Numerical and experimental studies on solidification control by alternating magnetic fields

1. Numerical and experimental studies on solidification control by alternating magnetic fields P. Nikrityuk1, K.Eckert1 , B. Willers2, S. Eckert2, U. Michel3, G. Zouhar3 1Institute of Aerospace Engineering, Dresden University of Technology, D-01062 Dresden, Germany 2Forschungszentrum Rossendorf (FZR), D-01314 Dresden, Germany 3Institute of Material Science, Dresden University of Technology Sino-German Workshop on Electromagnetic Processing of Materials October 11-12, 2004, Shanghai, China SFB 609

2. Solidification control by alternating magnetic fields Rotary stirring and mixing liquid metals during solidification: homogenization of the liquid phase The modification of thermosolutal and shrinkage-driven flows Applications of alternating magnetic fields to control of a metal solidification Affect the microstructure, e.g. modification of the grain structure Control of Columnar-Equiaxed Transition (CET) SFB 609

3. Classification of rotating magnetic fields (RMF) Magnetic Taylor number Hartmann number Reynolds number corresponding to the magnetic field rotation Angular frequency of the magnetic field Relative frequency of the magnetic field metals and semiconductors stirring SFB 609

4. Experimental set-up • Alloy: Pb-85wt%Sn • Cylindrical mold made from stainless steel • Ingot dimensions: R = 25 mm, H = 60 mm • Superheat: 90K • RMF: six coils B = 0...25mT, f = 10...400Hz (Ta = 1·105 ... 3·108) Sketch of the experimental facility (FZ Rossendorf) SFB 609

5. Continuum based model (Incropera, 1987) of a binary metal alloy solidification Mixture viscosity model (Roplekar & Dantzig, 2001) The energy equation is written for mixture enthalpy Volume fraction of liquid: Numerical formulation • Lorentz force - low-frequency and low induction approximation has been used (Gorbachev et al. 1974) Time averaged azimuthal Lorentz force (Ta = 5.8104, finite cylinder R = 25 mm H = 63 mm) SFB 609

6. Basic equations of the mixture model Mass Conservation Equation Momentum Conservation Equation Mixture viscosity approach: us=ul. Permeability approach: us=0. Energy Conservation Equation Species Mass Conservation Equation =0 (us=ul) =0 (us=ul) SFB 609

7. Mixture quantities • Mass Fraction of Liquid and Solid • Mixture Density • Mixture Enthalpy • Mixture Mass Fraction of Sn • Mixture thermal conductivity Dynamic viscosity of the mixture. (Roplekar J.K., and Dantzig J.A. 2001) Int. J. Cast. Metals Research. Vol. 14, No. 2, pp. 79-98. SFB 609

8. Numerical simulation of hypereutectic Pb85%wtSn alloy solidification • Mixture viscosity approach is used • to model fluid flow within mushy zone • Solidification front velocity is about 0.2 mm/sec • Volume fraction of liquid is calculated • from relation: SFB 609

9. Results I – Fluid flow during solidification UDV measurements, Ta = 5.8·106, r = 22 mm Numerical simulation • Two-phase problem • Modification of the geometry (aspect ratio!) • Modification of the effective Lorentz force • Modification of the material properties • Free surface Ta=2*106, Sn-15M%Pb SFB 609

10. Results II – Curvature of the solidification front Azimuthal velocity Volume fraction of liquid Pb85%wtSn, Ta=2 106 SFB 609

11. Results III – Modification of heat transfer Experiment Numeric • RMF driven convection enhances the heat transfer between liquid and solid phases • Temperature gradient is reduced by the forced convection • Increase of Ta number leads to the convective transport of Latent heat SFB 609

12. Results IV –The distribution of mass fraction of Sn after solidification with stirring, B=1mT, Ta=2.3 105. Numerical results. Permeability constant model Us=0 Mixture viscosity model Us=Ul Zero gravity Zero gravity SFB 609

13. Results V – Columnar-to-equiaxed transition (CET) Ta = 0 Ta = 1.4·108 • Convection promotes the CET • Vertical CET position depends on the Taylor number • Columnar crystallites are inclined towards the flow direction SFB 609

14. Results VI – Columnar-to-equiaxed transition (CET) B = 10 mT, f = 50 Hz, Ta = 2·107, Longitudinal section SFB 609

15. Outlook / Further steps • Variations of the alloy composition, alloy systems • Quantitative analysis of microstructure parameters • Coupling of microscale and macroscale models • Optimisation of the electromagnetic stirring SFB 609

16. Conclusions • Modification of a columnar into an equiaxed micro-structure of a directionally solidified Sn15wt%Pb alloy was achieved using a RMF • Forced convection modifies distribution of temperature and concentration • Significant effects of the flow on the convection in the mushy zone and on the shape of the interface solid/liquid can be observed • The flow structure is considerably more complex as compared with the steady-state flow structures SFB 609

17. Acknowledgement The research is supported by the Deutsche Forschungsgemeinschaft (DFG) in the frame of the SFB 609“Electromagnetic Flow Control in Metallurgy, Crystal Growth and Electrochemistry”. This support is gratefully acknowledged by the authors. SFB 609