U. Müller – författare

The phase transformation from liquid to solid is a phenomenon central to a wide range of manufacturing and natural processes. The presence of phase transformation can drive convection in the melt through the liberation of latent heat, the rejection of solute, and the change of density upon freezing. The fluid mechanics itself can playa central role; the phase transformation can be strongly altered by convective transport in the liquid through the modification of the thermal and solutal environment of the solid-liquid interface; these local fields control the freezing characteristics at the interface. The convection can be generated naturally by buoyancy forces arising from gradients of temperature and concentration in the liquid, by density changes upon freezing, and by thermocapillary and solutocapillary forces on liquid-solid interfaces. The interactive coupling between solidification and convection forms the subject of this volume. Such coupled processes are significant on a large range of scales. Among the applications of interest are the manufacture of single crystals, the processing of surfaces using laser or molecular beams, and the processes of soldering and welding. One wants to understand and predict macrosegregation in castings, transport and fractionation in geological and geophysical systems, and heat accumulation in energy redistribution and storage systems. This volume contains papers presented at the NATO Advanced Research Workshop on "Interactive Dynamics of Convection and Solidification" held in Chamonix, France, March 8-13, 1992.

The contents of this book has been the subject of a lecture course, which the first author has held regularly for engineering students at the Technical University of Karlsruhe beginning in 1987. The book serves two purposes. It introduces students in their fourth year study of basic engineering and grad­ uate students to the fundamentals of magnetohydrodynamics. Furthermore, it may be used by engineers and physicists in research establishments and industry as a practical tool to become familiar with the particular phenom­ ena of magneto-thermohydraulics that they may encounter in technical liquid metal flows under the influence of magnetic fields. The contents and structure of the book are motivated by the research and development work for a self-cooled liquid metal blanket of future nuclear fu­ sion reactors. The research requirements for such a challenging project natu­ rally lead to the frontiers of magnetohydrodynamic research. This is reflected in the book by references to several publications and reports performed at the Forschungszentrum Karlsruhe and other research establishments. However, we are convinced that the advancement of magnetohydrodynamic knowledge gained within the framework of the Fusion Reactor Project may be utilized in other fields of engineering sciences.

The contents of this book has been the subject of a lecture course, which the first author has held regularly for engineering students at the Technical University of Karlsruhe beginning in 1987. The book serves two purposes. It introduces students in their fourth year study of basic engineering and grad­ uate students to the fundamentals of magnetohydrodynamics. Furthermore, it may be used by engineers and physicists in research establishments and industry as a practical tool to become familiar with the particular phenom­ ena of magneto-thermohydraulics that they may encounter in technical liquid metal flows under the influence of magnetic fields. The contents and structure of the book are motivated by the research and development work for a self-cooled liquid metal blanket of future nuclear fu­ sion reactors. The research requirements for such a challenging project natu­ rally lead to the frontiers of magnetohydrodynamic research. This is reflected in the book by references to several publications and reports performed at the Forschungszentrum Karlsruhe and other research establishments. However, we are convinced that the advancement of magnetohydrodynamic knowledge gained within the framework of the Fusion Reactor Project may be utilized in other fields of engineering sciences.

Dedicated to Prof. Dr.-Ing. J. Zierep

In der vorliegenden Arbeit wurden die Wirbeltransportgleichung, die Poisson- Gleichung fUr die Stromfunktion und die Impulsgleichung in spharischen Koordina- ten mit Hilfe finiter Differenzenapproximationen integriert. Mit der Leisung werden rotationssymmetrische Str1:imungen in Kugelspalten fUr verschiedene Winkelbe- schleunigungen der Innenkugel untersucht. Der Vergleich der errechneten Ergebnis- se mit experimentellen Daten zeigt, dal3 die Auswahl des Gitternetzes die Ergebnisse entscheidend beeinflussen" kann. Wird die Schrittweite zu gr~13 gewahlt, stellt sich eine L1:isung ein, die nicht zu den vorgegebenen Randbedingungen geh1:irt. Es lal3t sich jedoch eine Genauigkeitsbedingung angeben, mit der diese Schwierig- keit umgangen werden kann. FUr stationare Str1:imungen sind die berechneten Drehmomente in guter Ubereinstimmung mit bekannten experimentellen Daten. Die bisher vorliegenden Ergebnisse lassen vermuten, dal3 einige instationare Str1:imungszustande zumindest wahrend der Beschleunigungsphase dreidimensionalen Charakter haben, jedoch werden bei kleineren Spaltweiten auch fUr rotationssym- metrische Str1:imungen instationare Zustande berechnet.Die resultierenden Dreh- momentenbeiwerte zeigen Schwankungen von etwa sechs Prozent. Eine Analyse der Stromlinienbilder ergibt, dal3 periodisch Wirbel in einiger Entfernung vom Aquator erzeugt und in seiner Nahe wieder unterdrUckt werden. Andere Rechnungen, die mit der angegebenen L1:isungsmethode durchgefUhrt wurden, bestatigen die Kirchgass- nersche Stabilitatsgrenze, die naherungsweise fUr Kugelspaltstr1:imungen auch in der Nahe des Aquators gilt. Die Integrationen wurden vom Zustand der Ruhe begonnen. Durch Anderung der Winkelbeschleunigung in Abhangigkeit von der Zeit lassen sich Verzweigungen der L1:isung bestimmen. ZukUnftige Arbeiten sehen die Konstruktion eines Verzwei- gungsdiagramms vor.

The contents of this book has been the subject of a lecture course, which the first author has held regularly for engineering students at the Technical University of Karlsruhe beginning in 1987. The book serves two purposes. It introduces students in their fourth year study of basic engineering and grad­ uate students to the fundamentals of magnetohydrodynamics. Furthermore, it may be used by engineers and physicists in research establishments and industry as a practical tool to become familiar with the particular phenom­ ena of magneto-thermohydraulics that they may encounter in technical liquid metal flows under the influence of magnetic fields. The contents and structure of the book are motivated by the research and development work for a self-cooled liquid metal blanket of future nuclear fu­ sion reactors. The research requirements for such a challenging project natu­ rally lead to the frontiers of magnetohydrodynamic research. This is reflected in the book by references to several publications and reports performed at the Forschungszentrum Karlsruhe and other research establishments. However, we are convinced that the advancement of magnetohydrodynamic knowledge gained within the framework of the Fusion Reactor Project may be utilized in other fields of engineering sciences.

The phase transformation from liquid to solid is a phenomenon central to a wide range of manufacturing and natural processes. The presence of phase transformation can drive convection in the melt through the liberation of latent heat, the rejection of solute, and the change of density upon freezing. The fluid mechanics itself can playa central role; the phase transformation can be strongly altered by convective transport in the liquid through the modification of the thermal and solutal environment of the solid-liquid interface; these local fields control the freezing characteristics at the interface. The convection can be generated naturally by buoyancy forces arising from gradients of temperature and concentration in the liquid, by density changes upon freezing, and by thermocapillary and solutocapillary forces on liquid-solid interfaces. The interactive coupling between solidification and convection forms the subject of this volume. Such coupled processes are significant on a large range of scales. Among the applications of interest are the manufacture of single crystals, the processing of surfaces using laser or molecular beams, and the processes of soldering and welding. One wants to understand and predict macrosegregation in castings, transport and fractionation in geological and geophysical systems, and heat accumulation in energy redistribution and storage systems. This volume contains papers presented at the NATO Advanced Research Workshop on "Interactive Dynamics of Convection and Solidification" held in Chamonix, France, March 8-13, 1992.