17.5 Momentum Equations

The enthalpy-porosity technique treats the mushy region (partially solidified region) as a porous medium. The porosity in each cell is set equal to the liquid fraction in that cell. In fully solidified regions, the porosity is equal to zero, which extinguishes the velocities in these regions. The momentum sink due to the reduced porosity in the mushy zone takes the following form:

where $\beta$ is the liquid volume fraction, $\epsilon$ is a small number (0.001) to prevent division by zero, $A_{\rm mush}$ is the mushy zone constant, and $\vec v_p$ is the solid velocity due to the pulling of solidified material out of the domain (also referred to as the pull velocity ).

The mushy zone constant measures the amplitude of the damping; the higher this value, the steeper the transition of the velocity of the material to zero as it solidifies. Very large values may cause the solution to oscillate.

The pull velocity is included to account for the movement of the solidified material as it is continuously withdrawn from the domain in continuous casting processes. The presence of this term in Equation  17.5-1 allows newly solidified material to move at the pull velocity. If solidified material is not being pulled from the domain, $\vec v_p=0$. More details about the pull velocity are provided in Section  17.8.