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Conference on Turbulence and Interactions TI2006 May June Porquerolles France

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Conference on Turbulence and Interactions TI2006, May 29 - June 2, 2006, Porquerolles, France AXISYMMETRIC MODELLING OF THE MIXING OF TWO MISCIBLE LIQUID METALS DRIVEN BY A ROTATING MAGNETIC FIELD P. A. Nikrityuk?, K. Eckert, R. Grundmann Institute of Aerospace Engineering, Technische Universitat Dresden, D-01062 Dresden, Germany ?Email: ABSTRACT This work is devoted to the numerical study of the mixing of two miscible liquid metals (Pb and Sn) driven by a rotating magnetic field from the state of rest under microgravity. The geometry studied is an enclosed cylindrical cavity with an aspect ratio equal to unity, i.e. the diameter of cylinder is equal to its height. The initial condition is a cylinder which lower half is filled with Pb and the rest with Sn, where the molecular viscosity of Pb is twice as high as that of Sn. Based on the mixture model of the two-fluid flow and the axisymmetric Navier-Stokes equations, the transient transport of momentum and species in a swirling flow is modeled. The numerical simulations were performed for Ekman numbers in the range from 10?3 to 10?4 corresponding to a turbulent flow. For comparison we present simulations for the laminar flow at an Ekman number 3 · 103. It was shown that the increase of the mixing rate occurs due to randomly-appearing Taylor- Gortler vortices moving up- and down along the sidewall of the cylinder and dissipating in the Bodewadt layers.

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Conference on Turbulence and Interactions TI2006, May 29 - June 2, 2006, Porquerolles, France
AXISYMMETRIC MODELLING OF THE MIXING OF TWO MISCIBLE LIQUID METALS DRIVEN BY A ROTATING MAGNETIC FIELD
P. A. Nikrityuk, K. Eckert, R. Grundmann
InstituteofAerospaceEngineering,TechnischeUniversit¨atDresden,D-01062Dresden,Germany Email: nikrityuk@tfd.mw.tu-dresden.de
ABSTRACT This work is devoted to the numerical study of the mixing of two miscible liquid metals (Pb and Sn) driven by a rotating magnetic field from the state of rest under microgravity. The geometry studied is an enclosed cylindrical cavity with an aspect ratio equal to unity, i.e. the diameter of cylinder is equal to its height. The initial condition is a cylinder which lower half is filled with Pb and the rest with Sn, where the molecular viscosity of Pb is twice as high as that of Sn. Based on the mixture model of the two-fluid flow and the axisymmetric Navier-Stokes equations, the transient transport of momentum and species in a swirling flow 34 is modeled. The numerical simulations were performed for Ekman numbers in the range from10to10 corresponding to a turbulent flow. For comparison we present simulations for the laminar flow at an Ekman 3 number310. It was shown that the increase of the mixing rate occurs due to randomly-appearing Taylor-G¨ortlervorticesmovingup-anddownalongthesidewallofthecylinderanddissipatingintheB¨odewadt layers.
INTRODUCTIONin [3].But in spite of its universality there are only a few works focusing on the fluid dynamics of mixing, namely on the numerical modeling of the temporal flow development until the homog-Rotating magnetic fields (RMF) are widely used enization of liquids is reached. In this work the for a control of heat and mass transfer in semicon-focus is on the numerical study of the influence ductor and metallurgical applications[1]. Par-of spin-up dynamics of the liquids on their mix-ticularly, RMF's can be used for a forced mixing ing and on the role of Taylor-Go¨rtler vortices in of a multicomponent liquid alloy before its solid-the mixing process. ification. Furthermore an important potential of RMF lies in the ability to promote the columnar-to-equiaxed transition (CET) during the solidi-PROBLEM FORMULATION fication of metal alloys [2]. From this point of view it is important to know the main mechanism responsible for the mixing of metals stirred byBased on the mixture model of the two-fluid flow RMF and to estimate the time, needed to homog-with the assumption of equal densities for two enize the liquid phase. The mixing processes oc-fluids we use Navier-Stokes equations: cur in various branches of science and engineer-ing. An overview of existing works can be found∇ ∙~u= 0(1)