Simulation of the Influence of Pulsed Magnetic Field on the Superalloy Melt with the Solid-Liquid Interface in Directional Solidification

doi:10.1007/s40195-020-01048-6

Abstract

Abstract:

The effect of the pulsed magnetic field on the grain refinement of superalloy K4169 has been studied in directional solidification. In the presence of the solid-liquid interface condition, the distributions of the electromagnetic force, flow field, temperature field, and Joule heat in front of the solid-liquid interface in directional solidification with the pulsed magnetic field are simulated. The calculation results show that the largest electromagnetic force in the melt appears near the solid-liquid interface, and the electromagnetic force is distributed in a gradient. There are intensive electromagnetic vibrations in front of the solid-liquid interface. The forced melt convection is mainly concentrated in front of the solid-liquid interface, accompanied by a larger flow velocity. The simulation results indicate that the grain refinement is attributed to that the electromagnetic vibration and forced convection increase the nucleation rate and the probability of dendrite fragments survival, for making dendrite easily fragmented, homogenizing the melt temperature, and increasing the undercooling in front of the solid-liquid interface.

Key words: Pulsed magnetic field, Solid-liquid interface, Simulation, Electromagnetic force, Melt convection Superalloy

Kuiliang Zhang, Yingju Li, Yuansheng Yang. Simulation of the Influence of Pulsed Magnetic Field on the Superalloy Melt with the Solid-Liquid Interface in Directional Solidification[J]. Acta Metallurgica Sinica (English Letters), 2020, 33(10): 1442-1454.

Figures/Tables 20

Fig. 1 Sketch of directional solidification equipment a, the liquid melt quenching sample with meniscus solid-liquid interface b, the finite element model c

Fig. 2 Variation in pulsed current density through the coil

Table 1 Material parameters for the electromagnetic simulation

-	Resistivity (Ω·m)	Permeability
Liquid	1.19 $\times$ 10^-6	1
Solid	6 $\times$ 10^-7	1
Coil	2 $\times$ 10^-8	1
Air	-	1

Table 2 Material parameters for the temperature simulation

Material	Temperature (K)	Density (kg/m³)	Thermal conductivity (J/(kg K))	Enthalpy (kJ/kg)
Superalloy	300	8150	10	592
	1523	7800	30	844
	1613	7800	30	1130
	1800	7800	30	1243
Mold	300-1800	4000	6	1250

Fig. 3 A comparison of the experimentally measured and theoretically predicated radial variation in the axial velocity component at the height of 0.225 m

Fig. 4 Distribution of the electromagnetic force at mid of ascending stage a, at peak b, at mid of descending stage c, at mid of pause stage d

Fig. 5 Evolution of the electromagnetic force at point A in one period

Fig. 6 Variation in the electromagnetic force without and with solid-liquid interface from point B to point C at peak

Fig. 7 Schematic illustration of the induced current

Fig. 8 Distribution of the magnetic pressure in the melt with the solid-liquid interface during the ascending stage a, during the descending stage b, during the pause stage c

Fig. 9 Distribution of the magnetic pressure in the melt without the solid-liquid interface during the ascending stage a, during the descending stage b, during the pause stage c

Fig. 10 Variation in the magnetic pressure with time at points D, E

Fig. 11 Flow field with the solid-liquid interface at the end of the ascending stage a, at the end of the descending stage b, and the end of the pause stage c. The flow field without the solid-liquid interface at the end of the ascending stage d

Fig. 12 Evolution of the flow velocity a, acceleration b with time at points F and G

Fig. 13 Distribution of the flow velocity along the axial direction

Fig. 14 Distribution of the temperature field without the PMF a, with the PMF b

Fig. 15 Shape of the solid-liquid interface without PMF a, with PMF b

Fig. 16 Evolution of the flow field with different liquid phase volumes

Fig. 17 Distributions of the Joule heat at mid of ascending stage a, at mid of descending stage b

Fig. 18 Microstructures of superalloy K4169 without the PMF a, with the PMF b

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