Nuclear Data Benchmark
for Sodium Voided Reactivity Worthwith Improved Neutronics Simulation Method
Go CHIBA
Japan Atomic Energy Agency[Background]- Sodium voided reactivity worth (SVRW) is one of the mostimportant core parameters in fast reactor design.
- The purpose of the present work is to assess the nuclear data
files for SVRW calculations,What does sodium voiding do?

CoreCore(1) Promoting neutron leakage… negative reactivity(3) Decreasing neutron capture bysodium … positive reactivity

Neutron flux

Neutron flux

[Importance]CoreNeutron energy(2) Hardening neutron spectrum… (normally) positive reactivity(4) Promoting self-shielding of U, Pu… positive or negative reactivity

Which nuclear data is important for SVRW calculations?

SodiumCore(Capture)

SodiumCore(Total, P1 elastic)(1) Promoting neutron leakage… negative reactivity(3) Decreasing neutron capture bysodium … positive reactivity

Neutron flux

Neutron flux

Sodium (Scattering) [Importance]&
Pu-239, U-238, …
(via importance function)

Core Sodium(Total)

Neutron energy(2) Hardening neutron spectrum… (normally) positive reactivity(4) Promoting self-shielding of U, Pu… positive or negative reactivity

SVRW is difficult to be well predicted … Why?
- SVRW is composed of several different components.
- These components take both positive and negative values.
For example,+ 1.0
Non-leakage component (positive)- 0.8
Leakage component (negative)+ 0.3
Net SVRW

5% error in non-leakage component -> 17% error in net SVRW
5% error in leakage component -> 13% error in net SVRWError in each component is seriously propagated to net SVRW.

Benchmark calculations for nuclear data
The following nuclear data files are assessed.
- JEFF-3.1- JENDL-3.3- ENDF/B-VII.0
SVRW experimental data obtained at MZA are utilized.
Z=0
Reflective

ZX

Voidedregion

AxialBlanket

Fuel

Reflective

4Vacuum

3Blanket
2Reflector
Y

10

VacuumCoreR

Numerical method
In order to reduce ambiguity caused by lattice homogenization,
only can regions are homogenized.
Fuel unit cell
0Sodium

Y=0

Reflective
0X

UO2Sodium
Pu

FuelC+SS*
UO2Blanket
ReflectorZVacuum

Sodium
SodiumUO2
C+SSPu
SodiumUO2
Sodium

0.58
1.28
1.82
2.14
2.54
3.17
3.75
4.33

Resonance cross section ofeach plate is calculated withthe ultra-fine group library.

4.96
5.36
5.68
6.22
6.92
7.5 (cm)

The above 3D model is calculated by a Sn code(with the double-Gaussian Tchebyshev quadrature set).

Results (1) C/E values
1.2
JENDL-3.3
JEFF-3.1
ENDF/B-VII.0

C/E

1.1

1

0.9

0.8
Fuel Reg.1

Fuel Reg.2

Fuel Reg.3

How do you feel this?

BlanketResults (2) “normalized” (C-E) values
In order to grasp a degree of difference between C- and E-values,
we introduce the following “normalized” absolute difference.

(C-E)/CNon-leakage :Relative error in the non-leakage component
under the assumption that there is no error in the leakage component(C-E)/Cleakage :Relative error in leakage component
under the assumption that there is no error in the Non-L component

Results (3) “normalized” (C-E) values

Fuel Reg.1
Fuel Reg.2
Fuel Reg.3
BlanketNon-Leakage
Non-Leakage
Leakage
Non-Leakage
Leakage
Leakage

JENDL-3.3
-0.02
0.02
-0.02
-0.06
0.02
-0.03

JEFF-3.1
00.03
-0.04
-0.09
0.03
-0.02

ENDF/B-VII.0
-0.05
0.02
-0.03
0.06
-0.02
-0.09

(Error)
0.05
0.06
-0.08
0.09
-0.03
-0.04

- All the libraries predict well SVRW within experimental uncertainties.
- However, ENDF/B-VII.0 clearly underestimates the leakage component.
(It is found through a sensitivity study that this difference is caused by a differencein P1 component of elastic scattering of sodium.)JAEA-Research 2007-xxx

5.2.4

Na 弾性散乱断面積の P1 ルジャンドル係数

Na の弾性散乱断面積の P1 ルジャンドル係数を図 5.2.4 に示す。
0.9

P1 Coef. of elastic scattering XS

0.8

JENDL-3.3
JEFF-3.1
ENDF/B-VII

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0-0.110000

図 5.2.4

100000

1e+06
Neutron energy [eV]

1e+07

1e+08

Na 弾性散乱断面積 P1 係数の比較

数百 keV から数 MeV のエネルギー領域で ENDF/B-VII の評価値が大きい。
ベンチマーク計算結果は以下のように整理される。

• ENDF/B-VII は、MOX 燃料炉心の臨界性を炉心の漏洩寄与が大きくなるにつれて過小評価した。すなわち中性子漏洩を大きめに評価した。

• ENDF/B-VII は、MOX 燃料炉心の Na ボイド反応度の漏洩項を他と比べて小さめに評価し、MOZART 炉心については C/E 値はその他と比較して良好であった。ただし前述のとおり計算手法に起因する誤差がある点に注意が必要である。
上記の計算結果は整合がとれないため、本ベンチマークテストで Na の弾性散乱断面積 P1 係数に対する評価を下すことは出来ない。計算手法に起因する誤差を低減させる必要がある。

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