MHD-Driven Solidification and Macro-Segregation of a Ga–In Alloy

Multiphysics simulation of directional solidification and macro-segregation of a Ga–In alloy under a rotating magnetic field (RMF) in ANSYS Fluent. The thermal gradient, growth rate and flow velocity at the solidification front are extracted as inputs for micro-scale phase-field (MiCRESS) simulations.

Solidification front	Indium segregation

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Overview

The model couples four physics: electromagnetic stirring, heat transfer, phase change and species transport. With them it predicts how RMF-driven flow shapes the solidification front and the macro-segregation of a binary Ga-75 wt% / In-25 wt% alloy.

The main aim is to connect scales. At the dendrite tip the model extracts:

• the thermal gradient G
• the growth rate R
• the flow velocity V

These values serve as boundary conditions for phase-field simulations of dendritic growth.

Key Results

Extracted at the solidification front ($f_L \approx 0.99$) at t = 20 s:

Parameter	Value	Extraction method
Temperature gradient $G$	≈ 12,000 K/m	Probed at the solid–liquid interface
Flow velocity $V$	≈ 0.013 m/s	Probed in the hydrodynamic boundary layer near the dendrite tips
Growth rate $R$	≈ 6.0 × 10⁻⁴ m/s	From the growth of the shell thickness over time
Segregation pattern	Confirmed	Solid shell depleted (< 25 % In), liquid bulk enriched (> 25 % In)

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Methodology

Domain: 2D axisymmetric cylindrical crucible, R = 12.5 mm, H = 100 mm.

Physics models

Model	Setting
Viscous	Laminar
Solidification & melting	Enthalpy–porosity, Scheil rule for micro-segregation
Species transport	Enabled, with solutal buoyancy
Gravity	−9.81 m/s² along the axial (X) direction
MHD forcing	Lorentz force as a tangential momentum source term (RMF)

Material properties (Ga–In)

Property	Value
Density	Boussinesq, reference 6326 kg/m³
Partition coefficient $k$	0.8 (indium rejected into the liquid)
Latent heat	70,000 J/kg
Solidus / liquidus	288 K / 290 K
Mass diffusivity	2.0 × 10⁻⁹ m²/s

Boundary and initial conditions

• Cooling: outer wall held at 280 K (below solidus), so the melt solidifies from the wall towards the axis.
• Initial state: melt at 300 K, uniform indium mass fraction 0.25.
• Time stepping: Δt = 5 × 10⁻⁴ s, 40,000 steps (20 s of flow time).

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Results

Solidification and segregation

The MHD-driven flow interacts with the solidification front. This produces a wavy interface and clear macro-segregation.

Liquid fraction	Indium mass fraction
Mushy-zone shape under RMF	Depleted at the wall (blue), enriched at the centre (red)

Parameters passed to the micro scale

Temperature gradient $G$	Swirl velocity $V$
≈ 12,000 K/m at the interface	≈ 0.013 m/s in the boundary layer

Temperature, pressure and convergence

Temperature	Pressure	Residuals

More animations: swirl flow and temperature

Swirl flow development	Cooling

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Reproducing the Simulation

1. Open ANSYS Fluent with the 2D axisymmetric solver.
2. Create gallium and indium fluids and define a mixture with Boussinesq density.
3. Enable energy, solidification/melting (Scheil rule) and species transport, and add the Lorentz-force source term.
4. Initialise with the standard method: T = 300 K, indium mass fraction 0.25.
5. Run 40,000 time steps with Δt = 5 × 10⁻⁴ s (20 s of flow time).

Related Work

• MHD-driven flow in continuous casting: validation against Zhang et al. (2022)
• Ga75In25 2D axisymmetric parametric study under RMF
• 3D MHD simulation: UDF vs. MHD module

Author

Burak Yörükçü, Space Engineering, University of Miskolc · GitHub · burakyorukcu@outlook.com