Calculation of Six-Group Delayed Neutron Fractions and Decay Constants

User Support
1

Hi everyone,

I have performed calculations using three different methods to compute six-group delayed neutron fractions and decay constants.

  1. First method (TALLY1/TALLY2): I used the MGXS API, specifically the decay rate calculation as described here: (openmc.mgxs.DecayRate — OpenMC Documentation)
  2. Second method (TALLY3/TALLY4): I created a DelayedGroupFilter using openmc.DelayedGroupFilter for the six delayed neutron groups and selected the scores for delayed-nu-fission and decay-rate.
  3. Third method (TALLY5): I used the IFP calculation feature from the development branch (Kinetics parameters using Iterated Fission Probability by JoffreyDorville · Pull Request #3133 · openmc-dev/openmc · GitHub).

My issue is that the total delayed neutron fractions calculated using the first two methods are identical (with a total around 0.0058), but differ from the result obtained with the third method (total around 0.0065). Since I’m using UMo fuel enriched to 93.1%, I believe the total delayed neutron fraction should be closer to 0.0065 (U-235). Which result is more reasonable in this case? Is there a problem with my Settings?

Additionally, the decay constants for the six delayed neutron groups seem to have a maximum magnitude of only around 10^−4 s^−1. Is this a reasonable result for these calculations?

Lastly, I used **CAD_to_OpenMC** to convert STEP files directly into a single universe. Could this process have caused any issues with the above calculations?

I would appreciate any insights or suggestions!

Thank you!
Zeqin Zhang

 ============================>     TALLY 1     <============================

 Universe 2
   Delayed Group 1
     Total Material
       Delayed-Nu-Fission Rate              0.000219771 +/- 7.83802e-08
   Delayed Group 2
     Total Material
       Delayed-Nu-Fission Rate              0.000975307 +/- 3.50142e-07
   Delayed Group 3
     Total Material
       Delayed-Nu-Fission Rate              0.000639236 +/- 2.27231e-07
   Delayed Group 4
     Total Material
       Delayed-Nu-Fission Rate              0.00129839 +/- 4.63439e-07
   Delayed Group 5
     Total Material
       Delayed-Nu-Fission Rate              0.00204504 +/- 7.3196e-07
   Delayed Group 6
     Total Material
       Delayed-Nu-Fission Rate              0.000618977 +/- 2.16205e-07
 ============================>     TALLY 2     <============================

 Universe 2
   Delayed Group 1
     Total Material
       Decay Rate                           2.73982e-06 +/- 9.77142e-10
   Delayed Group 2
     Total Material
       Decay Rate                           2.75931e-05 +/- 9.9061e-09
   Delayed Group 3
     Total Material
       Decay Rate                           2.71831e-05 +/- 9.66286e-09
   Delayed Group 4
     Total Material
       Decay Rate                           0.000172741 +/- 6.16568e-08
   Delayed Group 5
     Total Material
       Decay Rate                           0.000598108 +/- 2.14074e-07
   Delayed Group 6
     Total Material
       Decay Rate                           0.00041254 +/- 1.44098e-07
 ======================>     TALLY 3: NU-FISSION     <======================

 Total Material
   Nu-Fission Rate                      1.0088 +/- 0.000349121
 ================>     TALLY 4: DELAYED_NEUTRON_TALLY     <=================

 Material 1
   Delayed Group 1
     Total Material
       Delayed-Nu-Fission Rate              0.000219771 +/- 7.83802e-08
       Decay Rate                           2.73982e-06 +/- 9.77142e-10
   Delayed Group 2
     Total Material
       Delayed-Nu-Fission Rate              0.000975307 +/- 3.50142e-07
       Decay Rate                           2.75931e-05 +/- 9.9061e-09
   Delayed Group 3
     Total Material
       Delayed-Nu-Fission Rate              0.000639236 +/- 2.27231e-07
       Decay Rate                           2.71831e-05 +/- 9.66286e-09
   Delayed Group 4
     Total Material
       Delayed-Nu-Fission Rate              0.00129839 +/- 4.63439e-07
       Decay Rate                           0.000172741 +/- 6.16568e-08
   Delayed Group 5
     Total Material
       Delayed-Nu-Fission Rate              0.00204504 +/- 7.3196e-07
       Decay Rate                           0.000598108 +/- 2.14074e-07
   Delayed Group 6
     Total Material
       Delayed-Nu-Fission Rate              0.000618977 +/- 2.16205e-07
       Decay Rate                           0.00041254 +/- 1.44098e-07
 ======================>     TALLY 5: IFP-SCORES     <======================

 Total Material
   IFP lifetime numerator               6.50935e-06 +/- 3.87642e-08
   IFP delayed fraction numerator       0.00651876 +/- 7.32322e-05
   IFP common denominator               0.957423 +/- 0.000273481
2

Hi Zeqin Zhang, welcome to the openmc community.
Sorry if I am not giving a proper response, but if you want to know which methods fit your case scenario, then I think you could check with some benchmark cases which has the reference beta-eff value and within the same type of case scenario that you are doing.
Or if you are using another production code like serpent or mcnp, then you could compare your calculated results between each code.
Then regarding the methods, I think basically the 1st and 2nd approaches that you already mentioned are the same since both methods use the same tally score, delayed-nu-fission and decay-rate. So if you want to add more methods, then you could try the prompt methods that have been mentioned in this discussion
scores for delayed-nu-fission and decay-rate

Actually, thank you for mentioning Joffrey Dorville’s works for IFP. I didn’t know that that script existed before you mentioned it. However, I think Joffrey is still doing some tests with benchmark cases to make sure that the implementation in openmc was consistent with benchmark data. I hope this feature can be merged into the openmc main channel soon after the benchmark tests. IFP is one method that takes into account the adjoint weighted neutron flux, so it will be different from the prompt methods but honestly, I don’t know how much the difference will be, is it still below 50 pcm? Don’t know, I hope other experienced members will give their comments here.