Thixoforming : Semi-solid Metal Processing

200j 6 Modelling the Flow Behaviour of Semi-solid Metal Alloys
equations in differential form are then integrated over each control volume. Interpolation
profiles are then assumed in order to describe the variation of the concerned
variable between cell centroids. The resulting equation is called the discretized or
discretization equation. In this manner, the discretization equation expresses the
conservation principle for the variable inside the control volume.
The method is used in many computational fluid dynamics packages. The most
compelling feature of the FVM is that the resulting solution satisfies the conservation
of quantities such as mass, momentum, energy and species. This is exactly satisfied
for any control volume and also for the whole computational domain and for any
number of control volumes. Even a coarse grid solution exhibits exact integral
balances. Therefore, FVM is the ideal method for computing discontinuous solutions
arising in compressible flows. Since finite volume methods are conservative, they
automatically satisfy the jump conditions and hence give physically correct weak
solutions. FVM is also preferred while solving partial differential equations containing
discontinuous coefficients.
In the finite element method approach, the actual structure is assumed to be divided
into a set of unstructured discrete subregions or elements which are interconnected
only at a finite number of nodal points. The distinguishing feature of the finite
element method is that the equations are multiplied by a weight function before they
are integrated over the whole domain. The properties of the complete structure are
found by evaluating the properties of the individual finite elements and superposing
them appropriately. Due to the ability to model and solve large complicated structures
and to deal with arbitrary geometries, the method is widely used in computational
science.
6.2.3
Software Packages Used
Within this work, the well-known commercial software packages FLUENT, Flow-3D
and MAGMASOFT were used, in addition to the home-made numerical solver
PETERA and LARSTRAN/SHAPE.
. FLUENT is a CFD software package to simulate fluid flow problems. It uses the
finite-volume method to solve the governing equations for a fluid. It provides the
capability to use different physical models such as incompressible or compressible,
inviscid or viscous, laminar or turbulent and so on. To determine the phase
boundary in multiphase flows, and in particular free surface (or wave) flows, the
so-called volume of fluid (VOF) model is used. Motion of fluid interfaces based on
the solution of a conservative transport equation for the fractional volume of fluid
in a grid cell is the method employed in FLUENT.
. Flow-3D is a general-purpose CFD program with many capabilities, claiming to be
particularly good for free surface flows. Finite-difference or finite-volume approximations
to the equations of motion are used to compute the spatial and temporal
evolution of the flow variables. In FLOW-3D, free surfaces are modelled with the
VOF technique, incorporating some improvements beyond the original VOF