220
M. Yamanaka
of excess reactivity and control rod worth, in the critical core, the effective delayed
neutron fraction (β eff ) was acquired by MCNP6.1 (2,000 active cycles of 50,000
histories; 5 pcm statistical error) with JENDL-4.0. The values of β eff at critical state
of EE1 and E3 cores were 831 and 805 pcm, respectively; those of the neutron
generation time () were 3.027E-05 and 4.771E-05 s, respectively. Atomic number
densities of core components comprise fuel elements, moderator (reflector), control
rod, and Al sheath, for analyzing experimental values of excess reactivity and control
rod worth.
8.2.1.2 Deterministic Calculations
Numerical analyses by deterministic calculations were performed by combining the
SRAC2006 [7] and the MARBLE [8] code systems: collision probability calculations
(PIJ [7]) and eigenvalue calculations (CITATION [9]) of SRAC2006, sensitivity coefficient calculations (SAGEP [10]) and uncertainty calculations (UNCERTAINTY [8,
11]) of MARBLE, coupled with the JENDL-4.0 nuclear data library. Experimental
analyses of uncertainty were conducted with the use of covariance data of cross
sections contained in JENDL-4.0, including uncertainty of excess reactivity and
control rod worth induced by the nuclear data, and the effects of decreasing uncertainty on the accuracy of excess reactivity and control rod worth. Here, in a series of
deterministic calculations, the CITATION code was notably executed for obtaining
sensitivity coefficients by the SAGEP code based on the diffusion calculations.
8.2.2 Sensitivity and Uncertainty
8.2.2.1 Numerical Reactivity
The experimental values of excess reactivity (positive value) ρ
Exp
Excess and control rod
worth (negative value) (−ρ
Exp
Rod ) were deduced by effective multiplication factors
k
Exp
Clean and k
Exp
Rod in super-critical (clean core) and subcritical states (rod insertion core)
obtained by the positive period method and the rod drop method, respectively, as
follows:
ρ
Exp
E xcess = 1 −
1
k
Exp
Clean
,
(8.1)
−ρ
Exp
Rod = 1 −
1
k
Exp
Rod
.
(8.2)
In MCNP analyses, numerical value ρ
MCNP
Excess or (−ρ
MCNP
Rod ) was deduced by the
difference between two effective multiplication factors k
MCNP
Clean or k
MCNP
Rod
and k
MCNP
Critical
in the super-critical or subcritical and critical cores, respectively, as follows:
M. Yamanaka
of excess reactivity and control rod worth, in the critical core, the effective delayed
neutron fraction (β eff ) was acquired by MCNP6.1 (2,000 active cycles of 50,000
histories; 5 pcm statistical error) with JENDL-4.0. The values of β eff at critical state
of EE1 and E3 cores were 831 and 805 pcm, respectively; those of the neutron
generation time () were 3.027E-05 and 4.771E-05 s, respectively. Atomic number
densities of core components comprise fuel elements, moderator (reflector), control
rod, and Al sheath, for analyzing experimental values of excess reactivity and control
rod worth.
8.2.1.2 Deterministic Calculations
Numerical analyses by deterministic calculations were performed by combining the
SRAC2006 [7] and the MARBLE [8] code systems: collision probability calculations
(PIJ [7]) and eigenvalue calculations (CITATION [9]) of SRAC2006, sensitivity coefficient calculations (SAGEP [10]) and uncertainty calculations (UNCERTAINTY [8,
11]) of MARBLE, coupled with the JENDL-4.0 nuclear data library. Experimental
analyses of uncertainty were conducted with the use of covariance data of cross
sections contained in JENDL-4.0, including uncertainty of excess reactivity and
control rod worth induced by the nuclear data, and the effects of decreasing uncertainty on the accuracy of excess reactivity and control rod worth. Here, in a series of
deterministic calculations, the CITATION code was notably executed for obtaining
sensitivity coefficients by the SAGEP code based on the diffusion calculations.
8.2.2 Sensitivity and Uncertainty
8.2.2.1 Numerical Reactivity
The experimental values of excess reactivity (positive value) ρ
Exp
Excess and control rod
worth (negative value) (−ρ
Exp
Rod ) were deduced by effective multiplication factors
k
Exp
Clean and k
Exp
Rod in super-critical (clean core) and subcritical states (rod insertion core)
obtained by the positive period method and the rod drop method, respectively, as
follows:
ρ
Exp
E xcess = 1 −
1
k
Exp
Clean
,
(8.1)
−ρ
Exp
Rod = 1 −
1
k
Exp
Rod
.
(8.2)
In MCNP analyses, numerical value ρ
MCNP
Excess or (−ρ
MCNP
Rod ) was deduced by the
difference between two effective multiplication factors k
MCNP
Clean or k
MCNP
Rod
and k
MCNP
Critical
in the super-critical or subcritical and critical cores, respectively, as follows: