H.B. Robinson-2 Pressure Vessel Dosimetry Benchmark - Deterministic Analysis in Both Cartesian (X,Y,Z) and Cylindrical (R,Θ,Z) Geometries Using the TORT-3.2 3D Transport Code, the BUGJEFF311.BOLIB, BUGENDF70.BOLIB, BUGLE-B7 and the BUGLE-96 Cross Section

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Pag.

1. INTRODUCTION 3

2. DESCRIPTION 4

3. CORE POWER DISTRIBUTION AND POWER HISTORY 14

4. DOSIMETRY MEASUREMENTS 23

5. CROSS SECTION LIBRARIES AND NUCLEAR DATA IN TRANSPORT

CALCULATIONS 26

5.1 BUGJEFF311.BOLIB Cross Section Library 26

5.2 BUGENDF70.BOLIB Cross Section Library 26

5.3 BUGLE-B7 Cross Section Library 26

5.4 BUGLE-96 Cross Section Library 27

5.5 IRDF-2002 Dosimeter Cross Sections 27

5.6 Fission Neutron Spectra 28

6. TRANSPORT CALCULATIONS 48

6.1 Transport Calculation General Features 48

6.2 HBR-2 Fission Neutron Source 63

6.3 Specific Activity Calculations 70

7. RESULTS 76

8. CONCLUSIONS 117

REFERENCES 118

APPENDIX A.1 Input File to ADEFTA-4.1 - Generation of the Compositional Model 121 Used in the Calculations with the BUGJEFF311.BOLIB Library.

APPENDIX A.2 Input File to ADEFTA-4.1 - Generation of the Compositional Model 125 Used in the Calculations with the BUGENDF70.BOLIB Library.

APPENDIX A.3 Input File to ADEFTA-4.1 - Generation of the Compositional Model 129 Used in the Calculations with the BUGLE-B7 Library.

APPENDIX A.4 Input File to ADEFTA-4.1 - Generation of the Compositional Model 133 Used in the Calculations with the BUGLE-96 Library.

APPENDIX B.1 Partial Input File to BOT3P-5.3 - Generation of the (X,Y,Z) 137 Geometrical Model Used in the Calculations with the

BUGJEFF311.BOLIB, BUGENDF70.BOLIB, BUGLE-B7 and BUGLE-96 Libraries.

APPENDIX B.2 Partial Input File to BOT3P-5.3 - Generation of the (R,θ,Z) 148 Geometrical Model Used in the Calculations with the

BUGJEFF311.BOLIB, BUGENDF70.BOLIB, BUGLE-B7 and BUGLE-96 Libraries.

APPENDIX C.1 HBR-2 Neutron Flux Distribution Plots. P3-S8 TORT-3.2 (X,Y,Z)/(R,θ,Z) 159

Calculations Using the BUGJEFF311.BOLIB Library.

Calculations Using the BUGENDF70.BOLIB Library.

Calculations Using the BUGLE-B7 Library.

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H.B. Robinson-2 Pressure Vessel Dosimetry Benchmark -

Deterministic Analysis in Both Cartesian (X,Y,Z) and Cylindrical

(R,θ,Z) Geometries Using the TORT-3.2 3D Transport Code, the

BUGJEFF311.BOLIB and the BUGLE-96 Cross Section

Libraries

Roberto Orsi 1. INTRODUCTION

H.B. Robinson Unit 2 (HBR-2) is a commercial pressurized light-water reactor (PWR) designed by Westinghouse, with 2300 MW (thermal) power. It was placed in operation in March 1971 and is owned by Carolina Power and Light Company. Analysis of the HBR-2 benchmark /1/ /2/ can be used as partial fulfillment of the requirements for the qualification of the methodology for calculating neutron fluence in RPVs, as required by the U.S. Nuclear Regulatory Guide 1.190 /3/. The HBR-2 Pressure Vessel Dosimetry Benchmark, based on experimental data from an operating PWR reactor, is an in- and ex-Reactor Pressure Vessel (RPV) neutron dosimetry benchmark openly available through the SINBAD Database /4/ at the OECD/NEA data Bank. The measured (M) quantities, to be compared with the calculated values (C), are the specific activities at the end of fuel cycle 9 (cycle 9 time interval: from 21-08-1982 to 26-01-1984) on the midplane of the HBR-2 core in the surveillance capsule and in the cavity location. The provided experimental data are the measured specific activities of the radiometric monitors at the end of irradiation. The characteristic feature of the HBR-2 benchmark is that it provides measurements on both sides of the pressure vessel: in the surveillance capsule attached to the thermal shield and in the reactor cavity.

As underlined in Refs /1/ /2/, the measurements served several purposes. By performing the measurements on both sides of the pressure vessel, that is, in the surveillance capsule located in the downcomer region between the thermal shield and the pressure vessel, and outside the pressure vessel, in the cavity between the vessel and the biological shield, the consistency between the (traditional) in-vessel dosimetry and the cavity dosimetry (which was new at the time of these experiments) was tested. The cavity measurements were used to experimentally verify the effectiveness of the low-leakage fuel loading pattern which was introduced in the HBR-2 in fuel cycle 9 to reduce the pressure vessel irradiation. The measurements also provided a means to test the ability of neutron transport calculations to predict the through the wall attenuation.

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2. DESCRIPTION

All the data and description in this section and in the two following ones (3. and 4.) were obtained from Refs. /1/ and /2/, which are in turn based on Refs /5/ /6/ and personal communications among Westinghouse and Ref. 1 Authors (see pag. 2 of Ref. /1/).

The core of the HBR-2 reactor consists of 157 fuel elements and is surrounded by the core baffle, core barrel, thermal shield, pressure vessel, and biological shield.

Selected general data and dimensions of the HBR-2 reactor are given in Table 2.1.

An octant of the horizontal cross-section of the reactor is shown schematically in Fig. 2.1, which also shows the locations of the capsule and cavity dosimeters.

Axial geometry and dimensions are given in Fig. 2.2. The core baffle geometry is further specified in Fig. 2.3. Surveillance capsules are located in the down-comer region and are attached to the thermal shield. The details of the capsule mounting are shown in Fig. 2.4.

The reactor cavity is 17.10 cm (6.73 in.) wide, measured from the pressure vessel outer radius to the inner radius of the cylindrical biological (concrete) shield. A 7.62-cm (3-in.) thick insulation is installed in the cavity, leaving a 1.31-cm (0.52-in.) air gap between the pressure vessel and the insulation and an 8.18-cm (3.22-in.) air gap between the insulation and the concrete shield. The insulation consists of three steel sheets and eight steel foils with air gaps between them. The total thickness of the insulation steel sheets and foils is 0.2286 cm (0.090 in.). There are two relatively wide (38 cm, or 15 in.) and deep (80.645 cm, or 2 ft, 7.75 in.) detector wells at 0° and 45° azimuthal locations. In each well is a vertical cylinder with a 19.05-cm (7.5-in.) outer diameter and 0.635-cm (0.25-in.)-thick steel wall. The vertical axis of the cylinder is at 252.174 cm (8 ft, 3.28125 in.) from the core center. The concrete surfaces of the detector well are covered with a 0.635-cm (0.25-in.)-thick steel liner. Other concrete surfaces are bare.

The material composition of the reactor components (e.g., pressure vessel, thermal shield, etc.) is given in Table 2.2. Some components (e.g., fuel elements) have an elaborate design, but they are usually approximated as homogenized regions in the transport calculations of the out-of-the-core neutron field. To reduce the amount of data needed for such regions, the volume fractions of the materials are given in Table 2.2. The regions given in Table 2.2 correspond to the ones shown in Figs. 2.1 and 2.2.

The core-average water temperature during cycle 9 was ~ 280℃ (536℉), and the temperature of the water in the down-comer was approximately 267℃ (512℉). The pressure was 15.513 MPa (2250 psia). The cycle average boron concentration in the coolant was approximately 500 ppm. The corresponding water densities in different regions are also given in Table 2.2.

