Distributions of Electromagnetic Fields and Forced Flow and Their Relevance to the Grain Refinement in Al-Si Alloy Under the Application of Pulsed Magneto-Oscillation

doi:10.1007/s40195-021-01242-0

Abstract

Abstract:

Distributions of electromagnetic fields and induced forced flow inside a metal melt are crucial to understand the grain refinement of the metal driven by pulsed magneto-oscillation (PMO). In the present study, PMO-induced electromagnetic fields and forced flow in Ga-20wt%In-12wt%Sn liquid metal have been systematically investigated by performing numerical simulations and corresponding experimental measurements. The numerical simulations have been confirmed by magnetic and melt flow measurements. According to the simulated distribution of electromagnetic fields under the application of PMO, the strongest magnetic field, electric eddy current and Lorentz force with inward radial direction inside the melt are concentrated adjacent the sidewall of cylindrical melt at the cross section of middle height of coil. As a result, a global forced flow throughout the whole cylindrical column filled with Ga-20wt%In-12wt%Sn melt is initiated with a flow structure of two pair of symmetric vortex ring. The PMO-induced electromagnetic fields and forced flow in Al-7wt%Si melt have been numerically simulated. The contribution of electromagnetic fields and forced flow to the grain refinement of Al-7wt%Si alloy under the application of PMO is discussed. It indicates that the forced flow may play a key role in the grain size reduction.

Key words: Pulsed magneto-oscillation (PMO), Electromagnetic field, Forced flow, Solidification, Grain refinement

Yan-Yi Xu, Jing Zhao, Chun-Yang Ye, Yan-Ping Shen, Xin-Cheng Miao, Yun-Hu Zhang, Qi-Jie Zhai. Distributions of Electromagnetic Fields and Forced Flow and Their Relevance to the Grain Refinement in Al-Si Alloy Under the Application of Pulsed Magneto-Oscillation[J]. Acta Metallurgica Sinica (English Letters), 2022, 35(2): 254-274.

Figures/Tables 23

Fig. 1 Schematic views of a solidification experiment setup b waveform of pulsed electric current applied in PMO coil

Fig. 2 Schematic views of a magnetic field b flow field measurement setups

Table 1 Thermophysical properties of Al-7wt%Si and Ga-20wt%In-12wt%Sn alloy [5]

Thermophysical properties	Al-7wt%Si	Ga-20wt%In-12wt%Sn
Liquidus, T_L (°C)	615	10.5
Density, ρ (kg m^-3)	2422	6360
Viscosity, υ (m² s^-1)	0.5 × 10^-6	0.34 × 10^-6
Electrical conductivity, σ (S m^-1)	3.74 × 10⁶	3.27 × 10⁶
Relative permeability, m_r	1	1
Relative permittivity, ε	1	1

Fig. 3 Finite element model a and results including the validation of grid size b as well as the stabilization of simulation time c

Fig. 4 Macrostructures of Al-7wt%Si alloy in the longitudinal section with and without PMO: a reference sample; b PMO with Ip = 1500 A, f = 10 Hz, tp = 2.7 ms

Fig. 5 Microstructures of Al-7wt%Si alloy in the longitudinal section with and without PMO: a reference sample; b PMO with Ip = 1500 A, f = 10 Hz, tp = 2.7 ms

Fig. 6 a Measurement of magnetic flux density in the air induced by PMO with parameters of Ip = 1500 A, f = 10 Hz, tp = 2.7 ms along three directions at the center of coils b comparison between simulation and measurement results in the Z-direction

Fig. 7 Comparison of measured and calculated magnetic flux density (Z component) along central axis of coils in the air under the application of PMO with parameters of Ip = 1500 A, f = 10 Hz, tp = 2.7 ms

Fig. 8 Comparison of measured and calculated vertical velocity along central axis of Ga-20wt%In-12wt%Sn alloy under the application of PMO with parameters of Ip = 1500 A, f = 10 Hz, tp = 2.7 ms

Fig. 9 a Schematic view of selected position at the height of 47.5 mm and the radius of 25 mm b evolution of the conducted electric current, the magnetic field (Bz), the electric eddy current (J) and the radial Lorentz force (Fr) at the position in the Ga-20wt%In-12wt%Sn alloy induced by PMO with parameters of Ip = 1500 A, f = 10 Hz, tp = 2.7 ms

