Dear Bernd,
I am looking for proper numerical parameters (grid resolution and interface mobility). Starting from a suitable grid resolution (one calculation takes 12 h) and a small size of simulation area (unit_cell_symm) the interface mobility was increased systematically.
All simulations indicate the same growth (fraction solid vs. temperature). However the calculations are showing differences concerning the circumference of each dendrite (see attached figure). It should be mentioned that no instabilities occurred during the simulation. So what do you think is the best grid resolution/interface mobility setup?
Thank you very much for your support.
Kind regards.
Martin
Numerical parameters
Numerical parameters
- Attachments
-
- Figure 1
- Calibration.jpg (9.15 KiB) Viewed 4619 times
Last edited by WTMuser on Fri Feb 24, 2012 4:03 pm, edited 1 time in total.
Re: Numerical parameters
Dear Martin,
for me it is not so clear why the circumference is changing so drastically with mobility - you are sure that there is really no instability involved?
Essentially, the only way to find that out and to know the "real" shape of the dendrite is to stepwise increase resolution until the results (circumference) get independent from mobility (in a certain range at least) - the fact that the transformation kinetics is almost independent from mobility does not mean anything in this case, as the conditions are very close to Scheil...
I know that increasing resolution does increase calculation time drastically, using 0.4 µm instead of 0.8µm would e.g. increase the calculation time by a factor of 16 in worst case (assuming that the calculation effort consists mainly in diffusion solving) or a factor of 2 in the best case (when the effort is mainly due to the phase-field or list operations). You say that you already use the smallest possible geometry (1/4 dendrite with symmetric boundary conditions). But you have to do the calibration only once, and afterwards you can use a much coarser grid!
By the way, did you include precipitation of gamma-prime phase?
Bernd
for me it is not so clear why the circumference is changing so drastically with mobility - you are sure that there is really no instability involved?
Essentially, the only way to find that out and to know the "real" shape of the dendrite is to stepwise increase resolution until the results (circumference) get independent from mobility (in a certain range at least) - the fact that the transformation kinetics is almost independent from mobility does not mean anything in this case, as the conditions are very close to Scheil...
I know that increasing resolution does increase calculation time drastically, using 0.4 µm instead of 0.8µm would e.g. increase the calculation time by a factor of 16 in worst case (assuming that the calculation effort consists mainly in diffusion solving) or a factor of 2 in the best case (when the effort is mainly due to the phase-field or list operations). You say that you already use the smallest possible geometry (1/4 dendrite with symmetric boundary conditions). But you have to do the calibration only once, and afterwards you can use a much coarser grid!
By the way, did you include precipitation of gamma-prime phase?
Bernd
Re: Numerical parameters
Dear Bernd,
I calculated the circumference of dendrites using several resolutions (0.4 - 0.8 µm). I did not include precipitation of gamma-prime phase. The calculation was performed considering two phases (fcc_a1 and liquid) and symmetric boundary conditions (1/4 dendrite). Despite of an increased resolution the contour of dendrites is changing with mobility (see attached figure and driving file).
Thank you very much for your support.
Kind regards.
Martin
I calculated the circumference of dendrites using several resolutions (0.4 - 0.8 µm). I did not include precipitation of gamma-prime phase. The calculation was performed considering two phases (fcc_a1 and liquid) and symmetric boundary conditions (1/4 dendrite). Despite of an increased resolution the contour of dendrites is changing with mobility (see attached figure and driving file).
Thank you very much for your support.
Kind regards.
Martin
- Attachments
-
- Figure 1
- Calibration_2.jpg (13.14 KiB) Viewed 4620 times
-
- unit_cell_symm_dri.txt
- Driving file
- (12.81 KiB) Downloaded 239 times
Last edited by WTMuser on Fri Feb 24, 2012 4:05 pm, edited 1 time in total.
Re: Numerical parameters
Dear Martin,
it would be interesting to compare the develolpment of the dendrite shape with time for the different mobility values. I wonder whether the differences which you measure as circumference at a late stage of solidification are already developing at an early stage of dendrite growth, or whether this is something what happens in the last stage of solidification itself.
In the first case, i.e. if the dendrite shape is already different at the beginning, I can imaging two reasons:
1.) The mobility and/or resolution is still too small for getting a mobility-independent shape
2.) The initial condition makes the problem. The shape of a dendrite tip is not well-defined in a cross-section model, and starting with a "small" grain at the beginning introduces a grid-size dependency. May be, it would be better to start with an already existing solid tip with a radius of about 5-10 µm. This would not give "more correct" results, but would probably be less dependent on the numerical parameters like mobility and grid resolution.
(Take care: Apart from increasing the radius of the initial grain, you must set the "Number of iterations for initialisation" to e.g. 10 in order to have an already smooth interface, and to slightly correct the initial composition in order to assure the correct mixture composition!)
In the case that the differences start to occure not before the end of the solidification process, the question is whether the simulation is stable at this point and whether the problem is well-defined: Does it make sense make the simulation without gamma-prime? Is the ciruumference meaningful at this stage?
My guess is that the first case is observed and morphology differences are already visible at the beginning. If my suggestions above are not helpful, please send me the rest of your input files (CMSX4.ges5, mueVonT0_1) per PM and I will try to run it myself.
By the way, do you put constant mobility values inside mueVonT0_1, or do you have some temperature-dependency?
