Analysis of benchmark experiments of effective delayed neutron fraction βeff at FCA

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Progress in Nuclear Energy, Vol. 35, No. 2, pp. 209-225, 1999 © 1999 Published by Elsevier Science Ltd

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Analysis of Benchmark Experiments of Effective Delayed Neutron Fraction [3eff at FCA

Takeshi Sakurai and Shigeaki Okajima

Japan Atomic Energy Research Institute, Department of Nuclear Energy Systems Tokai-mura, Naka-gun, Ibaraki-ken, Japan 319-1195

Abstract - - To finalize the benchmark experiments of the effective delayed neutron fraction 13 elf at the FCA facility of the Japan Atomic Energy Research Institute, the 13eff'S w e r e compared between different measurement methods. The final values of the 13 elf were 742pcm+3%, 364pcm+3% and 25 lpcm±2% in the cores of XIX-1, XIX-2 and XIX-3 respectively. Correlations of the 13elf between the different methods were considered to derive these final values.

In the analysis of experiments, two sets of delayed neutron data were tested: JENDL-3.2 and ENDF/B-VI. Calculation-to-experiment ratios(C/E's) of the 13elf were 1.004, 1.005 and 0.972 in the cores of XIX-1, XIX-2 and XIX-3 respectively when the delayed neutron data of JENDL-3.2 were used. The C/E's of the 13eff were 1.033, 0.985 and 0.992 in the cores of XIX-1, XIX-2 and XIX-3 respectively when the delayed neutron data of ENDF/B-VI were used. Recom- mendations for the D.N. yields were drawn from these C/E's to improve the prediction accuracy of 13elf of fast reactor. © 1999 Published by Elsevier Science Ltd. Al l r igh ts r e se rved .

I. INTRODUCTION

To improve prediction accuracy of the effective delayed neutron fraction 13 elf of fast reactor, the benchmark experiments of 13 elf under the international collaboration have been carried out at the FCA facility of the Japan Atomic Energy Research Institute(JAERI). These experiments were composed of three different core configurations which were selected taking into consid- eration of the systematic change of nuclide contribution from 235U, 238U and 239pu to the 13elf : XIX-1 core fueled with 93% enriched uranium; XIX-2 core fueled with plutonium(92% fis- sile) and natural uranium; XIX-3 core fueled with the plutonium. Six organizations from five countries participated in these experiments. The 13 elf measurement was carded out by each par- ticipant with his measurement method. Comparisons of the (3 eel between these methods were planned to improve reliability of the measurements and to achieve the target accuracy of 3% required for the experimental 13 eff.

209

210 I", Sakurai and S. Okajima

The first part(Chap.H) of the present paper is devoted to finalization of the experimental 13 elf and estimation of its uncertainty through the comparisons. The second part(Chap.HI) is devoted to analysis of the experiments. Two evaluated delayed neutron(D.N.) data sets were tested: JENDL-3.2(Nakagawa et al., 1995) and ENDF/B-VI(Rose, 1991). Recommendations for the D.N. yields were drawn from results of these tests. Prior to the analysis of 13eff, the effective multiplication factor keff and the central fission rate ratios were also analyzed to check the reliability of neutron field calculation.

II. FINALIZATION OF EXPERIMENTAL 13 elf

II.1. Method for Finalization Table 1 compares the 13elf's measured by the different methods. Table 2 summarizes the prin-

cipal parameters used in the ~ elf measurement methods. This table shows that several common parameters were used in the different methods. In order to derive the final value of 13elf and it's uncertainty, a correlation of 13 elf'S between the different methods should be taken into account. The covariance matrix Cu of the 13elf's by the different methods was estimated by the error propagation law :

Cb = S - C p . S v (1)

where Cp is the covariance matrix of the parameters for ~eee measurement; S is the matrix whose elements are the sensitivity coefficients of the ~ elf to the parameter and T means the transpose of matrix.

Table 1 13 elf values obtained by different experimental methods

Unit : pcm

Core name XIX- 1 XIX-2 XIX-3

(1) Covariance-to-meanmethod 724-t-13(2%)* - - 252-t-5(2%)

(2) Modified Bennett method 7824-16(2%) 3684-6(2%) 2564-4(2%)

(3) Noise method 7434-19(3%) - - 2504-6(2%)

(4) Rossi-c~ method 7714-23(3%) - - - -

(5) Nelson-number method 737-4-20(3%) - - - -

(6) Cf source method JAERI/KAERI t 7354-20 358-4-10 2494-7 IPPE t 706-4-30 351 + 10 244-t-7 Mean of two participants 727-4-20(3%) 355-/-10(3%) 247+7(3%)

* Values in parentheses : relative uncertainty. t KAERI : Korea Atomic Energy Research Institute, Korea.

IPPE : Institute of Physics and Power Engineering, Russia.

Analysis of benchmark experiments 211

©

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*r

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0 ©

°~ ° ~

~ = o ~

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0 0

O 0 0

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• 0

~-s,

~ ~ ~ ~.~-

~ < ~ . .

z "L "4 . . 0 0

0 0 0 0 Q

Q 0 Q

0 0 0

0 0 0 O 0

0 0 0 O 0

0 0 0 O 0

i 0 0 O 0

~ ~ • ~ ~ ~ .F,~ ~ ~ooo~o.. .~.~ o ~ ~ ~ .~ oO

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212 T. Sakurai and S. Okajima

The (i., j)th element s U of the S is given by

a ffeffi/~eff( (2) s U - Bp}/p} '

where the iBeff i is the ~eff by the ith method and pJ is the }th parameter. As an example, the Beff by the covariance-to-mean method(Sakurai e t a l . , 1999b) is given by

1

C 1 +{1 P$) {Fee~teTF~ -) DD Ds

1 , (3)

{1 - os) [ c q {

Fcer~ter Fr ) DD Ds

~eff :

where definitions of the parameters except c are shown in Table 2. The c is a count rate of a neutron detector. In this method, the sensitivity coefficient of the IB elf to the covariance-to-mean ratio a v was given by -1/2. Other sensitivity coefficients were derived by similar procedures. Tables 3 show the correlation matrix of the iBeff's by different methods.

The mean value m. of the IBeff's was determined by

rrt = (u . Cb -1 .uT) - 1 . u . C b - l - p , (4)

where p is a column vector whose i th element is the ~eff and u is a row vector with all elements equal to one. The statistical parameter ×2 was estimated by

X 2 = ( r . Cb -1 -rT), (5)

where r is a row vector whose £ th element is the residual of the ~eff from the mean value. The internal uncertainty &~t of the mean value was estimated by the error propagation law:

8i~t = ~/(u. Cb -1 • uT) -1 . (6)

The external uncertainty 5e~t was estimated by

8e~t = T " &~t, (7)

where f is the degrees of freedom. The 8e×t reflects the scattering of the individual data around the mean value.

Table 3

Analysis of benchmark experiments

Correlation matrix* of 13 eff's by different methods

(a) XIX-1 core

Method (1) (2) (3) (4) (5) (6)

(1) Covariance-to-mean 1.00

(2) Modified Bennett 0.47 1.00

(3) Noise 0.47 0.43 1.00

(4)Rossi-oc 0.43 0.39 0.39

(5)Nelson-number 0.58 0.53 0.53

(6) Cfsource 0.21 0.18 0.18

1.00

0.48 1.00

0.23 -0.32 1.00

* Symmetrical matrix

213

(b) XIX-2 core

Method (2) (6)

(2) Modified Bennett 1.00

(6) Cf source 0.35 1.00

(c) XIX-3 core

Method (1) (2) (3) (6)

(1) Covariance-to-mean 1.00

(2) Modified Bennett 0.53 1.00

(3) Noise 0.45 0.43

(6) Cf source 0.48 0.39

1.00

0.23 1.00

11.2. Remits and Discussion of Finalization Table 4 presents the mean value m, X 2, 6i~t and 6e,~t. The 6trtt'S were not more than 2%.

Figures 1 show the residuals of individual 13elf's around the mean value. Range of the 6i~t is also shown in these figures. The residuals were almost within the 6t~t in the XIX-2 and XIX-3 cores except the XIX-1 core. The 6~,~t was found to be too small to reflect the scattering of data in the XIX-1 core.

Table 4 Final value and uncertainty of 13 eel


Mean value: m 742pcm 364pcm 25 lpcm

X 2 26 1.7 2.4

6ir~t q- 1 lpcm +Tpcm +4pcm

~×t +24pcm(3%) +9pcm(3%) +4pcm(2%)

Degrees of freedom: f 5 1 3


T T T T T ]

60 Range of internal s uncertainty i T of mean I +

-40 J J_ L L

o m a ) to I t - .Q P

--- "~3t- Z co _ o t~E o~ o ~c- to gb. " - 0 " z , b ( . ) ,

Experimental method

E 4 0 O

20

o

rr -20

(a) XIX-1 core.

2°t ~ 1 0

~ -10 . . . . . . . .

(~ [ Range of internal _ L rr -20{- uncertainty

I of mean - 3 0 ~ 1

m m k~- t'--

N g o o'/

Experimental method

(b) XIX-2 core.

2° F

0

-~ 0

-lo r r

-20

Range of internal uncertainty of mean

i .1

o ~ m m co o , - m u=,-- .~ = '~,E ~sg z o ".E t~o ~nn m

o 0 0

Experimental method

(c) XIX-3 core.

Fig. 1 Residuals of ~ e f f ' S by individual methods around the mean value of elf's. Range of internal uncertainty estimated by Eq.(6) is also shown by

dotted lines in each core.

The degrees of freedom f is also shown in Table 4. The X 2 was significantly larger than the f in the XIX-1 core. This significant difference indicates that the uncertainties of individual 13 elf'S were underestimated in this core. In accordance with the statistical theory, the ~e×t should be used instead of the ~mt in this case. The ~e×t was thus adopted as the uncertainty of the final value of 13elf in the XIX-1 and XIX-2 cores. The target accuracy of 3% was satisfied as shown in this table.


HI. ANALYSIS OF EXPERIMENT

215

IH.1. Data and Methods for Analysis The analyses were carried out for the kerr, the central fission rate ratios and the [3eff by using

the JENDL-3.2 nuclear data file. Three-dimensional diffusion theory was adopted in a standard analysis method. The core geometries and the compositions of fuel cells have already been described by the authors(Sakurai et al., 1999a). Flow diagram of the standard method is shown in Fig.2.

Cell calculation was made by the SLAROM code(Nakagawa et aL, 1984) which is based on the collision probability method; the group constants set JFS3-J3.2 with a seventy-energy-group structure(Takano et al., 1994). One-dimensional infinite slab model was used in this calculation. Cell averaged effective cross sections in seventy energy groups were prepared in each region in the reactor.

Core calculation was made by a diffusion theory code POPLARS(Iijima, 1999) using aniso- tropic diffusion constants(Benoist, 1968) in a three-dimensional X-Y-Z model. The ~eff was calculated using a perturbation theory code PERKY(Iijima, 1977).

Cell Calculation 70 energy groups Infinite slab model

SLAROM Collision probability theory

Core Calculation 70 energy groups 3 dimensional X-Y-Z model

~ JFS3-J3.2 70 energy group structure

~ ~ Effective cross "~ ~ sections

70 energy groups

POPLARS Diffusion theory (anisotro 3ic diffusion constant

~ Forward flux Adjoint flux

D.N. data / ~ ' ~ I PERKY JENDL-3.2 \ / / j Perturbation calculation ENDF/B-MI ~ J I (diffusion theory)

13e"

Fig.2

RADAMES Reaction rate calculation

Fission rate i [ ratios I,._.~

Flow diagram of standard analysis method.


where

The (3elf was calculated by

6 Z Z f (fXd~,mqbtdE)(J"va~,,~N.~cr, mqbdE) dv

(3e . = (8) J" (J'×~btdE)(J"vX,qbdE) (Iv

reactoT

: Space- and energy-dependent forward flux dpt : Space- and energy-dependent adjoint flux Nm : Region-dependent atomic number density of fissionable nuclide m Xcl:i,ra: D.N. spectrum of D.N. group i of nuclide m "Vd:i,m: Energy-dependent D.N. yield of D.N. group i of nuclide rrt of:m : Region-dependent effective microscopic fission cross section of nuclide m × : Region-dependent fission spectrum of fuel -v : Region- and energy-dependent number of neutrons emitted per fission of fuel ~'f : Region- and energy-dependent macroscopic fission cross section.

The evaluated delayed neutron(D.N.) data in JENDL-3.2 and ENDF/B-VI were used for the calculation. In the JENDL-3.2, the total D.N. yields are given at incident neutron energy of thermal, ~3MeV and ~7 MeV for the 235U, 239pu and 23SU below 10 MeV. Between these energy points, it is recommended to calculate the yields by linear interpolation in both energy and yield. As a result, the yields are dependent on energy as shown in figures 3. The energy dependent D.N. yields of ENDF/B-VI are also shown in this figure for a comparison. Below ~3MeV, the D.N. yields of 235U and 239pu in JENDL-3.2 increase with the incident neutron energy while those in ENDF/B-VI are constant. The energy dependence below ~ 3 MeV given in JENDL- 3.2 is similar to that recommended by Tuttle (1979). For the D.N. yield of 23SU, a significant difference of up to 9% is found between two D.N. data sets.

For the D.N. spectra, those evaluated by Saphier (1977) have been adopted in the JENDL-3.2. Figure 4 compares the spectra of third group of 239pu between JENDL-3.2 and ENDF/B-VI for instance. A marked difference of the spectra is found below 100 keV. Such differences are found for other groups. The same tendency was found for the 235U and 238U.

Furthermore, two corrections were considered on the results of standard method : a correction for transport effect('transport correction') and a correction for mesh effect('mesh correction').* The 'transport correction factor' was estimated by comparing the results between a P0-Ss transport calculation and the diffusion calculation using isotropic diffusion constants(i.e. D = 1/(3rtr)). Both calculations were made in the two-dimensional cylindrical model. For the transport calculation, TWOTRAN-II code(Lathrop and Brinkley, 1973) was used. The 'mesh correction factor' was estimated by changing the mesh width in the three-dimensional diffusion calculation. The 'mesh corrections' on the ~eff and the central fission rate ratios were negligibly small.

The 'transport corrections' on the kerr, central fission rate ratios and ~eff were 1~1.5%. The 'mesh correction' on the keff was at most 0.3%. The correction factors are summarized in APPENDIX.

*The cell heterogeneity effect and the geometrical effect were also estimated and are summarized in APPENDIX.


0,018 I I I I f I I I 1

0 . 0 1 6 1 . . . . . . . ~".,,,.. ,,.

0.01 Ei~'DF/B-VI ,~~

0.008 ~ t I i I t I i I 0 2 4 6 8

Incident Neutron Energy (MeV)

" ( 3 ~ 0.014 .~,

0.012 El

(a) 235U.

0.007 r r i r i i i ~ i

r- . . . . . . . . e

-Oz.~ 0.006

Ci 0.005

ENDF/B-VI "

0 .004 i I I f i i I t I 0 2 4 6 8

Incident Neutron Energy (MeV)

(b) 239pu.

-o 0 . 0 4

-~,

c5 0.03

0.05 I I t I I i i I I

JENDL-3.2 ,,

ENDF/B-Vl " ~

0.02 i l l i i ( l i

0 2 4 6 8 0 Incident Neutron Energy (MeV)

(c) 23SU.

Fig.3 Comparison of D.N. yields of Z35U, 239pu and 23SU between JENDL-3.2 and

ENDF/B-VI.

217

t - - O 0.1 O

ci 0.05

0.15 . . . . . . . . ~ . . . . . . . . i . . . . . . . . i . . . . .

- - JENDL-3.2

03 1 04 1 0 r 1 06 Energy (eV)

07

Fig.4 Comparison of D.N. spectra of third group of 239pu between JENDL-3.2 and ENDF/B-VI.


III.2. Results and Discussion of Analysis

1. Neutron field calculation Table 5 presents the comparison of the experimental and the calculated keff's. The 'transport

correction' and the 'mesh correction' have already been considered in these results. Good agreement of the keff was found between the experiment and calculation in the XIX-1 core. Some discrepancies were observed for the keff of the XIX-2 and XIX-3 cores between the experiment and calculation. These discrepancies however were not significant and less than 1%.

Table 6 presents the comparison of central fission rate ratios between experiment and calculation. The 'transport correction' has already been considered in these results. Good agreement within experimental errors was found between the experiment and calculation.

From these results, we conclude that the present neutron field calculation is reliable for the ~eff calculation.

Table 5 Comparison of keel between experiment and calculation


Experiment(E) 1.00674-0.0005 1.0039±0.0004 1.0030±0.0004

Calculation(C) 1.0063 0.9992 1.0116

C/E 0.9996 0.9953 1.0086

Table 6 Comparison of central fission rate ratios between experiment and calculation

Core name and XIX-1 XIX-2 XIX-3

fission rate ratio 23Su/235U 235U/239pu 23Su/239pu 235U/239pu 238U/239pu

Experiment(E) 0.0396 0.944 0.0386 0.926 0.0325 ±1.3% 4-1.3% 4-1.5% ±1.2% ±1.3%

Calculation(C) 0.0400 0.931 0.0380 0.915 0.0322

C/E 1.010 0.986 0.985 0.988 0.991

2. ~eff calculation To evaluate the D.N. data, the calculated ~eff was compared with the experimental one in the

following cases. : (a) The D.N. yields and the D.N. spectra in JENDL-3.2 were used for the calculation. (b) The D.N. yields and the D.N. spectra in ENDF/B-VI were used for the calculation. (c) The D.N. yields of JENDL-3.2 were used with the D.N. spectra of ENDF/B-VI.

