8 Sensitivity and Uncertainty of Criticality
231
uncertainty analyses of k eff induced by nuclear data were performed by TSUNAMI3D module of SCALE6.2 together with ENDF/B-VII.1 and its 56-group covariance
library (56groupcov7.1) for standard modeling of EE1 and E3 core configurations.
Here, the adjoint flux was obtained by the CLUTCH method [26].
Variation in the manufacturing tolerance of HEU plates is provided by statistically
processing the measured results (enrichment and thickness) of all plates at KUCA
and with specification sheet in the fabrication for length of each side, as shown in
Table 8.1. On the basis of the variation in HEU plates, the uncertainty analyses for
the enrichment and tolerance of length of both sides were conducted with KPERT
option in MCNP6.1 together with ENDF/B-VII.1. Since the variation is too small
to explicitly calculate the impact (difference in k eff values), a pseudo variation was
considered 10%, instead of the actual variation shown in Table 8.1, in the perturbation
for the enrichment and length of sides of the HEU plates. Here, while varying the
length of the sides of HEU plates, their mass was maintained by retaining the original
number of atoms. The pseudo uncertainty of k eff attributed to varying the enrichment
and length was converted to the actual one (Table 8.1) on the basis of the standard
method provided in the guideline by OECD/NEA [27] as follows:
k eff =
N
i = 1
1
n i
k eff, i
q i
·
q i
x i
2
,
(8.20)
where, k eff is the difference between k eff values before and after variation q i (the
intensity of the pseudo variation), x i the real uncertainty shown in Table 8.1, n i
the number of HEU plates involved in the variation, finally, i and N the region of
perturbation and the total number of regions, respectively. In the calculation for the
variation in the enrichment and the length of HEU plates, the core was divided into
fuel rod regions in the x-y plane (25 divisions in EE1 core; 21 divisions in E3 core)
and into three regions in z axis (N = 75 and 63 in EE1 and E3 cores, respectively).
The uncertainty of k eff by varying the thickness of HEU plates was evaluated by
setting all HEU plates 3.1% decreasing in thickness according to Ref. [14].
The uncertainty attributed to the reproducibility of control rod position was
approximately evaluated by eigenvalue calculations (Eq. (8.20)) with MCNP6.1, and
by varying control rod position (x-y directions) in the casing for 5.15 mm radially
(q i in Eq. (8.20)) and by 8 segments circumferentially. Then, the actual uncertainty
of control rod position in the x-y plane is limited to a radius of 1.15 mm (x i in
Eq. (8.20)). In the case of one (two) control rod(s) inserted, N in Eq. (8.20) becomes
8 (64). The uncertainty was finally deduced by subtracting the k eff value obtained at
the reference position from that obtained by varying the position.
231
uncertainty analyses of k eff induced by nuclear data were performed by TSUNAMI3D module of SCALE6.2 together with ENDF/B-VII.1 and its 56-group covariance
library (56groupcov7.1) for standard modeling of EE1 and E3 core configurations.
Here, the adjoint flux was obtained by the CLUTCH method [26].
Variation in the manufacturing tolerance of HEU plates is provided by statistically
processing the measured results (enrichment and thickness) of all plates at KUCA
and with specification sheet in the fabrication for length of each side, as shown in
Table 8.1. On the basis of the variation in HEU plates, the uncertainty analyses for
the enrichment and tolerance of length of both sides were conducted with KPERT
option in MCNP6.1 together with ENDF/B-VII.1. Since the variation is too small
to explicitly calculate the impact (difference in k eff values), a pseudo variation was
considered 10%, instead of the actual variation shown in Table 8.1, in the perturbation
for the enrichment and length of sides of the HEU plates. Here, while varying the
length of the sides of HEU plates, their mass was maintained by retaining the original
number of atoms. The pseudo uncertainty of k eff attributed to varying the enrichment
and length was converted to the actual one (Table 8.1) on the basis of the standard
method provided in the guideline by OECD/NEA [27] as follows:
k eff =
N
i = 1
1
n i
k eff, i
q i
·
q i
x i
2
,
(8.20)
where, k eff is the difference between k eff values before and after variation q i (the
intensity of the pseudo variation), x i the real uncertainty shown in Table 8.1, n i
the number of HEU plates involved in the variation, finally, i and N the region of
perturbation and the total number of regions, respectively. In the calculation for the
variation in the enrichment and the length of HEU plates, the core was divided into
fuel rod regions in the x-y plane (25 divisions in EE1 core; 21 divisions in E3 core)
and into three regions in z axis (N = 75 and 63 in EE1 and E3 cores, respectively).
The uncertainty of k eff by varying the thickness of HEU plates was evaluated by
setting all HEU plates 3.1% decreasing in thickness according to Ref. [14].
The uncertainty attributed to the reproducibility of control rod position was
approximately evaluated by eigenvalue calculations (Eq. (8.20)) with MCNP6.1, and
by varying control rod position (x-y directions) in the casing for 5.15 mm radially
(q i in Eq. (8.20)) and by 8 segments circumferentially. Then, the actual uncertainty
of control rod position in the x-y plane is limited to a radius of 1.15 mm (x i in
Eq. (8.20)). In the case of one (two) control rod(s) inserted, N in Eq. (8.20) becomes
8 (64). The uncertainty was finally deduced by subtracting the k eff value obtained at
the reference position from that obtained by varying the position.