Solidification simulation under casting

[Bernd]

Hi betleenkim,

I am not sure whether the basic concept is clear for you, and I think I should make some points more clear:

1.) The "3wt%_lat_heat_dTLat" file is (besides the initial temperature profile) the only source of information for the 1d-temperature solver (outside the microstructure domain) throughout the whole simulation! That means, that the tabulated values for Cp, H and lambda given there should cover all the temperatures which occur or will occur somewhere in the 1d-temperature field during the whole simulation run.

2.) In order to obtain such a file you can:
- use Thermo-Calc to calculate the cp and H for the whole temperature range, assume e.g. a constant value for lambda
- make first a solidification simulation without 1d_temp option, but with "lat_heat", "lat_heat_3d" or "lat_heat_dsc", and copy the resulting .dTLat file to "3wt%_lat_heat_dTLat"
- use the .dTLat output of an older similar simulation which covers the expected temperature ranges, and copy it to the "3wt%_lat_heat_dTLat" file. Sometimes it makes sense to combine data if e.g. you have low temperature data from one simulation and high temperature data from another one.
- make a solidification simulation with 1d_temp, but using a very short 1d-temperature field which has exactly the same length as the microstructure domain in z direction. Then, the "3wt%_lat_heat_dTLat" file is read but not used. Afterwards, copy the resulting .dTLat file to "3wt%_lat_heat_dTLat".

3.) To fulfill the "homoenthalpic" condition, a few iterations have to be made: After each simulation, copy the .dTLat output to the "3wt%_lat_heat_dTLat" file and rerun the simulation, until nothing is changing any more.

4.) If solidification is successfully finished, you should have a consistent "3wt%_lat_heat_dTLat" file which contains information over the whole temperature range, and which can be used for the heating simulation. If you use the "restart reset_time" option, you need to change only the temperature value at the bottom boundary condition of the 1d-temperature field. Changing the initial bottom and top temperatures does not change anything, because the temperature profile is overwritten from the restart file!

Please note, that you are trying to do something very advanced, and you are probably the first MICRESS customer who is doing so! But your plans are absolutely reasonable, so please don't worry if you do not understand everything immediately!

The .numR output is activated by the "out_relin" output option.

If the error persists, I would go on checking the following:

- in which interface (between which phases) does the error occur?
- at which temperature?
- at which place, dual interface, triple juncion? (see .numR output)
- if this phase interaction did exist before (i.e. not nucleation of new phase), are the linearisation parameters (.TabLin file, output option "tab_lin") consistent, and similar as during the solidification simulation, or are they completely wrong? And what about the initial linearisation parameters of this phase interaction (probably written in the .log file)?

Bernd

[betleenkim]

Dear Bernd

First of all, i really appreciate your continous support.

By following your advice, i could do cooling and heating simulation successfully
I used thermodynamic data such as Cp and entalphy from Thermo_calc. calculation.

However, when i try 1D_temp simulation with thermodynamic data from lat_heat mode.
There is an error message in the window as follow,

Data reading error.pdf

(142.44 KiB) Downloaded 305 times

It seems that MICRESS cannot read the data properly, i did not have such an error during simulation with the data from thermo_calc. I sent both of the files that are used for the simulation via your e-mail.

Thank you again.

Best regard

[Bernd]

Hi betleenkim,

this problem is easy to solve! For interpolation of the data for a given temperature, temperature has to continuously decrease in the data. In your case, temperature was increasing ("recalescence") at the beginning of your first simulation, leading to also increasing temperature at the beginning of the .dTLat output. This is not allowed, because interpolation is impossible!

The solution is to delete the first few lines where temperature is increasing!

If the tab_log interval is very small, it may occur that somewhere in the .dTLat file two lines have the same temperature value. Then MICRESS will also complain. Then just delete one of the two lines. Unfortunately, as the file internally is read starting from the end, the error message is somehow misleading - the line number is also counted from the end !

By the way: In the data you sent me by mail, the initial values of Cp which you calculated using Thermo-Calc are also given. Cp here should be the genuin heat capacity, not the "apparent" heat capacity (which implicitly includes latent heat from the phase transformation). If you compare with the .dTLat output, you see the difference!
But maybe this is not so important, because you use the data only as start values for the iteration...

Bernd

[betleenkim]

Dear Bernd

Thank you for your reply.

Now i understand what the problem is. Thank you.
And i checked result dTLab flie in the 1D_temp mode. And i found that the result value is not much different with the dTLab file from lat_heat mode. I think this is because the input dTLab file in 1D_temp mode is only for the initiation of simulation as you told me.

I will report you any progress in my simulation.

Best regard

[betleenkim]

Dear Bernd

I have a question about the cooling rate.

My simulation starts at 1765K and firstly it is cooled to 723K.
So far i set proper heat conductivity in lat_heat mode to have average cooling rate as 20 K/s.
However, in real case the cooling rate is much slower than it like 20k/h.
If i cool the system to 723K, it will take more than 100000s with this cooling rate.