The last case was prepared to see the effect of changing the D.N. spectra on the ~eff calculation. Table 7 presents the ratios of calculation to experiment(C/E's) of ~eff of three cases. The 'transport correction' has already been considered in these results.

The differences of 2~3% were observed for the 13eu's between (a) and (b). From cases (a) and (c), the effect of changing the D.N. spectra on the 13eff calculation was small(at most 0.6%) in the present benchmark cores. The principal source of the differences of ~eff between (a) and (b) therefore was the differences of D.N. yields between two D.N data sets. The D.N. yields were evaluated from these C/E's.

Analysis of benchmark experiments 2 1 9

Table 8 shows systematic change of nuclide contributions to the J3~if. Inthe XIX-1 core, the Z35U had a dominant contribution of ~ 90% to the 13 elf. The C/E of 13 elf in this core was used for evaluation of the D.N. yield of Z35U. In the XIX-3 core, the 239pu had a dominant contribution of ~ 80% to the ~eif. The C/E of I3eff in this core was used for evaluation of the D.N. yield of Z39pu. In the XIX-2 core, the 23Su had a large contribution of ~50% to the 13elf. The C/E of ~eff in this core was used for evaluation of the D.N. yield of 23Su.

Table 7 Ratio of calculation to experiment(C/E) of 13 elf

Core name XIX-1 XIX-2 XIX-3

Case D.N. yields D.N. spectra

(a) JENDL-3.2 JENDL-3.2 1.004 1.005 0.972

(b) ENDF/B-VI ENDF/B-VI 1.033 0.985 0.992

(c) JENDL-3.2 ENDF/B-VI 1.003 1.009 0.978

Table 8 Nuclide contribution to 13elf


235U 94% 11% 9%

e38U 6% 46% 11%

239pu - - 41% 77%

24°pu, zglPu, 241Am - - 2% 3%

In the XIX-1 core, the calculated ~eff agreed well with the experimental one when the D.N. yields of JENDL-3.2 were used. On the other hand, the calculation overpredicted the ~eff by -3% when the D.N. yields of ENDF/B-VI were used. Figure 5 shows energy dependent sensitivity of [3eff to the D.N. yield of Z35U in this core. The D.N. yields of 235U are also shown in this figure. The sensitivities below 1 MeV had a dominant contribution(80~90%) to the energy

0.1 ' ' ' ' " " 1 . . . . . . "1 ' ' ' . . . . . I ' ' ' ' " " 1 ' ' . . . . . . I ' ' ' ' " " l

0 ' 0 8 ~ J E N D L - 3 , 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ ~ I 0 . 0 1 6

o o o . . . . . . . . E N O S , 8 v , o o 1 2 o

~ O.OO8 4. 0.04

0.02 ~ 0.004

0 0 1 01 1 0 2 1 0 3 1 04 1 0 5 1 06 0 7

Energy(eV)

Fig.5 Energy dependent sensitivity of 13elf to D.N. yield of 235U in XIX-1 core. The D.N. yields of Z35U in JENDL-3.2 and ENDF/B-VI are also shown.


integrated sensitivity coefficient. From these results, it is concluded that the D.N. yield of Z35U in ENDF/B-VI should be decreased by ~3% in this energy range to get the good agreement of calculation and experiment.

In the XIX-3 core, the calculated 13eif agreed well with the experimental one when the D.N. yields of ENDF/B-VI were used. On the other hand, the calculation underpredicted the 13elf by ~3% when the D.N. yields of JENDL-3.2 were used. Figure 6 shows energy dependent sensitivity of 13elf to the D.N. yield of Z39Pu in this core. The D.N. yields of Z39Pu are also shown in this figure. The sensitivities below 1 MeV had a dominant contribution(~80%) to the energy integrated sensitivity coefficient. From these results, it is concluded that the D.N. yield of ~gPu in JENDL-3.2 should be increased by ~3% in this energy range to get the good agreement of calculation and experiment.

