## Transient Simulation Systematically Underestimates Keff

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terryphi
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### Transient Simulation Systematically Underestimates Keff

Hey,

Is anyone else having a problem where transient simulation systematically estimate a k-eff lower than that estimated by a static simulation?

two things I've noticed:
1) The degree of underestimation is inversely proportional to the length of the time step. A very short time step (the tmax [last] entry on the tme card) creates a very large underestimation whereas a large time step creates a small under estimation
2) The degree of underestimation is inversely proportional to the number of particles. A situation with many particles has a keff closer to the SS value.

Any clues as to what's going on?

Ville Valtavirta
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### Re: Transient Simulation Systematically Underestimates Keff

Hi,

the main problem with transient k-eff is that there actually is no such thing.

By definition, the k-eff is the eigenvalue of the k-eigenvalue formulation of the transport equation, which is not what we solve in transient simulations.

That said, Serpent does print out all manner of things that are named "KEFF" something in the _res.m file for transient simulations. The explanations for these things can be found in this post: http://ttuki.vtt.fi/serpent/viewtopic.p ... 2542#p7184

I think the best way to approach transient simulations would be to forget about k-eff completely. If you want to verify that the reactivity insertion in your transient model corresponds to the experimental value it is probably better to calculate and compare the data that was used to estimate the experimental reactivity insertion in the first place (i.e. time-dependent neutron flux signal or reactor period or something similar).

However, you can calculate something that resembles a time dependent k-eff by using detectors with time binning:

The tallied variables are

nsf = fission neutron production (prompt + delayed)
capt = capture reactions
fiss = fission reactions
nuxn = neutron production in inelastic reactions (n, xn), (n, alpha + n) etc.
leak = neutron leakage

Then, using these tallied variables the "multiplication factor" is calculated as

k = production/loss

or

k = nsf/(capt + fiss - nuxn + leak)

The inelastic production is subtracted from the loss terms.

The different variables can be tallied with different response functions for detectors:

nsf = dr -7
capt = dr -2
fiss = dr -6
nuxn = dr -16
leak = dr -17

You should note that this "multiplication" factor might not equal the time-independent eigenvalue mode multiplication factor at all points.

-Ville

vobavidiz
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### Re: Transient Simulation Systematically Underestimates Keff

Sorry to resurrect an old thread, but I would really appreciate some clarification on the MT numbers here (for myself and anyone else who finds this thread later on).
nsf = dr -7
capt = dr -2
fiss = dr -6
nuxn = dr -16
leak = dr -17
1. From what I can see in the ENDF MT page on the wiki, -6 and -7 aren't valid numbers. The ENDF-6 manual referenced on the page says that MT=6-9 are not valid in ENDF-6. Both of these actually work in Serpent 2.1.29 however.

2. Conversely, the wiki, the Serpent 1 manual and the ENDF-6 document all say that total fission is MT=18. Using that in a detector however, returns the following error:

Code: Select all

``MT -18 not allowed in response function``
3. According to the wiki, dr -17 points to the (n,3n) reaction. To estimate the leakage I have been using a surface current detector (ds) to get the net current through the outermost surface. Does this make sense?

4. Should I also be getting the inelastic production (MT=4?) to subtract from the losses?

Thanks a lot for your help.

EDIT: 5. Kind of off topic, but I've been questioning whether dr -17 actually is (n,3n) because the numbers I've been getting back are two orders of magnitude larger than those from dr -16 (n,2n).

Ville Valtavirta
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### Re: Transient Simulation Systematically Underestimates Keff

Hi,

a distinction should be made between positive and negative values for the detector response.

Positive values refer to ENDF reaction MT numbers (http://serpent.vtt.fi/mediawiki/index.p ... ion_MT.27s) and negative values refer to Serpent specific macroscopic reaction numbers (http://serpent.vtt.fi/mediawiki/index.p ... on_numbers).

-Ville