Solidification and Casting Simulation

It predicts the process where molten metal cools and solidifies. It deals with flow and heat transfer problems involving solid-liquid phase changes, such as mold filling and solidification analysis in casting, shell growth in continuous casting, bead formation in welding, and molten pool behavior in metal 3D printing (PBF/DED).

The Enthalpy Method (Enthalpy-Porosity method) is the standard approach. It does not explicitly track the solid-liquid interface; instead, it represents the progress of solidification using the liquid fraction $f_L$ (a continuous variable from 0 to 1) in each cell.

The energy equation is described in terms of enthalpy $H$.

Enthalpy is the sum of sensible heat and latent heat.

$h = \int_{T_{ref}}^{T} c_p dT$ is the sensible heat, $f_L$ is the liquid fraction, and $L$ is the latent heat of solidification. The liquid fraction is determined from the liquidus temperature $T_L$ and solidus temperature $T_S$.

In the Enthalpy-Porosity method, the solidified region is treated as a porous medium with high resistance. A Darcy drag source term is added to the momentum equation.

$C$ is the Mushy zone constant (typical values $10^5$ to $10^8$), $\epsilon$ is a small constant to avoid division by zero, and $\mathbf{u}_{pull}$ is the pulling speed (in continuous casting). As $f_L \to 0$ (complete solidification), the source term approaches infinity, causing the velocity to decay to zero.

Marangoni convection, caused by the temperature dependence of surface tension ($d\sigma/dT$), dominates the flow pattern in the molten pool.

For many metals, $d\sigma/dT < 0$ (surface tension is lower at higher temperatures), causing an outward flow from the center of the molten pool. However, the sign can reverse depending on oxygen or sulfur content, dramatically changing the flow pattern.

The biggest challenge is handling the latent heat of solidification. The release of latent heat creates nonlinearity in enthalpy and causes abrupt changes in the temperature field. Time step management and convergence of iterative calculations are key.

The value of $C$ has a significant impact on the results.

Ideally, it should be determined from experimental data on Darcy permeability, but in practice, it's common to start with $10^5$ to $10^6$ and perform a sensitivity analysis.

The filling process tracks the free surface of the molten metal using the VOF method, and solidification is calculated after filling is complete (or simultaneously with filling). In Fluent or Flow-3D, simultaneous calculation with VOF + Solidification/Melting models is possible.

Flow patterns during filling, oxide film entrapment, and gas entrainment directly lead to casting defects, making filling analysis a crucial element of casting simulation.

That's correct. They are specialized tools dedicated to casting processes, capable of integrated calculation of filling, solidification, shrinkage prediction, and deformation. They are more equipped with casting-specific physics models (e.g., feeding, Niyama criterion) than general-purpose CFD.