0.1 . . . . . . . . i . . . . . . . . i . . . . . . . . I . . . . . . . . I . . . . . . . . i . . . . . . . . I 0 .007 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

\ ~ ' ~ - " 1 0.006 0.08 . JENDL-3.2 0.005

~_ . . . . . . . . ENDF/B-V I ",.J 0.06 ~ 0.004 ~,

¢- , ,<

0 .04 F- 0 .003 ~$--

0 .002 0 .02

0.001

0 . . . . . . 1 0 ~0 1 01 1 02 1 03 1 04 1 05 1 0 B E n e r g y ( e V )

Fig.6 Energy dependent sensitivity of 13¢ff tO D.N. yield of 239pL1 in XIX-3 core. The D.N. yields of ~gPu in JENDL-3.2 and ENDF/B-VI are also shown.

In the XIX-2 core, the calculation slightly underpredicted the 13 eef by 1.5% when the D.N: yields of ENDF/B-VI were used. Figure 7 shows energy dependent sensitivity of 13 elf to the D.N. yield of 23SU in this core. The 23SU yields are also shown in this figure. The sensitivities between 1~10 MeV had a dominant contribution to the energy integrated sensitivity coefficient.

0 .14 . . . . . . . 0 .05

0 .12 F-" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . " " , , ' ~ - - - - ~ 0.1 m J E N D L - 3 . 2 _ _ " ' , , X _ _ - 0 . 0 4

. ~ - ~ . . . . . . . . ENDF / 0.08 0.03 z o

U) , ,~

0.06 0.o2 ~

0 .04

0 .02 0.01

0 L ' ' ' ' ~ ' ' ' ' ' ' ' ' ' 0

1 0 s 1 08 0 7

Energy(eV)

Fig.7 Energy dependent sensitivity of 13elf to D.N. yield of 238U in XIX-2 core, The D.N. yields of Z~U in JENDL-3.2 and ENDF/B-VI are also shown.

Analysis of benchmark experiments 221

This underprediction was within the experimental uncertainty of 3%. The better agreement of calculation and experiment is achieved by increasing the D.N. yield of 23Su in ENDF/B-VI in this energy range.

The calculated 13 elf agreed well with the experimental one in this core when the D.N. yields of JENDL-3.2 were used. However it is noted that the 239pu also had a large contribution(~40%) to the [3eu of this core and the D.N. yield of 239pu in JENDL-3.2 needs to be increased as discussed for the XIX-3 core. Therefore the D.N. yield of 23SU in JENDL-3.2 should be decreased.

IV. CONCLUSIONS

The comparisons of experimental ~eef'S between different methods were carried out in the 13 eel benchmark experiments at FCA. The final values of 13 elf were determined through these comparisons: 742pcm+3%, 364pcm-4-3% and 251pcm_-E2% at the cores of XIX-1, XIX-2 and XIX-3 respectively. The correlations of 13eef'S between the methods were considered in this finalization. The target accuracy of 3% was achieved for these final values. These results are recommended as reliable 13 eff benchmark data.

The analyses were carded out for the keff, the central fission rate ratios and the 13 eff using the JENDL-3.2 nuclear data file. The reliability of present neutron field calculation for the [3elf was shown through comparison of the experimental and calculated results for the keff and the central fission rate ratios. Two D.N. data sets of JENDL-3.2 and ENDF/B-VI were tested in these analyses. The C/E's of the 13elf were 1.004, 1.005 and 0.972 in the cores of XIX-1, XIX-2 and XIX-3 respectively when the D.N. data of JENDL-3.2 were used. The C/E's of the [3eff were 1.033, 0.985 and 0.992 in the cores of XIX-1, XIX-2 and XIX-3 respectively when the D.N. data of ENDF/B-VI were used. Furthermore, the effect of changing the D.N. spectra on the ~eef calculation was found to be small in the present benchmark cores. To improve the prediction accuracy of 13elf of fast reactor, recommendations for the D.N. yields were drawn from these C/E's :

(a) The D.N. yield of 235U in ENDF/B-VI should be decreased by ~3% below incident neutron energy of ~ 1 MeV.

(b) The D.N. yield of 239pu in JENDL-3.2 should be increased by ~3% below incident neutron energy o f - 1 MeV.

(c) The D.N. yield of Z3SU in ENDF/B-VI should be increased while that in JENDL-3.2 should be decreased.

