Some questions about lat_heat

dendritic solidification, eutectics, peritectics,....
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dingling312
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Some questions about lat_heat

Post by dingling312 » Wed May 13, 2020 12:23 pm

Dear Bernd,
Hi, there are some questions about lat_heat :
1、Why can't I control the cooling rate after choosing lat_heat without 1d_temp, but can only choose the heat flow? What equation is this based on?
2、If I couple TQ, do I not need to use 1d_temp?
3、If I choose no_lat_heat, do I completely ignore latent heat or use some implicit algorithm such as temperature compensation?

Best Regards
Ling

Bernd
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Re: Some questions about lat_heat

Post by Bernd » Wed May 13, 2020 4:22 pm

Hi Ling,

1. You cannot control both, temperature and heat flow at the same time. If you specify temperature, latent heat cannot have any effect - apart from the net heat flow, which you can get as an output if you use "no_lat_heat_dsc". If you specify "lat_heat", then the assumption is that latent heat is calculated and equally distributed over the simulation domain. In this case, the heat flow (integral over the domain boundaries) needs to be specified in order to calculate the temperature of the domain (in case you specify a temperature gradient, this would be added on top of that, which probably makes sense only for small gradients). For model equations see here:
- B.Böttger, J.Eiken, I.Steinbach, Phase field simulation of equiaxed solidification in technical alloys. Acta Materialia 54 10 (2006) 2697.
- B. Böttger, J. Eiken, M.Apel, Phase-field simulation of microstructure formation in technical castings – A self-consistent homoenthalpic approach to the micro–macro problem, J. Comput. Phys. 228 (2009), 6784-6795.

2. There is no connection between the temperature coupling model and using thermodynamic databases or not. The only difference is that Cp and H can taken from database in case of TQ coupling and must be specified otherwise.

3. Yes. In this case you specify temperature and latent heat has no effect.
However, I don't know what you mean by "temperature compensation", but if you specify the temperature time curve such that it already includes the effect of latent heat (e.g. calculated in a prior simulation or another tool), then this would also be an implicit way of including latent heat...

Bernd

dingling312
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Re: Some questions about lat_heat

Post by dingling312 » Thu May 14, 2020 10:09 am

Dear Bernd,

Thanks for your reply.
I learned from the article you provided that for larger temperature gradients, I can use the Bridgman approximation (directly using the temperature gradient G and the cooling rate v, ignoring latent heat), and for small temperature gradients, I can use the DTA approximation(Use lat_heat, add heat flow), I do not know if my understanding is correct? There is also how to distinguish the large and small temperature gradient G, how much can be considered large?
For a temperature gradient G (such as 10) that I think is small, is it due to the addition of latent heat leads to a more uniform temperature distribution, so it is more difficult to form dendrites than that no latent heat is added.
When the temperature gradient is 10, what range does heat flow usually take? How can I get this parameter for the solidification process?

Ling

Bernd
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Re: Some questions about lat_heat

Post by Bernd » Thu May 14, 2020 4:36 pm

Hi Ling,

For deciding which thermal boundary conditions should be used on the microscale it is important to have knowledge of the macroscopic problem. Heat diffusion appears on the length-scale of the macroscopic casting, while solute diffusion and curvature define the microstructural length scale. Coupling between the scales can be quite tricky, and it depends on the circumstances which variables have to be passed from the macro-scale to the micro-scale, and what has to be done to achieve a consistent solution between the macroscopic heat fluxes and the microscopic (i.e. microstructure-related) formation of latent heat (see the second paper about the "Homoenthalpic Approach" which I mentioned in my last post).

The situation is simple only in Bridgman-like castings where the heat flux is generated by simultaneous heating and cooling, and thus widely decoupled from latent heat release. Only in this case, the temperature field (gradient, cooling rate) can simply be taken from the macro-scale (experiment, process simulation). This is what we call "Bridgman approximation".

