188
C. H. Pyeon
Table 7.5 Comparison between the results of measured and calculated sample reactivities evaluated
by Eqs. (7.1) and (7.2), respectively, by substituting Al plates for Pb ones as shown in Fig. 7.5 (Ref.
[1])
Core
Experiment [pcm] C/E
JENDL-4.0
JENDL-3.3
ENDF/B-VII.0 JEFF-3.1
Case 1 94 ± 5
0.93 ± 0.11 0.91 ± 0.11 0.88 ± 0.11
0.99 ± 0.11
Case 2 110 ± 6
0.85 ± 0.09 0.95 ± 0.09 1.01 ± 0.09
1.08 ± 0.09
Case 3 145 ± 7
0.97 ± 0.07 1.01 ± 0.07 1.06 ± 0.07
1.02 ± 0.07
Case 4 156 ± 8
0.94 ± 0.06 1.03 ± 0.06 1.02 ± 0.06
1.04 ± 0.06
(ξ s / a : ξ, s and a indicate the average logarithmic energy decrement, macro
cross sections of scattering and absorption, respectively.) in Al and Pb. Second,
while the number of substitution of fuel rods was the same as in both Cases 1 and 2,
a significant difference between sample reactivities was involved in the forward and
adjoint functions of reactivity defined in the First-order perturbation theory with the
variation of core sizes in horizontal and vertical directions shown in Fig. 7.1.
7.2.2.3 Criticality Bias
As discussed in Sect. 7.2, the ability of MCNP6.1 calculations was confirmed in
terms of the general definition of sample reactivity by the MCNP approach. Here, the
main objective of this study was to compare the experimental and numerical sample
reactivities defined in Eqs. (7.1) and (7.3), respectively. By comparing Eqs. (7.1)
and (7.3), as shown in Table 7.6, considering the uncertainties of C/E values, the
accuracy of the numerical analyses by MCNP6.1 with JENDL-4.0 demonstrated
a relative difference of about 5% and an overestimation by more than 50% with
JENDL-3.3. By comparing JENDL-3.3 and JENDL-4.0, the calculated values with
JENDL-4.0 improved more with a high accuracy of 30% in the C/E values than
with the values calculated with JENDL-3.3. Regarding libraries ENDF/B-VII.0 and
JEFF-3.1, the calculated sample reactivities were considered well within the relative
difference of 10% as shown in Table 7.6.
Table 7.6 Comparison between the results of measured and calculated sample reactivities evaluated
by Eqs. (7.1) and (7.3), respectively, by substituting Al plates for Pb ones as shown in Fig. 7.5 (Ref.
[1])
Core
Experiment [pcm] C/E
JENDL-4.0
JENDL-3.3
ENDF/B-VII.0 JEFF-3.1
Case 1 94 ± 5
1.13 ± 0.10 1.63 ± 0.13 0.79 ± 0.08
0.89 ± 0.09
Case 2 110 ± 6
1.07 ± 0.08 1.53 ± 0.10 0.85 ± 0.07
0.97 ± 0.07
Case 3 145 ± 7
1.12 ± 0.06 1.65 ± 0.08 0.94 ± 0.05
1.00 ± 0.05
Case 4 156 ± 8
1.13 ± 0.06 1.76 ± 0.08 0.94 ± 0.05
0.98 ± 0.05
C. H. Pyeon
Table 7.5 Comparison between the results of measured and calculated sample reactivities evaluated
by Eqs. (7.1) and (7.2), respectively, by substituting Al plates for Pb ones as shown in Fig. 7.5 (Ref.
[1])
Core
Experiment [pcm] C/E
JENDL-4.0
JENDL-3.3
ENDF/B-VII.0 JEFF-3.1
Case 1 94 ± 5
0.93 ± 0.11 0.91 ± 0.11 0.88 ± 0.11
0.99 ± 0.11
Case 2 110 ± 6
0.85 ± 0.09 0.95 ± 0.09 1.01 ± 0.09
1.08 ± 0.09
Case 3 145 ± 7
0.97 ± 0.07 1.01 ± 0.07 1.06 ± 0.07
1.02 ± 0.07
Case 4 156 ± 8
0.94 ± 0.06 1.03 ± 0.06 1.02 ± 0.06
1.04 ± 0.06
(ξ s / a : ξ, s and a indicate the average logarithmic energy decrement, macro
cross sections of scattering and absorption, respectively.) in Al and Pb. Second,
while the number of substitution of fuel rods was the same as in both Cases 1 and 2,
a significant difference between sample reactivities was involved in the forward and
adjoint functions of reactivity defined in the First-order perturbation theory with the
variation of core sizes in horizontal and vertical directions shown in Fig. 7.1.
7.2.2.3 Criticality Bias
As discussed in Sect. 7.2, the ability of MCNP6.1 calculations was confirmed in
terms of the general definition of sample reactivity by the MCNP approach. Here, the
main objective of this study was to compare the experimental and numerical sample
reactivities defined in Eqs. (7.1) and (7.3), respectively. By comparing Eqs. (7.1)
and (7.3), as shown in Table 7.6, considering the uncertainties of C/E values, the
accuracy of the numerical analyses by MCNP6.1 with JENDL-4.0 demonstrated
a relative difference of about 5% and an overestimation by more than 50% with
JENDL-3.3. By comparing JENDL-3.3 and JENDL-4.0, the calculated values with
JENDL-4.0 improved more with a high accuracy of 30% in the C/E values than
with the values calculated with JENDL-3.3. Regarding libraries ENDF/B-VII.0 and
JEFF-3.1, the calculated sample reactivities were considered well within the relative
difference of 10% as shown in Table 7.6.
Table 7.6 Comparison between the results of measured and calculated sample reactivities evaluated
by Eqs. (7.1) and (7.3), respectively, by substituting Al plates for Pb ones as shown in Fig. 7.5 (Ref.
[1])
Core
Experiment [pcm] C/E
JENDL-4.0
JENDL-3.3
ENDF/B-VII.0 JEFF-3.1
Case 1 94 ± 5
1.13 ± 0.10 1.63 ± 0.13 0.79 ± 0.08
0.89 ± 0.09
Case 2 110 ± 6
1.07 ± 0.08 1.53 ± 0.10 0.85 ± 0.07
0.97 ± 0.07
Case 3 145 ± 7
1.12 ± 0.06 1.65 ± 0.08 0.94 ± 0.05
1.00 ± 0.05
Case 4 156 ± 8
1.13 ± 0.06 1.76 ± 0.08 0.94 ± 0.05
0.98 ± 0.05