Hello,
I want to do a 3D simulation of direct solidification and have already set up my Driving file.
The Simulation works quite well, but I have still two questions about it.
1)
Is there a standardised procedure to determine the two parameter:
# Anisotropy of interfacial stiffness? (cubic)
# Anisotropy of interfacial mobility? (cubic)?
I have looked up, but have found no result, and also tried a couple of parameters, and the variation has a big influence of the solidified structure.
So I wanted to know, if there is a procedure to find the right parameters, or is there reliable literature, or is it only trial and error?
2)
Is there a good way to improve the speed of the simulation?
I have already tried to change a view points and looked up all the things, which were mentioned in the topic "Performance Optimisation - when MICRESS gets very slow" but the simulation still takes a while. Is this normal, or have i overlooked something? Most time of the simulation is used to solve the Diffusion.
I would be delighted if anyone had any tips on this topic.
Sean
3D Simulation of direct solidification
3D Simulation of direct solidification
- Attachments
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- Direct solidification.png (243.71 KiB) Viewed 463 times
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- CM186LC_TabP.txt
- (66.85 KiB) Downloaded 71 times
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- direct solidification.dri
- (26.46 KiB) Downloaded 78 times
Re: 3D Simulation of direct solidification
Dear Sean,
Nice to hear from you. Your simulation results look very nice!
Let me try to start with the first question about the anisotropy coefficients. Unfortunately it is difficult to get physical values, and there is no general strategy what to do then.
But on top of that problem, I think there is some numerical mixing between the static and kinetic coefficient which comes from the low spatial resolution which we are forced to use for performance reasons. In MICRESS, (close to) correct interface kinetics are achieved by using "mob_corr". But this mobility correction method leads to an artificial reduction of kinetics in order to correct for the "tunneling" effect, which comes from a too large numerical interface thickness (in comparison to the diffusion length). This means that the kinetic part of the front undercooling gets relevant (while in reality the kinetic coefficient and kinetic anisotropy are typically not relevant). In my understanding, this means that some part of the static anisotropy should be addressed as kinetic anisotropy in order to achieve more realistic results. Therefore, I usually use a relatively high kinetic anisotropy coefficient (like 0.2-0.3), although this is perhaps far above the physical value, while choosing a smaller one for the static coefficient (e.g. 0.1).
But there is another issue when simulating 3D: When selecting cubic symmetry, MICRESS uses a four-folded anisotropy description by default which is fine for 2D, but not correct for 3D. To invoke the 3D-equivalent, you should add "harmonic_expansion" after the "anisotropic" keyword. The further changes which are necessary are to replace the static coefficient of stiffness by a static coefficient of energy (i.e. divide the value of the coefficient by 16), and to add a second coefficient with value "0" to the static and kinetic coefficients (in the same line). You will see that this makes a difference!
Your second question was about performance. If the time spent for diffusion (in .TabP) is already a big part of the total time, there is probably not so much to gain anymore. Of course, the diffusion solver runs in parallel, so using parallel computing should help significantly. Please make sure that you are really benefiting from parallelisation by putting all threads to the same CPU. But you also should keep in mind that the diffusion time also has some serial part which counts all the redistribution stuff. This part is similar to the list time and PF-time and could still profit from a larger time step if possible (see the discussion about minimum time step).
Finally, some further comments to your input file:
- interface energy: You use an unusually high value for all interface energies which is at least 10 times higher than normal. This should lead to coarser dendrite structures.
- boundary conditions: You use symmetric conditions for all sides. Remember that symmetric boundary conditions assume mirror symmetry with the symmetry plane being inside the domain (1/2 grid cell from the border of the domain). This condition requires dendrites either to grow exactly along the boundary, or far away. Otherwise, strange effects will occur, like a liquid layer between the dendrite and the boundary. And at the top boundary condition we should always use a fixed condition for concentration when we do directional solidification with moving_frame in order to fix the far-field concentrations. Thus, I propose to use ppppii for phase-field and ppppif for concentration (you will have to enter the initial composition as fixed values again at another place).
- diffusion data: You use "diagonal g" for all element and phases in your simulation. I think, this makes sense only in case of dilute alloys where the off-diagonal terms would be small anyway. Ni-superalloys are high-alloyed (almost "high-entropy") and show strong cross-diffusion effects. Thus, the best way here is to use "multi" instead. If this has to be avoided because of performance (liquid phase) or potential problems with miscibility gaps (γ/γ'-phase), the second best option is "diagonal_dilute g" which intends to evaluate an "effective" diagonal value which also cannot be negative.
- interface thickness: You use 2.5 cells which is legitimate (and what I also did for a long time). However, increasing it slightly to 2.84 (or above) gives a significant boost in phase-field accuracy, because then also diagonal neighbors come into play when evaluating Laplace and curvature.
Best wishes and good luck!
Bernd
Nice to hear from you. Your simulation results look very nice!
Let me try to start with the first question about the anisotropy coefficients. Unfortunately it is difficult to get physical values, and there is no general strategy what to do then.
But on top of that problem, I think there is some numerical mixing between the static and kinetic coefficient which comes from the low spatial resolution which we are forced to use for performance reasons. In MICRESS, (close to) correct interface kinetics are achieved by using "mob_corr". But this mobility correction method leads to an artificial reduction of kinetics in order to correct for the "tunneling" effect, which comes from a too large numerical interface thickness (in comparison to the diffusion length). This means that the kinetic part of the front undercooling gets relevant (while in reality the kinetic coefficient and kinetic anisotropy are typically not relevant). In my understanding, this means that some part of the static anisotropy should be addressed as kinetic anisotropy in order to achieve more realistic results. Therefore, I usually use a relatively high kinetic anisotropy coefficient (like 0.2-0.3), although this is perhaps far above the physical value, while choosing a smaller one for the static coefficient (e.g. 0.1).
