Delta-tracking and boron control rods.

Share your results and discuss how Serpent compares to other neutron transport codes or experimental data
Post Reply
User avatar
Jaakko Leppänen
Site Admin
Posts: 2446
Joined: Thu Mar 18, 2010 10:43 pm
Security question 2: 0
Location: Espoo, Finland
Contact:

Delta-tracking and boron control rods.

Post by Jaakko Leppänen » Tue May 08, 2012 9:53 am

The fact that the sampling efficiency of Woodcock delta-tracking deteriorates in the presence of localized high-absorbing materials is a well-known flaw for the tracking method, and Serpent attempts to avoid this problem by switching to surface-tracking when the probability of sampling a virtual collision is above a certain threshold value (set to 0.9 by default). The methodology is described in reference:

J. Leppänen. "Performance of Woodcock Delta-Tracking in Lattice Physics Applications Using the Serpent Monte Carlo Reactor Physics Burnup Calculation Code." Ann. Nucl. Energy, 37 (2010) 715-722.

and it has been shown to perform well with burnable absorber pins containing gadolinium.

However, discussions at UC Berkeley last week brought up a potential concern related to the performance of delta-tracking with other absorber types, specifically control rods containing boron. Unlike Gd-155 and -157, which are essentially thermal absorbers, boron-10 is a 1/v absorber, with a relatively high absorption cross section spanning a much wider energy range (see the attached figure). The fact that the combined DT/ST method works so well with thermal absorbers may be due to the fact that the performance is good at higher energies, where the neutron mfp's are also long. This is almost certainly not the case if the majorant cross section is clearly dominated by a 1/v absorber.

To test whether this is the case with some typical boron absorbers, I ran a set of calculations in two geometries:

1) a VVER-440 lattice calculation with a flux-trap control element containing boron steel
2) a BWR lattice calculation with a cruciform control rod containing boron carbide

The boron in both cases was of natural composition, with about 20% B-10. The atomic density of B-10 was 1.58921E-03 barn/cm3 in the first case and 1.51714E-02 barn/cm3 in the second case. I repeated the calculations in full surface-tracking, full delta-tracking and the combined mode, with and without the control rod. The running times (minutes) for the VVER case are:

Code: Select all

------------------------------------------
                  with CR      without CR
------------------------------------------
Surface-tracking: 84.3         84.4
Delta-tracking:   32.4 (2.6x)  23.9 (3.5x)
Combined ST/DT:   29.9 (2.8x)  23.9 (3.5x)
------------------------------------------
and for the BWR case:

Code: Select all

------------------------------------------
                  with CR      without CR
------------------------------------------
Surface-tracking: 82.4         69.0
Delta-tracking:   45.2 (1.8x)  40.4 (1.7x)
Combined ST/DT:   35.9 (2.3x)  32.7 (2.1x)
------------------------------------------
The use of delta-tracking shows a significant improvement for both calculation cases, especially when used in the combined mode. In my opinion this shows that the concentrations of the 1/v absorber are not high enough to significantly deteriorate the efficiency of delta-tracking. The question is, can the concentration be high enough in some practical case to make a significant difference? It should also be noted that the absorber concentration is not the only factor that affects the efficiency of rejection sampling. In both geometries the volume occupied by the absorber is relatively large, which is not always the case.
Attachments
kuva.png
kuva.png (72 KiB) Viewed 5289 times
- Jaakko

Post Reply