Fig. 10 Distribution of the magnetic field inside the Ga-20wt%In-12wt%Sn alloy under PMO with parameters of Ip = 1500 A, f = 10 Hz, tp = 2.7 ms: (I) schematic view of selected points in the curve of the vertical magnetic field at position of height 47.5 mm and radius 25 mm; a 0.3 ms; b 0.6 ms; c 1.0 ms; d 1.3 ms; e 1.6 ms; f 1.9 ms; g 2.3 ms; h 2.7 ms

Fig. 11 Distribution of the electric eddy current inside the Ga-20wt%In-12wt%Sn alloy under PMO with parameters of Ip = 1500 A, f = 10 Hz, tp = 2.7 ms: (I) schematic view of selected points in the curve of the electric eddy current at position of height 47.5 mm and radius 25 mm; a 0.1 ms; b 0.2 ms; c 0.3 ms; d 0.6 ms; e 0.9 ms; f 1.2 ms; g 1.5 ms; h 1.9 ms; i 2.2 ms; j 2.7 ms; k 3.2 ms; l 4.0 ms

Fig. 12 Distribution of the radial Lorentz force in the Ga-20wt%In-12wt%Sn alloy under PMO with parameters of Ip = 1500 A, f = 10 Hz, tp = 2.7 ms: (I) schematic view of selected points in the curve of the radial Lorentz force at position of height 47.5 mm and radius 25 mm; a 0.1 ms; b 0.2 ms; c 0.4 ms; d 0.6 ms; e 0.8 ms; f 0.9 ms; g 1.1 ms; h 1.4 ms; i 1.7 ms; j 2.1 ms; k 2.4 ms; l 2.7 ms

Fig. 13 Numerical simulation of vertical forced flow in the Ga-20wt%In-12wt%Sn alloy under PMO with parameters of Ip = 1500 A, f = 10 Hz, tp = 2.7 ms: a contour in the middle plane; b arrow surface in the middle plane

Fig. 14 Contours of the vertical velocity measured in the Ga-20wt%In-12wt%Sn alloy under PMO with parameters of Ip = 1500 A, f = 10 Hz, tp = 2.7 ms: a center, b 1/4D1 and c 4/5D1

Fig. 15 Schematic views of selected positions along radial direction at the height of 47.5 mm a, vertical direction at the radius of 27 mm c, and the corresponding curves of the radial Lorentz force along radial direction b and time-averaged radial Lorentz force along vertical direction d in the Ga-20wt%In-12wt%Sn alloy induced by PMO with parameters of Ip = 1500 A, f = 10 Hz, tp = 2.7 ms

Fig. 16 Numerical simulation of Al-7wt%Si alloy under PMO with parameters of Ip = 1500 A, f = 10 Hz, tp = 2.7 ms in the middle plane: a magnetic field; b electric eddy current; c Lorentz force; d vertical velocity

Fig. 17 Selected curves (see Fig. 15) of the Lorentz force along radial direction a and time-averaged radial Lorentz force along vertical direction b inside Al-7wt%Si alloy induced by PMO with parameters of Ip = 1500 A, f = 10 Hz, tp = 2.7 ms

Fig. 18 Numerical simulated forced flow in the Al-7wt%Si alloy under PMO parameters of a Ip = 1500 A, f = 2 Hz, tp = 2.7 ms; b Ip = 500 A, f = 14 Hz, tp = 2.7 ms

Fig. 19 Curves of the magnetic flux density a, the electric current density b and the Lorentz force c at position of height 47.5 mm and radius 25 mm inside Al-7wt%Si alloy induced by PMO

Table 2 Maximum values of PMO magnetic pressure, Lorentz force and time-averaged Joule heating at position of height 47.5 mm and radius 25 mm inside Al-7wt%Si

PMO parameters	Magnetic pressure (Pa)	Joule heating (W/m³)	Lorentz force (N/m³)
1500 A, 2 Hz, 2.7 ms	6.33 × 10³	3.44 × 10⁴	7.98 × 10⁵
500 A, 14 Hz, 2.7 ms	0.68 × 10³	2.64 × 10⁴	0.88 × 10⁵ N/m³

Fig. 20 Macrostructures of Al-7wt%Si alloy in the longitudinal section with different PMO parameters: a Ip = 1500 A, f = 2 Hz, tp = 2.7 ms; b Ip = 500 A, f = 14 Hz, tp = 2.7 ms

Fig. 21 Microstructures of Al-7wt%Si alloy in the longitudinal section with different PMO parameters: a Ip = 1500 A, f = 2 Hz, tp = 2.7 ms; b Ip = 500 A, f = 14 Hz, tp = 2.7 ms

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