Fig. 1. (a) Sketch of directional solidification apparatus with the LVPMF; (b) Liquid melt quenching sample with a meniscus solid-liquid interface; (c) 2D finite element model.

Fig. 2. Solidification structure of superalloy K4169 under different pulse voltages: (a) 0 V, (b) 100 V, (c) 150 V, (d) 200 V.

Fig. 3. Average grain size with different pulse voltages.

Fig. 4. Distribution of the grain aspect ratios under different pulse voltages.

Fig. 5. Solidification structure of superalloy K4169 under different pulse frequencies: (a) 0 Hz, (b) 2.5 Hz, (c) 5 Hz, (d) 10 Hz.

Fig. 6. Distribution of the grain aspect ratios under different pulse frequencies.

Fig. 7. Solidification structure of superalloy K4169 with different withdrawal speeds under LVPMF: (a) 0.25 mm/s, (b) 0.75 mm/s, (c) 1.25 mm/s, (d) 1.75 mm/s.

Fig. 8. Average grain size with different withdrawal speeds.

Fig. 9. Comparison of the experimentally measured and theoretically predicated radial variation of the axial velocity component at a height of 225 mm.

Fig. 10. Distribution of electromagnetic force in the upward period (a) and in the falling period (b); (c) Variation of electromagnetic force along the axial direction in the melt.

Fig. 11. Position of maximum electromagnetic force in the front of the solid-liquid interface.

Fig. 12. Distribution of pressure in the upward period (a) and in the falling period (b); (c) Variation of the pressure at point A and point B.

Fig. 13. (a) Distribution of flow field at the peak; (b) Variation of axial flow velocity.

Fig. 14. Stress simulation of flowing melt acts on the dendrite. (a) Finite element mesh; (b) Distribution of fluid velocity; (c) Stress distribution of the dendrite.

Fig. 15. Shape of solid-liquid interface with different pulse voltages: (a) 0 V, (b) 100 V, (c) 200 V.

Fig. 16. Sketch showing the variation of liquid undercooling in the front of the solid-liquid interface without LVPMF (a) and with LVPMF (b) in the melt.

Fig. 17. Solidification structure of superalloy K4169.