Further study is needed to make a detailed evaluation for the D.N. yield of 238U.

ACKNOWLEDGEMENT

The authors are grateful to all the participants of the ~ eff benchmark experiments for their kind cooperation to summarize the experimental results. We also thank Drs. A. D'Angelo of ENEA/Italy, R. Soule and J. F. Lebrats of CEA/France for valuable discussions in finalizing the experimental results.


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Lathrop K.D., Brinkley EW. (1973) TWOTRAN-II: An Interfaced Exportable Version of the TWOTRAN Code for Two-Dimensional Transport. LA- 4848-MS.

Nakagawa, M., Tsuchihashi, K. (1984) SLAROM : A Code for Cell Homogenization of Fast Reactor. JAERI 1294.

Nakagawa, T., et al. (1995) Japanese Evaluated Nuclear Data Library Version 3 Revision-2 JENDL-3.2. Journal of Nucl. Sci. Technol. 32, 1259.

Rose, P.E, (Ed.) (1991) ENDF-201, ENDF/B-VI Summary Documentation, BNL-NCS- 17541, 4th Edition.

Sakurai, T., et al. (1999a) Experimental Cores for Benchmark Experiments of Effective Delayed Neutron Fraction 13 elf at FCA. in this volume of Progress in Nuclear Energy.

Sakurai, T., Sodeyama, H., Okajima, S. (1999b) Measurement of Effective Delayed Neutron Fraction 13 el f by Covariance to Mean Method for Benchmark Experiments of 13 elf at FCA. ibid.

Sakurai, T., et aL (1999c) Measurement of Effective Delayed Neutron Fraction ~eff by 252Cf Source Method for Benchmark Experiments of 13elf at FCA. ibid.

Saphier, D., et al. (1977) Evaluated Delayed Neutron Spectra and Their Importance in Reactor Calculations. NucL Sci. Eng. 62, 660.

Takano, H., et aL (1994) Benchmark Tests of JENDL-3.2 for Thermal and Fast Reactors. Proc. Int. Conf. Nuclear Data for Science and Technology. Gatlinburg, USA 809.

Tuttle, R.J. (1979) Delayed-Neutron Yields in Nuclear Fission. Proc. Consultants' Meeting on Delayed Neutron Properties. Vienna INDC(NDS)-107/G+ Special, 29.

APPENDIX

1. Correlation of 13 elf's by 252Cf Source Method between JAERI/KAERI and IPPE

The JAERI/KAERI determined the ~ elf by(Sakurai et al. 1999c)

~t Scf . (~_yf_g), ~ef f = PCf " Fcer~ter " ~ " Ft fuet

The IPPE determined the ~eff by(Doulin et aL 1999)

Scf ~eff

Ipl" Q" Af~ete,imVortar~ce" Aft~ete,ftssior~" ~ " f

(A1)

• g ; , (A2)

where

Scf

Pcf Fce~t~

Fi

Ipl Q

m

"v R

f

0;

A n a l y s i s o f b e n c h m a r k exper iments 223

: Neutron emission rate of calibrated 252Cf source : Apparent reactivity worth of 252Cf source at the core center in dollars unit

: Central fission rate of core material per volume : Average number of neutrons emitted per fission of fuel at the core center : Normalization integral defined below

: Importance ratio of the 252Cf source neutrons to the reactor fission

: neutrons at the core center defined below : Subcriticality : Increase in central fission rate of principal nuclide which is caused by

introduction of 252Cf source (Principal nuclide : 235U in the XIX-1 core and 239pu in the XIX-2 and XIX-3 cores)

: Number of neutrons emitted per fission of fuel averaged in reactor : Fission integral defined below : Spatial correction factor defined below

AftteteAravortarLce : Correction factor for cell heterogeneity on fission importance at the core center

Afhete,fi.ssio~ : Correction factor for cell heterogeneity on fission rate at the core center.