There are some types of processes on the micro-scale where the same "Bridgman" approach can also be used without problems:
- Slow processes which are occurring during isothermal holding or slow cooling or heating, like homogenisation, Ostwald ripening, rafting, etc. Here, no temperature gradient is assumed, and latent heat can be dissipated without changing temperature considerably.
- Processes which do not have a significant latent heat, like grain growth
- Processes in thin films on a substrate,which can fully absorb latent heat

In all other cases, latent heat must lead to temperature gradients, because any heat flux is always accompanied by a temperature gradient. Then, heat flux and heat production are not independent, which means that the macro and the micro-problem must be solved simultaneously or iteratively. With MICRESS we generally recommend the "Homoenthalpic Approach" for that.
But there is an exception: If samples are very small ("DTA approximation"), due to fast heat diffusion no temperature differences exist inside the sample, and latent heat can be equally distributed to the whole sample (= microstructure simulation domain).

For the approach which you should apply for solidification simulations, this means that the value of the temperature gradient is not the only criterion for the approach you should use. In the initial stage of a continuous casting process, e.g., you may have huge temperature gradients, and (at least for a short time period) latent heat may not be relevant for microstructure formation. However, the development of the temperature gradient with time will strongly depend on microstructure formation! Thus, using the Bridgman approach and taking the time-dependent gradient e.g. from a macrosimulation would not be correct, as long as the latent heat assumed in this simulation does not exactly correspond to the microstructure evolution which will be predicted on the micro-scale. Even if you would have the temperature-time behaviour from reliable experiments, the microstructure prediction could be wrong, if the thermodynamic database used does not fully correspond with reality...
Therefore, we used the Homoenthalpic Approach for this type of simulation despite the high temperature gradient (see B.Böttger, M.Apel, B.Santillana, and D.G.Eskin, Relationship Between Solidification Microstructure and Hot Cracking Susceptibility for Continuous Casting of Low-Carbon and High-Strength Low-Alloyed Steels: A Phase-Field Study, Metallurgical and Materials Transactions A 44 5 (2013) 3765.)

Of course, with simulation work we are generally used to make simplifications, and it may be accurate enough to use the "Bridgman" or "DTA" approximation also in some cases which strictly speaking do not belong to those described above. However, to make this decision, it is important to know the macroscopic process details. On the other hand, using the Homoenthalpic approach is often not that complicated, especially if the temperature problem can be (locally) approximated as 1-dimensional (plate, cylinder, sphere), and the built-in 1d-temperature solver of MICRESS can be used for that purpose.

Can you say more about the macroscopic casting problem you want to address?

Bernd

dingling312
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Re: Some questions about lat_heat

Post by dingling312 » Sun May 17, 2020 10:19 am

Hi, Bernd

Thank you once again.
For example, I simulate the dendrite growth of the solidification process of the titanium alloy prepared by VAR. I have used comsol finite element to simulate the temperature field change of the solidification process (have considered the influence of latent heat). Can I directly import the obtained local temperature gradient and cooling rate parameters into micress as Bridgman approximation, is this reasonable?
Or the temperature field parameters obtained by the finite element simulation can be imported into micress as a 1d_temp and the lat heat calculated by TC can be used to obtain the Homoenthalpic approximate results. I do n’t know if my understanding is correct?

Ling

Bernd
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Re: Some questions about lat_heat

Post by Bernd » Mon May 18, 2020 10:07 am

Hi Ling,

I think VAR is an example where you really should apply the Bridgman approximation, i.e. just take temperature trend and gradient from your macroscopic simulation. In VAR, similar as in Bridgman furnaces, you indeed have simultaneous heating and cooling which efficiently takes away effects of latent heat on the microscale.

Just for your understanding: If you would need to use the Homoenthalpic approach, you would have the choice either to use your macroscopic solver or the 1d-temp field of MICRESS for the iterative determination of a consistent temperature solution. In the first case, you would import the temperature field (temperature trend, gradient) into MICRESS and export the latent heat data (.dTLat, obtained in no_lat_heat_dsc mode) to the macroscopic solver (if this is technically possible). Then you would redo the macrosimulation and the MICRESS simulation with the new data and iterate until the solution doesn't change anymore.
In case of using the 1D_temp solver in MICRESS it is essentially the same, just that you need no extra tool, but (locally) approximate your temperature solution to 1D. You can see in our A002_AlCu_Temp1d_dri standard Application example, how the data from the .dTLat file are re-imported into MICRESS.

Bernd

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