cimlib\tests\modele\Binary_DirectionalSolidification\Temperature_gsTabule_couplageCA

Note:
Changes to do to transform the test case to an Exercice and obtain outputs corresponding to curves below:
In Maillage.mtc: change the value of TemperatureInitialeC from 630 to 800
In Increment.mtc: change the value of TempsFin from 50 to 1000
Results of reference for the long simulation are available in the test folder

Table of caracteristics of the model

In this model, the solid fraction is linked to the temperature through a tabulation. For temperatures is the mushy zone, this tabulation corresponds to the Gulliver-Scheil model ($f_S\rvert_{GS} = 1- \left(\frac{T_M-T}{T_M-T_L}\right)^{1/(k-1)} $ where $k$ is the segregation coefficient; $T_M$ is the melting temperature and $T_L$ is the liquidus temperature corresponding to the nominal composition). For temperatures under the eutectic temperature, the solid fraction is equal to $1$.

In this test case, the temperature evolution is coupled with a grain growth process modeled with the cellular automaton (CA) model (Cellule.mtc).
In the CA model, four grains nucleate in the bottom surface of the domain, with a nucleation undercooling of 0.1K. One has to note that the nucleation process can also be modeled through a nucleation surface density description (see the file grainsSurface.dat). In agreement with the front tracking model, the growth law chosen is the law “Puissance”, with “NbTermes”=1; “Coefficients”=2.9e-6 and “Exposants”=2.7 such that grain tips have a velocity $v=2.9e^{-6} \Delta T^{2.7}m.s^{-1}$. “TFusion” is taken equal to the liquidus temperature of the alloy.

Due to the CA coupling, the link between the temperature and th solid fraction is not straightforward. In order to compute a solid fraction which permits to conserve the enthalpy, a H2T conversion is performed after the CA model instead of a T2H conversion (see Increment.mtc).

In the simulation, the temperature field and the solid fraction field are recorded on sensors which are placed every 2 cm along the z direction. In the following figures, solid lines correspond to outputs of the simulation on these sensors and dotted lines correspond to results of the fornt tracking model presented on page Front tracking 1D (for interfaces with low undercoolings).

Outputs on the temperature field on sensors

Outputs on the solid fraction field on sensors

It can be observed that, at the beggining of th solidification process, the solid fraction computed on sensor 1 is lower than the one given by the front tracking model. This is because the coupling with the CA model generates a mushy fraction $f_m$ which is lower than 1. Therefore, $f_S=f_m f_S\rvert_{GS}$.