The Scf, Pcf, Ipl, FcerLter and Q are the measured parameters. The Afkete,importance and Afket e ,f~ss,o~ are correction factors applied to the Ipl and Q in the case of IPPE. The others are semi- experimental or calculated parameters described by Sakurai et al. (1999a). t These parameters are defined by

J" (J'XqbfdE)(fwY-fqbdE) dv F~ = reactor , (A3)

(f Xqbt dE)o (j"vYfqb dE)o

f (J' fg dE) d . f = ~eactor (A4)

5 qUdE)o ' _ (J"vYfqb dE)o

(f)-fqbdE)o ' (A5)

f (J'wZfdp dE) dv - - r e a c t o r (A6) w R - f (f)-fdpdE)dv '

r e a c t o r

(J" xcf4 tdE)o - (j'XqbfdE)o ' (A7)

(fXcfqb*dE)0 f ( f w g d p d E ) dv * _ _ reactor , (A8)

0-~ -- f (J 'xdfdE)(fwYfqbdE) dv r e a c t o r

qbt / , a t Cf / '+ ' fue t

tThe f was evaluated from the common fission integral FR(Doulin et al., 1999).

224

where X Xcf

"V

N×

T. Sakurai and S. Okajima

: Region-dependent fission spectrum of fuel : Spontaneous fission spectrum of ZSZCf : Space- and energy-dependent forward and adjoint flux : Region- and energy-dependent number of neutrons per fission of fuel : Region- and energy-dependent macroscopic fission cross section : Region- and energy-dependent microscopic fission cross section of principal

nuclide x : Region-dependent atomic number density of principal nuclide x

and where ( )0 denotes the central value for the quantity in parentheses. When these expressions for the semi-experimental and calculated parameters are used in

Eqs.(A1) and (A2), the [3eff by JAERI/KAERI becomes

Scf [~eff = • Fu (A9)

PCf " Fc~ter

and the [~eff by IPPE becomes

eff Scf Fb

[PI" Q" Af~ete,importa~ee" Afhete , fbs ior t f× ' (AIO)

where Fb and f~ is given by

Fb = (f xcf(h t dE)0 (f Zf haE)0 (Al l )

I (Ix*t E)(Iwzf* dE) av' ~eactor

f , = (]" Zf@dE)o (A12) I o ,aE)o "

The Eqs. (A9) and (A10) show that the products of semi-experimental and calculated parameters become Fb and Fb/fx for the JAERI/KAERI and IPPE respectively. The central fission rate of JAERI/KAERI FeerLter includes all the fissionable nuclides(Sakurai et al., 1999a) while that of IPPE Q takes account of only the principal nuclide. This difference cause the factor fx in IPPE. Moreover, the correction for cell heterogeneity on the central fission rate(Afkete,~ssb~) that is shown in Eq. (A10) of IPPE has already been included in the Fce~t~r of JAERI/KAERI.

Furthermore, the common 252Cf source was used by both participants. The reactivity worth Ocf of JAERI/KAERI and the subcfiticality 1Ol of IPPE were measured by using the control rods. The uncertainties of the Pcf and IPl were dominated by that of the control rod calibration which were common to both participants. Consequently, the 13 elf'S of JAERI/KAERI and IPPE are highly correlated.


2. Correction Factors on Calculated Physics Parameters

225

Tables A1 summarize the 'transport correction factor' and 'mesh correction factor'. Further- more, these tables show two additional correction factors that were prepared to serve when the physics parameters are calculated by using the cylindrical model and the homogeneous compo- sition. These additional correction factors are

Correction factor for cell heterogeneity effect(' heterogeneity correction factor') and Correction factor for cylindrization effect('cylindrization correction factor').

To estimate these correction factors, the parameters were calculated by the diffusion theory with homogeneous compositions in the two-dimensional cylindrical model. The 'heterogeneity correction factor' was estimated by comparing the calculated result with the homogeneous compositions and that with the heterogeneous compositions. The 'cylindrization correction factor' was estimated by comparing the calculated results between the two-dimensional cylindrical model and the three-dimensional X-Y-Z model.

Table A1 Correction factors on calculated physics parameters

(a) ~eff


'Heterogeneity' 0.987 0.969 0.990

'Cylindrization' 1.000 0.995 0.994

'Transport' 0.990 0.991 0.988

(b) Central fission rate ratio

Core name and XIX-1 XIX-2 XIX-3 fission rate ratio 23Su/23SU 235U/239pu 238U/239pu 23Su/239pH 238U/239pu

'Heterogeneity' 1.121 0.991 0.936 0.996 0.991

'Transport' 1.002 1.000 0.996 1.000 0.991

(C) keff


'Heterogeneity' 1.0040 1.0083 1.0067

'Cylindrization' 0.9994 1.0002 1.0010

'Transport' 1.0133 1.0139 1.0136

'M~sh' 0.9974 0.9990 0.9982

Documents

Analysis of benchmark experiments of effective delayed neutron fraction βeff at FCA