Parameters for latent heat?

[Antoine]

Hello,

Can one provide me informations concerning the meaning of the
value "crit. matrix fraction" that one is enjoined to answer when
using the "lat_heat_3d" keyword?

Thanks

# Parameters for latent heat and 1D temperature field
# ===================================================
# Simulate release of latent heat?
# Options: lat_heat lat_heat_3d [matrix phase] no_lat_heat
lat_heat_3d 0
# Simulation with release of pseudo-3D latent heat of phase 1 (FCC_A1)?
# Options: pseudo_3D [crit. matrix fraction] no_pseudo_3D
pseudo_3D XXX

[Bernd]

Hi Antoine,

If latent heat is used in a 2D MICRESS simulation, a 3D correction may be necessary, depending on the symmetry of the simulation domain. If all three spacial directions are equivalent like in equiaxed solidification, the 2D shape corresponds to a projection of the 3D structure to the 2D plane, and, as a consequence, there is a systematic error of the 2D phase fraction of the primary phase, leading to a corresponing error for the release of latent heat. By use of the keyword "lat_heat_3d" a correction may be possible, depending on the situation.

There are two different situations:

a) If, e.g. for a growing equiaxed dendrite, the solutal diffusion fields are not yet touching the calculation domain boundaries (initial stage of growth), then growth in the third direction (perpendicular to the 2D plane) can be considered as independent from growth in the 2D plane. Then, a geometic correction of the fraction of the primary phase is possible:

f*_alpha = ( f_alpha / (f_alpha + f_matrix ))^3/2 * ( f_alpha + f_matix )

Here, f_alpha is the fraction of a growing phase, and f_matrix is the fraction of the (vanishing) matrix phase.

b) If the solutal diffusion fields are already touching the boundaries of the simulation domain or diffusion fields of other dendrites, growth in the three dimensions is no longer independent, and the mass balance comes into play. Then the 2D fractions are correct and need no transformation.


So, one would need a 3D correction in the initial stage of solidification (e.g. for heterogeneous nucleation using the seed density model, where these corrections are essential!), but switch it off in a later stage. The critical fraction your question is referring to exactly is used for this purpose:

f*_alpha = ( f_alpha / (f_alpha + f_matrix* ))^3/2 * ( f_alpha + f_matix* )
with f_matrix* = f_matrix -f_crit if f_matrix > f_crit
and f_matrix* = f_matrix else

f_crit is the critical fraction of the matrix phase at which the solutal diffusion fields are substantially touching each other or the domain boundary. This part of the matix phase is essentially regarded as an inert phase with respect to the correction of the phase fractions, and therefor it is substracted from the matrix phase fraction. When f_matrix comes close to f_crit, the correction is automatically switched off smoothly.
Unfortunately, f_crit has to be estimated by the user, so we have one fiddle parameter more...

Bernd

[Bernd]

Of course, the last formula must read:

f'_α=(f_α/(f_α+f^*_m))^3/2 ∗ (f_α+f^*_m)

with

f^*_m = f_m -f_crit if f_m ≥ f_crit
f^*_m = 0 else