Arbitrary Lagrangian-Eulerian Method

When the phase change interface is tracked using the arbitrary Lagrangian-Eulerian (ALE) method, the phase change interface velocity is defined explicitly by the Stefan condition, which expresses the energy balance at the interface.

It applies to the case of phase change between a solid (or immobile fluid) and a fluid phase, with a sharp transition between the phases, and no topology changes.

The Phase Change Interface boundary condition is applicable on the boundaries located at the interface between a solid and a fluid domain, two solid domains, two fluid domains or two porous medium domains.

The Phase Change Interface, Exterior boundary condition is applicable on the exterior boundaries adjacent to a solid, fluid, or porous medium domain.

The latent heat of phase change is taken into account through the definition of the phase change velocity.

The Stefan condition defines the phase change interface velocity vn as follows:

with Ls → f the latent heat of phase change from solid to fluid (SI unit: J/kg), ρs the solid density (SI unit: kg/m3), and q the conductive heat flux jump across the interface (SI unit: W/m2), defined as

with ks the solid thermal conductivity (SI unit: W/(m·K)), kf the fluid thermal conductivity (SI unit: W/(m·K)), and Ts, Tf the temperatures on each side of the interface.

When the density changes during the phase change, the volume change is compensated by a velocity at the interface in the fluid phase. The normal fluid velocity is expressed as:

The phase change velocity vn appearing in Stefan condition is relative to the solid position. In case of translation of the solid (using Translational Motion subfeature under Solid with Translational Motion feature for instance), as in a continuous casting process, the solid translation velocity us contributes to vn to describe the interface velocity relative to the spatial frame: