4 Effective Delayed Neutron Fraction
99
Fig. 4.3 Correlated and
uncorrelated probabilities of
fiber detector in Case II-1 by
Rossi-α method in PNS
experiment (Ref. [12])
0.000
0.005
0.010
0.015
0.0
20.0
40.0
60.0
80.0
Correlation term P C
Uncorrelation term P U
0
0
Probaability in Rossi- method [-]
Time [s]
[x10
5
]
the correlation probability is negligible. From the PNS histogram shown in Fig. 4.2,
the decay of the correlation probability was confirmed at 0.025 s, and intensity B
was obtained by fitting for the joint probability by the Rossi-α method in the PNS
experiments, on the basis of Eq. (4.25) in the region between 0.025 and 0.125 s. The
intensity of the correlation term in Eq. (4.22) was then obtained by subtracting the
uncorrelated term from the joint probability in Eq. (4.26) and fitting by Eq. (4.27).
The uncorrelated probability decreased rapidly, compared with the correlated
probability as shown in Fig. 4.3. Instead of decreasing exponentially, the correlated
probability increased in the vicinity of zero, the reason being the overestimation
of the uncorrelated probability in the region arising by varying the shape of the
external neutron source from the Gaussian to the pulsed, because the formulation
of uncorrelated probability has the sensitivity to the shape of the external neutron
source.
In the fitted parameters, α and B values differed from each other when the subcriticality was varied, as shown in Figs. 4.4a, b, respectively, because of the increase of
the subcriticality in the α value and the decrease of neutrons in B. For the intensity of
correlated probability C, the optical fiber indicated an asymptotic tendency of monotonic decrease, by the change in the subcriticality attributed to control rod insertion
and fuel rod replacement in Cases II-1 to II-7, as shown in Fig. 4.4c; the intensity of
fission reactions decreased by the subcriticality. The BF 3 detector, however, showed
the increasing tendency in Cases II-4, II-5, and II-6. Since the low correlated probability of the fission neutrons could be predicted in BF 3 installed outside the core, the
accuracy of the reconstruction of correlated probability is considered low.
4.2.3.2 Estimation of β eff
To obtain correction factors g and g* by Eqs. (4.30) and (4.31), respectively, the
calculations of reaction rates and adjoint flux were performed by MCNP6.1 together
99
Fig. 4.3 Correlated and
uncorrelated probabilities of
fiber detector in Case II-1 by
Rossi-α method in PNS
experiment (Ref. [12])
0.000
0.005
0.010
0.015
0.0
20.0
40.0
60.0
80.0
Correlation term P C
Uncorrelation term P U
0
0
Probaability in Rossi- method [-]
Time [s]
[x10
5
]
the correlation probability is negligible. From the PNS histogram shown in Fig. 4.2,
the decay of the correlation probability was confirmed at 0.025 s, and intensity B
was obtained by fitting for the joint probability by the Rossi-α method in the PNS
experiments, on the basis of Eq. (4.25) in the region between 0.025 and 0.125 s. The
intensity of the correlation term in Eq. (4.22) was then obtained by subtracting the
uncorrelated term from the joint probability in Eq. (4.26) and fitting by Eq. (4.27).
The uncorrelated probability decreased rapidly, compared with the correlated
probability as shown in Fig. 4.3. Instead of decreasing exponentially, the correlated
probability increased in the vicinity of zero, the reason being the overestimation
of the uncorrelated probability in the region arising by varying the shape of the
external neutron source from the Gaussian to the pulsed, because the formulation
of uncorrelated probability has the sensitivity to the shape of the external neutron
source.
In the fitted parameters, α and B values differed from each other when the subcriticality was varied, as shown in Figs. 4.4a, b, respectively, because of the increase of
the subcriticality in the α value and the decrease of neutrons in B. For the intensity of
correlated probability C, the optical fiber indicated an asymptotic tendency of monotonic decrease, by the change in the subcriticality attributed to control rod insertion
and fuel rod replacement in Cases II-1 to II-7, as shown in Fig. 4.4c; the intensity of
fission reactions decreased by the subcriticality. The BF 3 detector, however, showed
the increasing tendency in Cases II-4, II-5, and II-6. Since the low correlated probability of the fission neutrons could be predicted in BF 3 installed outside the core, the
accuracy of the reconstruction of correlated probability is considered low.
4.2.3.2 Estimation of β eff
To obtain correction factors g and g* by Eqs. (4.30) and (4.31), respectively, the
calculations of reaction rates and adjoint flux were performed by MCNP6.1 together