The densities and chemical compositions of the other materials are given in Table 2.3.

The concrete of the biological shielding is assumed to be type 02-B ordinary concrete /7/ with water content reduced to 4.67% by weight and iron concentration increased to reflect an estimated 0.7% by volume addition of rebar /5/.

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Table 2.1 Selected General Data and Dimensions of the H.B. Robinson Unit 2. Plant

Location South Carolina,Hartsville

Owner Carolina Power and Light

Beginning of operation March 1971

Reactor Vendor Westinghouse Type PWR Coolant H2O Number of loops 3 Thermal power 2300 MW Core

Number of fuel assemblies 157

Pitch 21.504 cm 8.466 in.

Fuel Element

Type 15 × 15 array of fuel pins

Fuel pins per element 204

Horizontal cross section rectangular,

(including gap) 21.504 cm × 21.504 cm

Height of fuel 365.76 cm 12 ft.

Core Baffle*

Dimensions See Fig. 3

Thickness 2.858 ± 0.013 cm 1.125 ± 0.005 in.

Core Barrel†

Inner radius 170.023 ± 0.318 cm 66.938 ± 0.125 in.

Thickness 5.161 ± 0.107 cm 2.032 ± 0.042 in.

Thermal Shield

Thickness 6.825 ± 0.160 cm 2.687 ± 0.063 in.

Pressure Vessel

Cladding

Thickness (minimal) 0.556 cm 7/32 in.(0.219 in.)

Base metal

Inner radius‡ 198.041 cm 77.969 in.

Thickness** 23.614 ± 0.041 cm 9.297 ± 0.016 in.

Total thickness (wall + cladding ) 24.170 cm 9.516 in.

Pressure Vessel Thermal Insulation

Inner radius 222.964 cm 87.781 in.

Total insulation thickness 7.620 cm 3.0 in.

(including voids)

Insulation steel components

1 steel sheet 0.079 cm 0.031 in.

8 steel foils 0.005 cm 0.002 in.

Total thickness of the steel in the

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Table 2.1. (continued) Pressure Vessel Cavity See Fig. 1

Dimensions

Vessel-to-insulation gap 1.31 cm 0.52 in.

Insulation 7.62 cm 3.00 in.

Insulation-to-concrete gap 8.18 cm 3.22 in.

Total width of the cylindrical part 17.10 cm 6.73 in.

Biological Shield

Dimensions See Fig. 1

Inner radius of cylindrical surfaces 238.760 cm 7 ft 10 in.

* The baffle units are positioned symmetrically about the core center within 0.025 cm (0.010 in.) measured at the top and bottom former elevations.

† The annular gap between the core barrel outer radius and the thermal shield inner radius is maintained uniform within 0,381 cm (0.150 in.).

‡ The pressure vessel base metal inner radius is obtained as the cladding inner radius plus specified minimum cladding thickness of 0.556 cm (7/32 in.). **The pressure vessel thickness is based on a single measurement of the lower

shell and three measurements of the intermediate shell (S.L. Anderson,

Westinghouse Electric Corporation, personal communication to I. Remec, Oak Ridge National Laboratory, 1996).

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Fig. 2.3 Core Baffle Geometry.

Nominal dimensions are given for the core-side surfaces of the baffle plates. Deviations from nominal are for the maximum and minimum dimensions (e.g., for A the nominal dimension is 64.607 cm, with the maximum value of 64.643 cm and the minimum value of 64.571 cm).

DIMENSION A 64.607 ± 0.036 cm (25.436 ± 0.014 in.) B 150.663 ± 0.046 cm (59.316 ± 0.018 in.) C 193.680 ± 0.056 cm (76.252 ± 0.022 in.) D 236.698 ± 0.066 cm (93.188 ± 0.026 in.) E 279.715 ± 0.076 cm (110.124 ± 0.030 in.) F 322.684 ± 0.084 cm (127.041 ± 0.033 in.)

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Fig. 2.4 Sketch of the Surveillance Capsule Mounting on the Thermal Shield (not to scale).

