## Calculation of heat distribution

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Kotov_Y
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### Calculation of heat distribution

Hello, I want to ask about heat detectors (dr -4 and -8).
I want to get correct power distrubition in both fuel and non-fissile materials, but when I'm using detectors with macroscopic total heating cross section response (dr -4), total power is lesser (9-14%) than described in "set power". Relative power distribution looks similar in comparison to other codes.
Value from detector with total fission energy production (dr -8) matches, but there is no heating in non-fissile materials (obviously) and distributions slightly differs.
In coupled calculations with gamma-transport, the contribution of gamma heating is smaller than the difference (3-6%, not ~10).
Am I making a mistake in detector definition or is there any problems with neutron data (using ENDF/B-7.1 processed with NJOY, same result with libraries from distribution package)? Which is the correct way to get heat distribution in all materials?
Thanks!

Riku Tuominen
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### Re: Calculation of heat distribution

Hi,

the differences you are seeing are related to the normalization to total fission power (set power). With this option the normalization is based on the total energy deposition in fission reactions. Energy deposition per fission for nuclide i is calculated as:

E_dep = Q_i/Q_235*H_235,

where Q_i is the fission Q-value for nuclide i, Q_235 is the fission Q-value for U235 and H_235 = 202.27 MeV (by default). The fission Q-values are read from ACE-data and the H_235 is an empirical value for energy deposited per U235 fission in a light water reactor. It includes all of the recoverable components of fission energy release, which are kinetic energy of fission products, kinetic energy of prompt and delayed neutrons, energy of prompt and delayed gammas and energy of delayed betas. In addition it includes a contribution by additional energy released in capture reactions. Response number -8 uses the same energy deposition per fission values as the normalization and therefore the result from dr -8 detector matches the power given in input with set power option.

With dr -4 the energy deposition or heating is calculated based on KERMA (Kinetic Energy Release in Materials) coefficients, expressed in eV*barns. These coefficients relate the neutron flux to the neutron heating rate and they can be calculated with the HEATR module of NJOY. More information on KERMA coefficients is available in the HEATR part of NJOY manual. When you calculate the heating with KERMA coefficients (dr -4), you get more specifically the local prompt neutron heating. Therefore delayed heating and energy of prompt gammas created in reactions are not included. For fission this means that the energy of the delayed betas, prompt gammas and delayed gammas are not included in the heating. Energy of prompt gammas created in reactions such as inelastic scattering and radiative capture are not included either. The result is that the tallied energy deposition per fission is lower with dr -4 compared to dr -8 . In coupled neutron-gamma transport calculation you can tally the energy of prompt gammas but you are still missing the delayed heating.

So the real issue is the fact, that energy deposition used for the normalization is calculated in a non-consistent way with regard to the detectors you are using. At the moment, there is no option in Serpent to normalize the results based on the energy deposition calculated with KERMA coefficients. We are currently developing a new energy deposition treatment for Serpent with similar features as those presented in [1]. The new features should solve this issue with normalization. What you could do at the moment, is to simply scale the sum of the energy deposition detectors (dr -4 and photon heating) to match the total system power, i.e. multiply the detector values with the ratio of the total system power and the current sum of the detector powers. Since the normalization simply sets a scalar scaling factor for all of the results, this should give you the power you want. However, you are still missing the delayed heating.

Riku

[1] D. P. Griesheimer and M. H. Stedry, “A Generalized Framework for In-line Energy Deposition During Steady-state Monte Carlo Radiation Transport", in Proceedings of International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M & C) 2013, Sun Valley, Idaho, May 5-9, 2013.

Kotov_Y
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### Re: Calculation of heat distribution

And one more clarifying question, energy carried away with neutrinos is not included in E_dep which is used for normalization to total fission power? Total potential heating energy per fission is ~193.4 MeV for U235 (according to ENDF/B-7.1 MT458), is this value used in Serpent 2 by default or ~202.2 MeV (for U235)?

Jaakko Leppänen
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### Re: Calculation of heat distribution

The difference doesn't come from neutrinos. The 202.2 MeV value includes an approximation for additional binding energy released in capture reactions. The numbers are confusingly similar.
- Jaakko

Kotov_Y
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### Re: Calculation of heat distribution

Thank you! With power distribution calculation everything is clear.

I am asking about energy carried away by neutrino because some other codes are using total fission energy without this component (~193.4 MeV for U235) for normalization to power.
I compared fluxes in a simple task and found that Serpent 2 gives ~4.3% less flux value then other software. When adding to input

Code: Select all

``set U235H 193.4``
the result becomes the same. It turns out that Serpent includes neutrino energy into power for normalization, сorrect me if I am wrong.
So, it looks like it also can lead to some deviations in direct results comparison.

Jaakko Leppänen
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### Re: Calculation of heat distribution

You are wrong. The difference between 193.4 MeV (recoverable energy) and 202.2 MeV (deposited energy) does not come from neutrinos. It comes from an approximation that neutrons produced in fission are absorbed in the geometry, and additional binding energy is released in (n,gamma) reactions.
- Jaakko

Kotov_Y
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### Re: Calculation of heat distribution

Yes you are absolutely right.
I was really confused by the fact that neutrinos energy is very similar to photons energy from radiative capture (as you wrote) and radiative capture gamma usualy isn't listed in fission energy components.
Thanks for the clarification!

MohammedQah
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### Re: Calculation of heat distribution

Hi serpent users,

Thank you for your active participation which indeed is valuable for all users.

As I am doing some heating calculation from light particles, mainly gamma, so if I used dr -4 I will get (b.eV) at a specific location. This (b.eV), as I understood, came from both n and p (if I used photon transport). You mentioned that there is no delay heat contribution. My question what If I have isotopes that emit gamma from the inventory, does dr -4 will count it? and what about dr -8, does it give the same unit?

Regards

Ville Valtavirta
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### Re: Calculation of heat distribution

Hi,

dr -4 will give you results in Watts (criticality source mode) or Joules (external source / dynamic simulations). Furthermore dr -4 is the KERMA cross section only for neutrons (not gammas). See: http://serpent.vtt.fi/mediawiki/index.p ... on_numbers

Each detector will only score one particle type, which you can choose in the detector definition http://serpent.vtt.fi/mediawiki/index.p ... manual#det. The default particle type to be scored is neutron.

dr -8 will also give Watts (criticality source mode) or Joules (external source / dynamic simulations), but the physics behind the response are different as explained earlier in this topic.

For photon heating it is probably better to use the analog photon heating response (dr -12) with a photon detector. The output unit is the same as in the neutron dr -4 and dr -8, but the physics is obviously different.

For coupled neutron-photon simulations, the only photons that are tracked are those that are directly born from neutron reactions. These do not include photons coming from, e.g. fission or activation products.

There is the option to run a separate simulation using depleted material compositions to calculate the heating due to photons emitted from the radioactive decay of the compositions: http://serpent.vtt.fi/mediawiki/index.p ... al_example

-Ville

MohammedQah
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### Re: Calculation of heat distribution

Thank you Ville, that was exactly what am looking for.