Numerical Investigation of Horizontal Twin Roll Casting of the Magnesium Alloy AZ31

189 Pages·2014·20.98 MB·English

Numerical Investigation of Horizontal Twin-Roll
Casting of the Magnesium Alloy AZ31
By the Faculty of Mechanical, Process and Energy Engineering
of the Technische Universität Bergakademie Freiberg
approved
Thesis
to attain the academic degree of
Doktor-Ingenieur
(Dr.-Ing.)
submitted by Dipl.-Ing. Anja Miehe
born March 17th 1985 in Haldensleben
Assessor: Prof. Dr.-Ing. habil. U. Groß
Prof. Dr.-Ing. habil. R. Schwarze
Date of the award: Freiberg, July 22th 2014
I
Acknowledgement
TheresearchforthisthesiswascarriedoutduringmytimeattheInstituteofThermalEngineering
at the Technische Universität Bergakademie Freiberg. First and foremost, I would like to express
my sincere gratitude to my advisor, Prof. Dr.-Ing. habil. U. Groß, for giving me the opportunity
to work at his chair and write this thesis. Further, I would like to thank Prof. Dr.-Ing. habil.
R. Schwarze of the Institute of Mechanics and Fluid Dynamics for agreeing to be the second
advisor. I would also like to thank the members of my PhD committee.
IamverygratefultotheEuropeanSocialFund(ESF)fortheirfinancialsupportwithintheyoung
researchers group Micro-crystalline magnesium material for sheet products with high-quality
properties. I thank Prof. Dr.-Ing. Prof. E.h. R. Kawalla and Dr.-Ing. Dipl.-Inform. Dipl.-
Wirt.-Ing. H.-P. Vogt for their permission to use data from the MgF Magnesium Flachprodukte
GmbH Freiberg pilot plant, as well as Dr. Kurz and Dr. Letzig for their permission to use data
from their pilot plant at the Magnesium Innovation Centre MagIC of the Helmholtz-Centre
Geesthacht. The access to the high-performance computing facilities of the University Computer
Centre of the TU Bergakademie Freiberg was greatly appreciated.
Furthermore, I would like to express my particular gratitude to Dr. A. Vakhrushev for his
constant support in OpenFOAM coding, his understanding, and his encouragement. Without
your help, this thesis would look quite different. I want to thank my colleagues, especially Dr.-Ing.
A. Hantsch, Dr.-Ing. R. Wulf, and Dr.-Ing. I. Riehl for their support, encouragement, and
comments, and because their doors were always open. Special thanks go to Andreas for putting
up with me in one office for so long.
Finally, I wish to thank my parents for their support and encouragement throughout my life I am
deeply grateful to you. Also, I want to thank my partner for his patience and understanding.
II
Abstract
The horizontal twin-roll casting (TRC) process is an energy saving and cost-efficient method
for producing near-net-shape sheets of castable metals for light-weight production. In order to
investigate the TRC process numerically, a code is generated in OpenFOAM and the commercial
software STAR-CCM+ is used. Both are validated with the Stefan problem, the gallium melting
test case, and a continuous casting experiment for magnesium AZ31. Different solidification
models are tested that are similar to solution domain definitions and solid-fraction temperature
relations. The comparison with temperature measurements of the MgF GmbH Freiberg pilot
plant and the final microstructure exhibits good correlation. Sensitivity studies are carried
out for thermophysical properties of AZ31 as well as pilot plant parameters. Furthermore,
the rolls are incorporated into the simulation to determine the effect of a location-dependent
heat-transfer coefficient. Finally, the results are compared to a second pilot plant situated at the
Helmholtz-Centre Geesthacht in order to explore differences and similarities.
Zusammenfassung
Das horizontales Gießwalzen ist eine energiesparende und kostengünstige Methode zur Erzeugung
von Flachprodukten, die im Leichtbau verwendet werden. Um dieses Verfahren numerisch
zu untersuchen wurde ein Programmcode in OpenFOAM entwickelt und die kommerzielle
Software STAR-CCM+ verwendet, wobei beide mit dem Stefan Problem, dem Schmelzen von
Gallium und Messdaten des Stranggusses von Magnesium AZ31 validiert wurden. Verschiedene
ErstarrungsmodellewerdenebensogetestetwieVariationendesSimulationsbereichesundFeststoff-
Temperatur-Verläufe. Vergleiche mit Temperaturmessdaten der Pilotanlage MgF GmbH Freiberg
und der finalen Mikrostruktur zeigen gute Übereinstimmungen. Sensitivitätsanalysen werden
durchgeführt, um die Einflüsse von thermophysikalischen Eigenschaften und Anlagenparametern
abzuschätzen. Des Weiteren werden die Walzen in die Simulation mit einbezogen, um den Effekt
eines lokal veränderlichen Wärmeübergangskoeffizienten zu beurteilen. Schließlich werden die
Ergebnisse mit denen einer zweiten Pilotanlage am Helmholtz-Zentrum Geesthacht verglichen.
III
Résumé
Le laminage de coulée continue horizontal possède une faible consommation d’énergie et est bon
marché pour la production des feuilles de métaux coulables utilisés dans la construction légère.
