102
M. Yamanaka
Table 4.10 Comparison between measured and calculated β eff values (Ref. [12])
Case
k *
eff
Effective delayed neutron fraction β eff [pcm]
MCNP6.1
MCNP6.1
Area ratio method
Optical fiber
BF 3
II-1
0.99093
817 ± 11
763 ± 21
(6.6 ± 0.2)
870 ± 81
(−6.5 ± 0.6)
911 ± 29
(−11.5 ± 0.4)
II-2
0.98274
794 ± 11
874 ± 26
(−10.0 ± 0.3)
876 ± 58
(−10.3 ± 0.7)
845 ± 33
(−6.5 ± 0.3)
II-3
0.97627
814 ± 11
919 ± 24
(−12.3 ± 0.3)
855 ± 45
(−5.0 ± 0.3)
725 ± 36
(11.0 ± 0.6)
II-4
0.97662
801 ± 11
721 ± 5
(10.0 ± 0.2)
903 ± 109
(-12.7 ± 1.5)
704 ± 28
(12.1 ± 0.5)
II-5
0.95680
826 ± 12
737 ± 6
(10.8 ± 0.2)
915 ± 75
(−10.8 ± 0.9)
303 ± 7
(63.3 ± 1.7)
II-6
0.95278
817 ± 11
729 ± 6
(10.8 ± 0.2)
921 ± 84
(−12.7 ± 1.2)
189 ± 19
(76.9 ± 7.8)
II-7
0.93358
815 ± 11
729 ± 6
(14.3 ± 0.3)
811 ± 72
(−0.4 ± 0.1)
162 ± 14
(90.1 ± 7.1)
(): Relative difference (%); *Standard deviation of 9 pcm
to the same family in fission chain is largely detected. Inversely, when the detector
is located outside of the core, the measurement accuracy is considered deteriorated
by the difficulty in the extraction of the correlated term related to correlated neutron
detections with Eq. (4.26). To estimate the measurement accuracy of β eff by proposed
methodology, β eff was compared with the simple estimation by the area ratio method
and the relation between reactivity in dollar and pcm units. With the use of the
subcriticality in Table 4.8 and k eff in Table 4.10, β eff can be estimated as follows:
β
Area ratio method
eff
=
ρ
ρ $
=
1
ρ $
1 −
1
k eff
.
(4.41)
Here, measured β eff by proposed methodology indicated comparable or more
accurate results in the comparison with β eff by Eq. (4.41) (named Area ratio method)
in Cases II-1 to II-7 for the optical fiber detector, as shown in Table 4.10. Thus,
the applicability of the measurement methodology for β eff was demonstrated in the
subcritical range of the ADS operation around k eff = 0.93. Furthermore, to obtain
good accuracy of β eff values with the proposed methodology, improvement of correlated probability is attainable with the use of a specific shape (Gaussian distribution)
of the external neutron source.
M. Yamanaka
Table 4.10 Comparison between measured and calculated β eff values (Ref. [12])
Case
k *
eff
Effective delayed neutron fraction β eff [pcm]
MCNP6.1
MCNP6.1
Area ratio method
Optical fiber
BF 3
II-1
0.99093
817 ± 11
763 ± 21
(6.6 ± 0.2)
870 ± 81
(−6.5 ± 0.6)
911 ± 29
(−11.5 ± 0.4)
II-2
0.98274
794 ± 11
874 ± 26
(−10.0 ± 0.3)
876 ± 58
(−10.3 ± 0.7)
845 ± 33
(−6.5 ± 0.3)
II-3
0.97627
814 ± 11
919 ± 24
(−12.3 ± 0.3)
855 ± 45
(−5.0 ± 0.3)
725 ± 36
(11.0 ± 0.6)
II-4
0.97662
801 ± 11
721 ± 5
(10.0 ± 0.2)
903 ± 109
(-12.7 ± 1.5)
704 ± 28
(12.1 ± 0.5)
II-5
0.95680
826 ± 12
737 ± 6
(10.8 ± 0.2)
915 ± 75
(−10.8 ± 0.9)
303 ± 7
(63.3 ± 1.7)
II-6
0.95278
817 ± 11
729 ± 6
(10.8 ± 0.2)
921 ± 84
(−12.7 ± 1.2)
189 ± 19
(76.9 ± 7.8)
II-7
0.93358
815 ± 11
729 ± 6
(14.3 ± 0.3)
811 ± 72
(−0.4 ± 0.1)
162 ± 14
(90.1 ± 7.1)
(): Relative difference (%); *Standard deviation of 9 pcm
to the same family in fission chain is largely detected. Inversely, when the detector
is located outside of the core, the measurement accuracy is considered deteriorated
by the difficulty in the extraction of the correlated term related to correlated neutron
detections with Eq. (4.26). To estimate the measurement accuracy of β eff by proposed
methodology, β eff was compared with the simple estimation by the area ratio method
and the relation between reactivity in dollar and pcm units. With the use of the
subcriticality in Table 4.8 and k eff in Table 4.10, β eff can be estimated as follows:
β
Area ratio method
eff
=
ρ
ρ $
=
1
ρ $
1 −
1
k eff
.
(4.41)
Here, measured β eff by proposed methodology indicated comparable or more
accurate results in the comparison with β eff by Eq. (4.41) (named Area ratio method)
in Cases II-1 to II-7 for the optical fiber detector, as shown in Table 4.10. Thus,
the applicability of the measurement methodology for β eff was demonstrated in the
subcritical range of the ADS operation around k eff = 0.93. Furthermore, to obtain
good accuracy of β eff values with the proposed methodology, improvement of correlated probability is attainable with the use of a specific shape (Gaussian distribution)
of the external neutron source.