IV. Numerical Result
4.11. Test for Computing Time
temperature profile is used. However, the non-uniform material compositions do not cause the noticeable bias in the results from PSM.
Although STREAM and SERPENT2 use the common kappa data, they are using still many different data and libraries for the depletion calculation. Therefore, the error from the use of the different data is included in the comparisons. It is difficult to say how much difference in k-inf is caused by the difference in the depletion libraries. Because the depletion results with PSM and PSM- CPM show very good agreement with that of SERPENT2, it is expected that the error is not significant. More detailed examination is necessary
From the verification with the depletion problem, it is verified that PSM and PSM-CPM calculate the accurate and consistent results for the depletion. To get a high accuracy in the depletion calculation, it is important to calculate the accurate reaction rates of the every nuclide. The resonance interference treatment is also important because a lot of resonant nuclides are mixed together.
Although the material compositions are not uniform in the fuel pellet, PSM calculates very close results to PSM-CPM. The difference between PSM and PSM-CPM is less than 10 pcm. The non- uniform material compositions made by the depletion do not cause a noticeable error in PSM.
Table 22. Comparison for elapsed time (unit: sec).
Category
Coarse MOC condition Rigorous MOC condition
EQ PSM PSM-
CPM EQ PSM PSM-
CPM
Reading librarya) 0.36 0.37 0.37 0.37 0.37 0.37
MOC FSP solver for fuelb) 0.36 0.03 0.03 4.65 0.31 0.31
MOC FSP solver for claddingc) 0.36 0.35 0.36 4.62 4.63 4.61 Interpolation in
multi-group XS & RI librariesd) 0.97 0.15 0.14 0.96 0.15 0.16 Nuclide groupinge)
& XS condensationf) - 0.23 0.22 - 0.22 0.22
Slowing-down solverg) - 0.42 5.21 - 0.41 5.21
Total XS generationh) 2.25 1.67 6.44 10.81 6.20 10.98
Total simulation 7.78 7.16 11.95 70.06 65.26 71.39
a) Elapsed time in reading the XS and RI libraries.
b) Elapsed time in solving MOC fixed-source problem for the fuel.
c) Elapsed time in solving MOC fixed-source problem for the cladding.
d) Elapsed time in interpolating the multi-group XS and RI from the multi-group XS library and the RI library.
e) Elapsed time in calculating the macroscopic pointwise energy XSs of the nuclide groups.
f) Elapsed time in collapsing the pointwise energy XS to the multi-group XSs.
g) Elapsed time in solving the slowing-down equation and calculating the collision probabilities.
h) Total elapsed time in calculating the multi-group XSs
The time comparison results are shown in Table 22. The results were generated in an OSX system with 3.1 GHz Intel Core i7. PSMs perform the energy independent fixed-source calculations to consider the shadowing effect. On the other hand, EQ need the 15 fixed-source solutions for the fuel.
The STREAM code performs the fixed-source MOC calculation for the resonance energy groups upper than 4 eV [5]. In case of the 17x17 FA problem, the Dancoff factors are calculated for the fuel and the cladding. PSM is not applied on the resonance treatment for the cladding. Both PSM and EQ use the common resonance treatment method [5] for the cladding. The cladding resonance treatment method is based on the equivalence theory therefore PSM and EQ perform energy group dependent MOC fixed-source calculations. Finally, PSM requires 16 MOC fixed-source solutions (1 for the fuel;
15 for the cladding) while EQ requires 30 fixed-source solutions (15 for the fuel; 15 for the cladding).
That is why PSM needs about half the computation time in the fixed-source calculation (MOC FSP in Table 22) compared to EQ. Obviously, the elapsed time in the fixed-source MOC calculation depends on the MOC ray conditions. PSMs solve the slowing-down equations for the individual fuel pins. In case of the 17x17 FA problem with the octant symmetry, the slowing-down equations are solved for the 39 fuel pins. About 0.41 seconds are spent in the pointwise energy slowing-down calculations for all the fuel pins in the problem. PSM spends additional time in the grouping the nuclides and the energy condensations. Not negligible time is consumed in these calculations although the calculations
are quite simple. Because the pointwise energy XS data are used in PSM, these calculations are inevitable. PSM-CPM takes more long time in the slowing-down solver because PSM-CPM calculates the collision probability with the CPM solver for all energy points. PSMs spend less time in interpolating the RI from the multi-group RI library because PSMs do not use RI look-up table to calculate effective XSs of fuel materials.
The same problem was solved with the different number of radial sub-regions in the fuel pellet. Fig. 84 shows the calculation time as a function of the number of sub-regions in the fuel pellet.
Both PSM and PSM-CPM are tested with the different number of regions. When the number of rings is small, the differences in the calculation time between PSMs are not noticeable. As the number of sub-regions increases, the elapsed time used in the XS generation significantly increases with PSM- CPM. With PSM-CPM, the XS generation has a very big portion of the total simulation. On the other hand, the elapsed time in the XS generation with PSM is not much compared to the total simulation time. PSM is very effective in reducing the calculation time in the XS generation.
Fig. 84. Elapsed time as a function of the number of radial meshes.
As a conclusion, PSM can calculate the multi-group XS within reasonable computation time.
PSM saves the calculation time by reducing the number of MOC fixed-source calculations. Even though PSM solves the pointwise energy slowing-down equations, the calculation time is not problematic because the various techniques are applied to enhance the performance of PSM. PSM- CPM takes significantly long time in calculating the multi-group XSs with the many number of sub- regions in the fuel pellet. Nevertheless, PSM-CPM is still useful because more than 5 sub-regions are hardly used in the practical calculation for the UO2 pin-cell. As discussed in the previous sections, PSM-CPM shows better accuracy than PSM when the significantly non-uniform temperature profile is used. There are pros and cons of PSM-CPM, i.e., better accuracy but slower. Users or developer can