# Discussion Forum

## COMSOL Continuous Casting Example

Hello,

I have a question regarding the Volume force density equations (F_r & F_z) used in this example model:

f = (1-alpha)^2/(alpha^3+epsilon)

F_r = -f.A_mush.u

F_z = -f.A_mush.(w-v_cast)

1) Why do (w-v_cast)? I am not able to understand the physical meaning behind this 2) At a z distance of 0.6 m, alpha (liquid volume fraction) is zero and the z-velocity is 0.0016 m/s which is the same as the casting velocity. But when I plot F_z I don't see it go to zero to further along the z-direction. According to the above equation shouldn't it be zero?

1 Reply Last Post Oct 15, 2021, 3:45 a.m. EDT

Posted: 3 months ago
Updated: 3 months ago

Hi,

The casting is continuous hence the solidified part is having a constant velocity downstream while it is not moving in the transverse direction. Hence in the solid part we expect u = v = 0 and w=v_cast.

A fluid flow equation is solved for the liquid and solid parts. In order to mimic the translation of a rigid body in the solid part, a volumetric force is added. The term F_z=-fA.mush.(w-vcast) penalizes any solution where w is different from vcast in the solid part. The larger fA is, the smaller the difference between w and vcast can be in the solid part for a converged solution.

With best regards,
Nicolas, COMSOL