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Computation of Convection and
Alloy Solidi cation with the
Software Package CrysVUn
Der Technischen Fakultat der
Universitat Erlangen-Nurn berg
zur Erlangung des Grades
DOKTOR-INGENIEUR
vorgelegt von
Marc Hans Ernst Hainke
Erlangen 2004Als Dissertation genehmigt von
der Technischen Fakultat der
Universitat Erlangen-Nurn berg
Tag der Einreichung: 23. Januar 2004
Tag der Promotion: 08. Juli 2004
Dekan: Prof. Dr. A. Winnacker
Berichterstatter: Prof. Dr. G. Mul ler
Prof. Dr. L. RatkeTo my FamilyManyalloysaresolidifyingwithadendriticcolumnarstructure. The
region, where solid and liquid phase are co-existent within a certain
temperature interval, is usually called the mushy zone. The resulting
microstructure is a consequence of transport processes, capillarity ef-
fects and thermodynamic constraints. Whereas the theory of purely
diusivesolidi cationisnowadayswelldeveloped,thee ectsofconvec-
tive heat and mass transport experience enhanced attention. Thereby,
phenomena on di erent length scales are in uenced by convection. On
the scale of a single dendrite, convection may lead to a changed mor-
phology of the dendrites or may even lead to fragmentation. On the
scale of the whole sample, convection is mainly responsible for the
e ect of macrosegregation.
Time dependent magnetic elds are considered as a promising op-
tionforsystematicinvestigationsofthee ectsof uid owduringalloy
solidi cation. It is well known, that the use of rotating magnetic elds
is an e cient tool for controlling the melt ow and thus can a ect
the temperature and species distribution. This eld con guration is
also industrially commonly in use to in uence the solidi cation pro-
cess, mostly to create a nely dispersed equiaxed growth morphology.
Nevertheless,thenumberofpublicationswithnumericalinvestigations
on the resulting macrosegregation during alloy solidi cation is very
limited. This is mostly due to the high computational costs of the
corresponding calculations.
In this work, the software package CrysVUn was extended with suit-
able models for the global simulation of directional solidi cation of
binary alloys. The methodology of the model implementation and its
application is subject of this work.
Basis for the tasks in this work is an accurate computation of the
oweld. Forthisreason, anovelapproachbasedonthenitevolume
technique on unstructured grids was realized. The velocity compo-
nents are interpolated with quadratic Ansatz functions, scalar values
are interpolated linearly on a triangular element. The performance of
this approach is compared to a commonly used colocated arrangement
with linear Ansatz functions for all physical quantities for a number
of representative test cases. It is observed, that the quadratic scheme
may lead to higher accuracy at smaller computation times, dependent
on the problem under consideration.

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