semi-solid casting (a novel casting process for the fabrication of high quality metals). The review reveals a wealth of interesting rheological and microstructural features, illustrating qualitative and quantitative data. The analysis is supported by relevant numerical results and examples. It is shown how numerical studies can lead to significant insights into these processes by providing more detailed information on the fundamental mechanisms of morphology development (during phase change) and profile forming. The die filling and More >

A.K. Plappally¹, M.A.R. Sharif¹, R.C. Bradt²

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.2, pp. 115-128, 2007, DOI:10.3970/fdmp.2007.003.115

Abstract A novel physical chemical filtration process in a tundish for removal of inclusion particles from molten steel is proposed and analyzed. The considered inclusion particles are mainly composed of the minerals alumina (Al2O3 and spinel (MgAl2O4, which have an affinity to adhere (on contact) to an inclusion trap. An industrial tundish is considered and modified with a zigzag channel block insert installed across the molten steel flow so that when the molten steel flows through the zigzag channels, the inclusion particles are driven into contact with the channel surfaces by increased recirculation and turbulence. The More >

Evgeny V. Votyakov¹, Egbert A. Zienicke¹

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.2, pp. 97-114, 2007, DOI:10.3970/fdmp.2007.003.097

Abstract We simulated numerically the laminar flow in the geometry and the magnetic field of the experimental channel used in [Andreev, Kolesnikov, and Thess (2006)]. This provides detailed information about the electric potential distribution for the laminar regime (numerical simulation) and in the turbulent regime as well (experiment). As follows from comparison of simulated and experimental results, the flow under the magnet is determined by the interaction parameter N = Ha² / Re representing the ratio between magnetic force, determined by the Hartmann number Ha, and inertial force, determined by the Reynolds number Re. We compared two variants: (i)(Re,N)=(2000,18.6)… More >

Xiaofeng Yang¹, Ashley J. James^1,2

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 65-96, 2007, DOI:10.3970/fdmp.2007.003.065

Abstract An arbitrary Lagrangian-Eulerian (ALE) method for interfacial flows with insoluble surfactants is presented. The interface is captured using a coupled level set and volume of fluid method, which takes advantage of the strengths of both the level set method and the volume of fluid method. By directly tracking the surfactant mass, the method conserves surfactant mass, and prevents surfactant from diffusing off the interface. Interfacial area is also tracked. To accurately approximate the interfacial area, the fluid interface is reconstructed using piece-wise parabolas. The surfactant concentration, which determines the local surface tension through an equation… 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 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 >