Is there any way to speed up the simulation?

Best regard

[Bernd]

Hi betleenkim,

in general, if a solidification (or any other) reaction is very slow, the microstructure which forms will be coarse. This allows you to increase the grid spacing, which results in a huge performance gain due to much bigger time steps.
This helps you when simulating slow processes!

Bernd

[betleenkim]

Dear Bernd

Thank you for your reply.
But i have still question about your answer.

For example, I set the domain size as 150um X 150um and the size of grid cell is 10um.
Then i have to put 15 cells along the x and z direction. When i listen to one of your lectures in Germany, i have to put the interface thickness over than "4" to get reasonable result. In this case, the numerical interface thickness should be 40um!!
Is this acceptable for a simulation? I even cannot resolve phase when i checked result phas.mcr file.

Best regard

[Bernd]

Dear betleenkim,

Indeed, I recommend the use of 4 cells interface thickness (or at least 3.5) for solidification simulations which are concentration coupled. But please keep in mind that in case of using fd_correction (which we recommend) you have to substract 1 cell due to the changed interface thickness definition: Then you should use at least 2.5 cells, better 3.
The question how fine the resolution has to be depends not only on the cooling rate but also on the segregation behaviour of the alloy. It is of great help if you know the secondary arm spacing which depends on t_solidification^1/3. As a rule of thumb, you need at least 30 cells per secondary arm spacing.
100000s is a long time, but important is the solidification time, i.e. the time between solidus and liquidus temperature. This is considerably shorter. I guess that 10µm is too much...

The correct (but time-consuming) method is the following (see also here):
1.) Select the smallest representative domain size (1/2 dendrite in 2D in case of directional solidification), under typical thermal conditions. Make a reference simulation for high resolution. Resolution has to be such high that for systematically increasing the interface mobility, a plateau is reached for the solidification rate (e.g. fraction solid over time). This plateau is the reference solution. It is sufficient to do that for the first part of solidification (dendrite tip), because for the later solidification time, grid resolution is much less critical as the speed of the solidification front is decreasing rapidly.
2.) Increase grid spacing step-wise, and adjust mobility such that the correct kinetics of the reference solution from 1.) is reached. If the interface is crashing before reaching the needed interface mobility, grid spacing is too high.

In many cases, qualitative kinetics are sufficient, e.g. if the focus is on secondary phases or subsequent solid-solid transformations.

Bernd

[betleenkim]

Dear Bernd

Thank you so much for your reply
I have several questions regarding your suggestions.

1) You mentioned i should have at least 30 cells per secondary arm spacing. What does it mean? Does it mean that if the arm spacing is like 5 um for example, i have to have 150 cells at least for simulation so i can make 150 um in domain size along z-direction when i put cell spacing as 1 um? In addition, how do you get the value of 30 cells?

2. As you know, if i change cooling rate, the liquidus and solidus lines are also changed. In this case, i think i have to start a simulation with a specific cooling rate (in this case very slow cooling rate) in high resolution domain first to make reference simulation. If then, i think it does not have any meaning changing grid spacing to speed-up the simulation (anyway i have to do a simulation that takes much time). Do you mean that do the simulation with a specific cooling rate in high resolution system until second phase (BCC) is started to be formed?

3. Finally, what does it mean? "1/2 dendrite in 2D in case of directional solidification"

Thank you again!!

Best regard

[Bernd]

Dear betleenkim,

Here my answers to your points:

1.) Yes! The number 30 is only an estimation, which is based on my personal experience and which takes into account that the dendrite arms, which have to be resolved by the numerical grid, are fine when they form and coarsen during solidification.

2.) The solidification interval (temperature interval between solidus and liquidus) does not depend so much on cooling rate, because the typical lengthscales (grain size, primary and secondary dendrite arm distances) also change with cooling rate! Anyway, the high-resolution simulation has to be performed with the required cooling conditions, therefore it is important to restrict the domain size to the smallest representative "unit cell" (see below).
Another question is which is the critical process part which defines the requirements for the grid resolution. In case of a peritectic system, it can be either the primary dendrite growth or the peritectic reaction. I cannot answer this question because it depends on one side on your interests (i.e. the questions you want to answer with the simulations), and on the other side on the specific conditions like alloy composition, nucleation undercooling etc.
If you want to obtain quantitative results for both processes, you should include both steps (onset of dendrite growth until onset of peritectic growth) into your calibration. But don't forget that for dendrites, 2D growth kinetics are very different from 3D kinetics, and a 3D calibration of this kind is (practically) impossible because of the huge calculation times!

3.) Formation of secondary arms depends on the primary distance, therefore you cannot make the domain width smaller than half of this distance (using symmetric boundary conditions in east and west direction). Setting the size of the domain to the half primary dendrite spacing, putting the initial seed to the lower right or left corner and a temperature gradient in z-direction corresponds to the "unit cell" for
directional dendritic solidification. In 3D, it would be analog, but 1/4 dendrite.

Bernd