Stefan Melt Velocity (single region)

Description

The onePhaseStefanMeltVelocity provides a boundary condition for the mesh velocity that calculates the melting/refreezing velocity according to the classical Stefan condition while assuming the adjacent phase to be at constant melt temperature. The velocity is calculated as

\[ \mathbf{v} = - \frac{\kappa}{\rho_s h_m} (\nabla T \cdot \mathbf{n}) \mathbf{n} + (\mathbf{\Phi} \cdot \mathbf{n}) \mathbf{n}, \]

where

• \(\mathbf{v}\): mesh velocity
• \(\mathbf{n}\): surface normal vector
• \(\kappa\): thermal conductivity
• \(\rho_s\): density of the material at solid state
• \(h_m\): latent heat of fusion
• \(\nabla T\): temperature gradient
• \(\mathbf{\Phi}\): constant velocity of the solid phase relative to a chosen referenece frame

Usage

Property	Description	Required	Default value
kappaOverRhoH	\[\frac{\kappa}{\rho_s h_m}\]	yes
URef	Velocity of the solid phase \(\mathbf{\Phi}\) in chosen reference frame	no	(0 0 0)
TName	Name of the temperature field	no	T
linearUpwindBlendingFactor	blending between linear and upwind for the face-to-point interpolation (1 corresponds to full linear and 0 corresponds to full upwind interpolation)	no	0
laplaceSmoothing	apply lapalace smoothing?	no	no

For a more detailed description of the more general settings, see mesh velocity boundary conditions.

Example of the boundary condition specification:

<patchName>
{
    type            onePhaseStefanMeltVelocity;
    kappaOverRhoH   1.8e-9; //liquid water
    linearUpwindBlendingFactor  0;
    laplaceSmoothing    yes;
    value           uniform (0 0 0);
}