Afin d’examiner ce processus numériquement, un code est généré dans OpenFOAM et le logiciel
commercial STAR-CCM+ est utilisé, tous les deux sont validés en utilisant le problème de Stefan,
la fusion du gallium et la coulée continue verticale de magnésium AZ31. Plusieurs modèles de
solidification sont testés, ainsi que la variation du domaine de simulation, et des rélations entre
la teneur en matière solide et la température. Des comparaisons avec des résultats de mesures
de la température à l’installation pilote de MgF GmbH Freiberg ainsi que la microstructure
donnent des bons résultats. Des analyses de sensibilité sont effectuées afin d’évaluer l’influence
des propriétés thermophysiques et des paramètres de l’installation. De plus, les cylindres sont
intégrés dans la simulation pour estimer l’impact du coefficient de transfert de chaleur dépendant
du lieu. Finalement, les résultats sont comparés avec ceux du Helmholtz-Centre Geesthacht.
Keywords
OpenFOAM, CD-adapco, STAR-CCM+, twin-roll casting, continuous casting, direct-chill cast-
ing, magnesium alloys, AZ31, solidification, melting, phase change, d’Arcy, viscosity model,
temperature-dependent properties, MgF GmbH Freiberg, Helmholtz-Zentrum Geesthacht HZG
IV
Table of contents
List of figures VI
List of tables VIII
List of symbols IX
1 Introduction 1
1.1 Magnesium – a light-weight material . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Twin-roll casting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 State of the art 4
2.1 Non-dimensional numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Literature review of twin-roll casting simulations . . . . . . . . . . . . . . . . . . 6
2.3 Conservation equations with interfaces . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.1 Dealing with interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.2 Conservation equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Solid-fraction models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.1 Models for the solid fraction . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.2 Release of latent heat using the solid fraction . . . . . . . . . . . . . . . . 13
2.4.3 Effect of solidification on momentum . . . . . . . . . . . . . . . . . . . . . 15
3 Model description 18
3.1 MeltFoam: basic code by F. Rösler . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Extensions to castFoam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 Commercial code STAR-CCM+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4 Validation 26
4.1 Stefan problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2 Gallium-melting test case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.3 Continuous DC casting of magnesium AZ31 . . . . . . . . . . . . . . . . . . . . . 36
5 Magnesium alloy AZ31 42
5.1 Designation of magnesium alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.2 Choice of a basic configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.3 Thermophysical properties of magnesium AZ31 . . . . . . . . . . . . . . . . . . . 44
Table of contents V
6 Simulation of the MgF pilot plant 50
6.1 MgF Pilot Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.1.1 Basic test-case description . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.1.2 Heat-transfer coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.1.3 Comparison with measurements. . . . . . . . . . . . . . . . . . . . . . . . 58
6.2 Influence of different models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.2.1 Axis symmetry and inlet region . . . . . . . . . . . . . . . . . . . . . . . . 65
6.2.2 Viscosity vs. d’Arcy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.2.3 Linear vs. lever vs. Scheil . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.3 Variation of parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.3.1 Thermophysical properties. . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.3.2 Plant parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.4 Incorporating the rolls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7 Comparison of the MgF and HZG pilot plants 89
8 Summary and future work 92
A Tabled literature review 94
B OpenFOAM 2.1.1 castFoam coding 96
C Settings for test-case simulations 112
C.1 One-phase Stefan problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
C.2 Gallium melting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
C.3 MagNET direct-chill casting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
C.4 Twin-roll casting of MgF GmbH Freiberg Pilot Plant . . . . . . . . . . . . . . . . 141
D Property table magnesium AZ31 161
References i
VI
List of figures
1.1 Schema of twin-roll casting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Modelling the solid fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Solidification in the energy equation . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Solidification modelled in the momentum equation . . . . . . . . . . . . . . . . . 15
3.1 Temperature-dependent thermal conductivity in OpenFOAM . . . . . . . . . . . 21
3.2 Velocity and temperature gradient vectors in TRC . . . . . . . . . . . . . . . . . 24
4.1 Schema of the 1D Stefan problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2 Comparison of analytical and numerical solutions of the one-phase Stefan problem 30
4.3 Schema of pure gallium melting test case. . . . . . . . . . . . . . . . . . . . . . . 31
4.4 2D grid convergence for the gallium-melting test case . . . . . . . . . . . . . . . . 33
4.5 Results of the gallium-melting test case . . . . . . . . . . . . . . . . . . . . . . . 33
4.6 Velocity vectors of the gallium-melting test case . . . . . . . . . . . . . . . . . . . 35
4.7 Not-true-to-scale schema of direct-chill casting test case . . . . . . . . . . . . . . 37
4.8 Temperature curves for the MagNET DC casting . . . . . . . . . . . . . . . . . . 40
5.1 Solid-fraction curve of AZ31 according to Scheil . . . . . . . . . . . . . . . . . . . 46
5.2 Comparison of thermal conductivity and specific heat . . . . . . . . . . . . . . . 47
6.1 Physical dimensions of the pilot plant . . . . . . . . . . . . . . . . . . . . . . . . 50
6.2 Location of evaluation points for TRC . . . . . . . . . . . . . . . . . . . . . . . . 59
6.3 Verification of grid independence . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.4 TRC simulation results without meniscus . . . . . . . . . . . . . . . . . . . . . . 61
6.5 TRC simulation results with meniscus . . . . . . . . . . . . . . . . . . . . . . . . 64
6.6 TRC simulation cooling rates with meniscus . . . . . . . . . . . . . . . . . . . . . 64
6.7 TRC symmetric results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.8 TRC symmetric cooling rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.9 TRC results for asymmetric domain . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.10 Temperature difference at roll surface for asymmetric domain . . . . . . . . . . . 67
6.11 Comparison of dynamic viscosity curves according to the solid fraction . . . . . . 69
6.12 Belt cast comparison of d’Arcy and viscosity model . . . . . . . . . . . . . . . . . 70
6.13 Belt cast comparison of sampled data . . . . . . . . . . . . . . . . . . . . . . . . 71
6.14 TRC solid velocity field from Stokes fluid flow solution . . . . . . . . . . . . . . . 72
6.15 TRC comparison of momentum models. . . . . . . . . . . . . . . . . . . . . . . . 74
List of figures VII
6.16 Solid-fraction models and sampled temperature data . . . . . . . . . . . . . . . . 75
6.17 Fraction model comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.18 Comparison of end-point solidification for varied thermophysical properties . . . 78
6.19 Comparison of last roll contact temperature for varied thermophysical properties 79
6.20 Temperature distribution along the midplane for tested sets of properties . . . . 80
6.21 Comparison of end-point solidification for varied plant parameters . . . . . . . . 82
6.22 Comparison of last roll contact temperature for varied plant parameters . . . . . 83
6.23 Incorporating the rolls: reaching a steady state . . . . . . . . . . . . . . . . . . . 84
6.24 Incorporating the rolls: solid fraction and velocity . . . . . . . . . . . . . . . . . 85
6.25 Incorporating the rolls: temperature distribution in the upper role . . . . . . . . 86
6.26 Incorporating the rolls: travelling-point cycle and heat-transfer coefficient . . . . 87
7.1 Comparison of two TRC plant simulations . . . . . . . . . . . . . . . . . . . . . . 90
VIII
List of tables
4.1 Employed fluid properties and boundary conditions of the Stefan problem . . . . 27
4.2 Employed fluid properties and boundary conditions of the pure gallium melting . 32
4.3 Boundary conditions of the direct-chill casting test case . . . . . . . . . . . . . . 37
4.4 Casting conditions of the direct-chill casting test case. . . . . . . . . . . . . . . . 38
4.5 Heat-transfer coefficients of the direct-chill casting test case . . . . . . . . . . . . 38
4.6 Casting conditions of the direct-chill casting test case. . . . . . . . . . . . . . . . 39
4.7 Sump depths different casting speeds of the DC casting . . . . . . . . . . . . . . 40
5.1 ASTM code of main magnesium alloying elements . . . . . . . . . . . . . . . . . 42
5.2 Final basic choice of properties of AZ31 . . . . . . . . . . . . . . . . . . . . . . . 43
5.3 SDAS of twin-roll cast magnesium AZ31 . . . . . . . . . . . . . . . . . . . . . . . 45
5.4 Density of magnesium AZ31 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.1 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.2 Average heat-transfer coefficient to the rolls . . . . . . . . . . . . . . . . . . . . . 52
6.3 Heat-transfer coefficient for solidified magnesium-alloy sheet . . . . . . . . . . . . 53
6.4 Heat-transfer coefficient for the meniscus . . . . . . . . . . . . . . . . . . . . . . . 54
6.5 Heat-transfer coefficient for the outer roll surface . . . . . . . . . . . . . . . . . . 56
6.6 Heat-transfer coefficient for the inner roll shell surface . . . . . . . . . . . . . . . 57
6.7 Comparison of sDAS correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.1 Comparison of the MgF GmbH Freiberg and Helmholtz-Centre Geesthacht plants 89
A.1 Literature review of the simulation of twin-roll casting . . . . . . . . . . . . . . . 94
IX
List of symbols
List of latin symbols
a − exponent
A m2 cross-sectional area
b m width
b m/s2 body force vector
B − constant
c J/(kgK) specific heat
p
c J/(kgK) apparent specific heat
app
C − alloy composition
CR K/s cooling rate
c ,c − constants
1 2
d m characteristic length scale of solidification
d m hydraulic diameter
h
f − liquid fraction
l
f − solid fraction
s
F − coefficient of inertia
g m/s2 gravity vector
g m/s2 gravity magnitude
h W/(cid:0)m2K(cid:1) heat-transfer coefficient
H J/kg specific enthalpy
I − unit matrix
k W/(mK) thermal conductivity
k − partition coefficient
p
K m2 permeability
l m length
l m characteristic length
char
L J/kg latent heat
L(t) m location of the interface at time t
m˙ kg/s mass flow rate
n − number of channels
N 1/m3 density of grains
p N/2 pressure
P m perimeter