Stefan Melt Velocity (multi region)

Description

The twoPhaseStefanMeltVelocity provides a boundary condition for the mesh velocity that calculates the melting/refreezing velocity according to the classical Stefan condition. Made for multi-region cases where one region represents the liquid phase while another region represents the solid phase. This boundary condition can be used on the boundary between both phases and will move the boundary accoring to

\[ \mathbf{v} = \frac{1}{\rho_s h_m} \left( -\kappa_1 \left. \nabla T \right\vert_{\Omega^1} \cdot \mathbf{n} + \kappa_2 \left. \nabla T \right\vert_{\Omega^2} \cdot \mathbf{n} \right) \mathbf{n} + (\mathbf{\Phi} \cdot \mathbf{n}) \mathbf{n}, \]

where

• \(\mathbf{v}\): mesh velocity
• \(\mathbf{n}\): surface normal vector
• \(\kappa_1\): thermal conductivity for this region
• \(\kappa_2\): thermal conductivity for adjacent region
• \(\rho_s\): density of the material at solid state
• \(h_m\): latent heat of fusion
• \(\left. \nabla T \right\vert_{\Omega^1}\): temperature gradient evaluated at this region
• \(\left. \nabla T \right\vert_{\Omega^2}\): temperature gradient evaluated at adjacent region
• \(\mathbf{\Phi}\): constant velocity of the solid phase relative to a chosen referenece frame

Usage

Property	Description	Required	Default value
rhoTimesH	\[\rho_s h_m\]	yes
kappa	thermal conductivity at this region \(\kappa_1\)	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.

Needs to be on an underlying mapped patch that is globally conforming (the touching patches on both sides of the interface must be equivalent). The boudary condition of the corresponding pointPatch on the other region must also be of type twoPhaseStefanMeltVelocity. The specification of the boundary condition should match on on both sides except for the thermal conductivity which might be different in the two regions.

Example of the boundary condition specification:

<patchName>
{
    type        twoPhaseStefanMeltVelocity;
    rhoTimesH   334e6;
    kappa       0.56; //liquid water close to melt temperature
    linearUpwindBlendingFactor  0;
    laplaceSmoothing    yes;
    value       uniform (0 0 0);
}