Best wishes
Bernd
it would be interesting to compare the develolpment of the dendrite shape with time for the different mobility values. I wonder whether the differences which you measure as circumference at a late stage of solidification are already developing at an early stage of dendrite growth, or whether this is something what happens in the last stage of solidification itself.
In the first case, i.e. if the dendrite shape is already different at the beginning, I can imaging two reasons:
1.) The mobility and/or resolution is still too small for getting a mobility-independent shape
2.) The initial condition makes the problem. The shape of a dendrite tip is not well-defined in a cross-section model, and starting with a "small" grain at the beginning introduces a grid-size dependency. May be, it would be better to start with an already existing solid tip with a radius of about 5-10 µm. This would not give "more correct" results, but would probably be less dependent on the numerical parameters like mobility and grid resolution.
(Take care: Apart from increasing the radius of the initial grain, you must set the "Number of iterations for initialisation" to e.g. 10 in order to have an already smooth interface, and to slightly correct the initial composition in order to assure the correct mixture composition!)
In the case that the differences start to occure not before the end of the solidification process, the question is whether the simulation is stable at this point and whether the problem is well-defined: Does it make sense make the simulation without gamma-prime? Is the ciruumference meaningful at this stage?
My guess is that the first case is observed and morphology differences are already visible at the beginning. If my suggestions above are not helpful, please send me the rest of your input files (CMSX4.ges5, mueVonT0_1) per PM and I will try to run it myself.
By the way, do you put constant mobility values inside mueVonT0_1, or do you have some temperature-dependency?
Best wishes
Bernd
Re: Numerical parameters
Dear Martin,
you told me in a PM that you use a T-dependent mobility. How does that go together with the variation of mobility you showed - does the given value correspond to the high temperature during the initial stage of solidification?
Bernd
you told me in a PM that you use a T-dependent mobility. How does that go together with the variation of mobility you showed - does the given value correspond to the high temperature during the initial stage of solidification?
Bernd
Re: Numerical parameters
Dear Bernd,
You are right. The mobility plotted in the diagram corresponds to the high temperature during initial state of solidification (T > 1630 K). This is only a simplification in the shown diagram. Of course all values within the mobility file ("mueVonT0_1") were multiplied by the same factor (1; 1.5; 2; 2.5; 3) - assuring a consistent investigation.
Should I use a constant value?
Kind regards.
Martin
You are right. The mobility plotted in the diagram corresponds to the high temperature during initial state of solidification (T > 1630 K). This is only a simplification in the shown diagram. Of course all values within the mobility file ("mueVonT0_1") were multiplied by the same factor (1; 1.5; 2; 2.5; 3) - assuring a consistent investigation.
Should I use a constant value?
Kind regards.
Martin
Re: Numerical parameters
No, I think that anyway it is the initial stage of solidification which determines the final shape...
Bernd
Bernd
Re: Numerical parameters
Dear Bernd,
I performed a few calculations with constant start conditions ("Grain radius" = 10 µm / "Number of iterations for initialization" = 10). Unfortunately the contour of dendrites is changing with mobility (see attached figure). Do you think I should increase resolution and mobility? Maybe you can have a look on several files. I will send both, CMSX4.ges5 and mueVonT0_1 via PM.
Kind regards.
Martin
I performed a few calculations with constant start conditions ("Grain radius" = 10 µm / "Number of iterations for initialization" = 10). Unfortunately the contour of dendrites is changing with mobility (see attached figure). Do you think I should increase resolution and mobility? Maybe you can have a look on several files. I will send both, CMSX4.ges5 and mueVonT0_1 via PM.
Kind regards.
Martin
- Attachments
-
- Figure 1
- Calibration_3.jpg (13.03 KiB) Viewed 4619 times
Last edited by WTMuser on Fri Feb 24, 2012 4:05 pm, edited 1 time in total.
Re: Numerical parameters
Dear Martin,
what you show is quite reasonable! In order to see whether you get a plateau at higer mobility values you should make a series of simulations with increasing mobilities. I would increase stepwise by a factor of two up to about 1 cm^4/Js or up to when the interface profile is distroyed, i.e. the dendrite is growing in a diffuse mannor - then anyway a too high mobility value is reached for the given resolution.
If no plateau for the circumferences is found for at least 3 consecutive results, you should repeat the same procedure with a higher resolution. As the differences in circumference already appear at an early stage of dendrite growth, the simulation time for this calibration should not be so big...
Unfortunately, as I am now in New York, I cannot do such simulations myself. I will be back the 5th of March and can do it if you do not succeed up to then!
Bernd
PS: When you submit images to the forum, please use low resolution, otherwise they are displayed very big and are difficult to view!
what you show is quite reasonable! In order to see whether you get a plateau at higer mobility values you should make a series of simulations with increasing mobilities. I would increase stepwise by a factor of two up to about 1 cm^4/Js or up to when the interface profile is distroyed, i.e. the dendrite is growing in a diffuse mannor - then anyway a too high mobility value is reached for the given resolution.
If no plateau for the circumferences is found for at least 3 consecutive results, you should repeat the same procedure with a higher resolution. As the differences in circumference already appear at an early stage of dendrite growth, the simulation time for this calibration should not be so big...
Unfortunately, as I am now in New York, I cannot do such simulations myself. I will be back the 5th of March and can do it if you do not succeed up to then!
Bernd
PS: When you submit images to the forum, please use low resolution, otherwise they are displayed very big and are difficult to view!