But there is another issue when simulating 3D: When selecting cubic symmetry, MICRESS uses a four-folded anisotropy description by default which is fine for 2D, but not correct for 3D. To invoke the 3D-equivalent, you should add "harmonic_expansion" after the "anisotropic" keyword. The further changes which are necessary are to replace the static coefficient of stiffness by a static coefficient of energy (i.e. divide the value of the coefficient by 16), and to add a second coefficient with value "0" to the static and kinetic coefficients (in the same line). You will see that this makes a difference!
Your second question was about performance. If the time spent for diffusion (in .TabP) is already a big part of the total time, there is probably not so much to gain anymore. Of course, the diffusion solver runs in parallel, so using parallel computing should help significantly. Please make sure that you are really benefiting from parallelisation by putting all threads to the same CPU. But you also should keep in mind that the diffusion time also has some serial part which counts all the redistribution stuff. This part is similar to the list time and PF-time and could still profit from a larger time step if possible (see the discussion about minimum time step).
Finally, some further comments to your input file:
- interface energy: You use an unusually high value for all interface energies which is at least 10 times higher than normal. This should lead to coarser dendrite structures.
- boundary conditions: You use symmetric conditions for all sides. Remember that symmetric boundary conditions assume mirror symmetry with the symmetry plane being inside the domain (1/2 grid cell from the border of the domain). This condition requires dendrites either to grow exactly along the boundary, or far away. Otherwise, strange effects will occur, like a liquid layer between the dendrite and the boundary. And at the top boundary condition we should always use a fixed condition for concentration when we do directional solidification with moving_frame in order to fix the far-field concentrations. Thus, I propose to use ppppii for phase-field and ppppif for concentration (you will have to enter the initial composition as fixed values again at another place).
- diffusion data: You use "diagonal g" for all element and phases in your simulation. I think, this makes sense only in case of dilute alloys where the off-diagonal terms would be small anyway. Ni-superalloys are high-alloyed (almost "high-entropy") and show strong cross-diffusion effects. Thus, the best way here is to use "multi" instead. If this has to be avoided because of performance (liquid phase) or potential problems with miscibility gaps (γ/γ'-phase), the second best option is "diagonal_dilute g" which intends to evaluate an "effective" diagonal value which also cannot be negative.
- interface thickness: You use 2.5 cells which is legitimate (and what I also did for a long time). However, increasing it slightly to 2.84 (or above) gives a significant boost in phase-field accuracy, because then also diagonal neighbors come into play when evaluating Laplace and curvature.
Best wishes and good luck!
Bernd
Re: 3D Simulation of direct solidification
Hello Bernd,
thank you very much for your comments and suggestions.
I'll try out the implementation and will get back to you if there are any problems.
Many thanks already,
Sean
thank you very much for your comments and suggestions.
I'll try out the implementation and will get back to you if there are any problems.
Many thanks already,
Sean
Re: 3D Simulation of direct solidification
Hello Bernd,
i have tried to implement the harmonic_expansion model to the simulation, but now i have a problem with the formation of the dendrites.
As you can see, solidification does not take place in the typical formation of dendrites in the cubic system. I have other directions of growth in the solidification that make no sense.
I have already tried different values for the anisotropy parameters, but the results are always similar.
Could it be that I have overlooked something else that needs to be taken into account with "harminic_expansion"?
Best regards and many thanks already
Sean
i have tried to implement the harmonic_expansion model to the simulation, but now i have a problem with the formation of the dendrites.
As you can see, solidification does not take place in the typical formation of dendrites in the cubic system. I have other directions of growth in the solidification that make no sense.
I have already tried different values for the anisotropy parameters, but the results are always similar.
Could it be that I have overlooked something else that needs to be taken into account with "harminic_expansion"?
Best regards and many thanks already
Sean
- Attachments
-
- direct solidification.png (132.48 KiB) Viewed 413 times
-
- direct solidification.dri
- (26.68 KiB) Downloaded 63 times
Re: 3D Simulation of direct solidification
Hi Sean,
it seems you applied the factor of 16 also to the kinetic anisotropy coefficient, which is not correct: It should be only the static one!
Thus, you are missing kinetic anisotropy. This, although physically viable, is not useful with phase-field simulations which are not extremely fine resolved.
Please try a higher kinetic anisotropy coefficient (0.2-0.3) which hopefully will bring your dendrites back.
Bernd
it seems you applied the factor of 16 also to the kinetic anisotropy coefficient, which is not correct: It should be only the static one!
Thus, you are missing kinetic anisotropy. This, although physically viable, is not useful with phase-field simulations which are not extremely fine resolved.
Please try a higher kinetic anisotropy coefficient (0.2-0.3) which hopefully will bring your dendrites back.
Bernd
Re: 3D Simulation of direct solidification
Hi Bernd,
I must have misunderstood.
With the higher kinetic anisotropy, I have a dendritic form again.
Thank you very much
Sean
I must have misunderstood.
With the higher kinetic anisotropy, I have a dendritic form again.
Thank you very much
Sean