The capsule centerline is at 191.155 ± 0.152 cm (75.258 ± 0.060 in.) (S. L. Anderson, Westinghouse Electric Corporation, personal communication to I. Remec, Oak Ridge National Laboratory, 1996).

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Table 2.2 Materials of the Components and Regions

Region Material* Volume Fraction

UO2, enriched to 2.9%, 0,2997 density 10.418 g cm−3

Reactor core Zircaloy-4 0,1004

Inconel-718 0,00281

Stainless steel SS-304 0,00062

Water 0,5886

density 0.766 g cm−3

Core baffle Stainless steel SS-304 1,000

Bypass region Water See Fig. 2

Core barrel Stainless steel SS-304 1,000

Downcomer Water 1,000

region No. 1 density 0.787 g cm−3

Thermal shield Stainless steel SS-304 1,000

Surveillance capsule

Mounting Stainless steel SS-304 1,000

Content Steel A533B 1,000

Downcomer Water 1,000

region No. 2 density 0.787 g cm−3

Pressure vessel Stainless Steel SS-304 1,000

cladding

Pressure vessel Steel A533B 1,000

Insulation Stainless steel SS-304 0,030

Air 0,970

Reactor cavity Air 1,000

Biological shield Concrete 1,000

Core support Stainless steel SS-304 0,049

Water 0,951

Lower core plate Stainless steel SS-304 0,668

Water 0,332

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Table 2.2 (continued)

Nozzle legs Stainless steel SS-304 0,070

Water 0,930

Bottom nozzle plate Stainless steel SS-304 0,717

Water 0,283

Water gap No. 1 Stainless steel SS-304 0,007

Water 0,993

End plugs Stainless steel SS-304 0,300

Water 0,700

Fuel plenum Stainless steel SS-304 0,224

Water 0,560

Water gap No.2 Stainless steel SS-304 0,017

Water 0,983

Top nozzle Stainless steel SS-304 0,275

Water 0,725

Formers Stainless steel SS-304 0,900

Water 0,100

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Table 2.3 Densities and Chemical Compositions of Materials MATERIAL Carbon steel A533B Stainless steel

SS-304 Inconel-718 Zircalloy-4 Concrete* Density (g/cm3₎ _7,83 _8,03 _8,3 _6,56 _2,275 Element Weight % Fe 97,90 69,00 7,00 0,50 3,82 Ni 0,55 10,00 73,00 Cr 19,00 15,00 Mn 1,30 2,00 C 0,25 0,10 Ti 2,50 Si 2,50 34,09 Zr 97,91 Sn 1,59 Ca 4,40 K 1,31 Al 3,43 Mg 0,22 Na 1,62 O 50,50 H 0,51

* The concrete is assumed to be type 02-B ordinary concrete with water content reduced to 4.67% by weight and increased iron concentration to reflect an estimated 0.7% by volume addition of rebar.

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3. CORE POWER DISTRIBUTION AND POWER HISTORY

The fuel assemblies in the core are numbered as shown in Fig. 3.1 These numbers are used in the description of the core power distribution during cycle 9. The data files referred to in this paragraph were provided as ASCII files.

For each assembly in the core, the mass of uranium, burnup at the beginning of cycle life (BOL) and end of cycle life (EOL), burnup increment in cycle 9, and cycle-average relative power were listed in the data file FILE1.DAT. Part of the file is shown in Fig. 3.2. Assembly powers are normalized to the core-wise average of 1.00.

Cycle-average, assembly-wise axial power distributions were given in FILE2.DAT. Part of FILE2.DAT is shown in Fig. 3.3. Each assembly is divided vertically into 12 equal-length segments, covering the active length of the fuel, with the first segment on the top and the twelfth segment at the bottom. Cycle-average relative power for each segment is given. Assembly segment powers are normalized to the average value 1.00.

The cycle-average assembly-pin-power distributions were given in FILE3.DAT. The content of the file is illustrated in Fig. 3.4. Distributions are given for the assemblies in the top right quadrant of the core (e.g., assemblies 2, 3, 7, 8, 9, 10, ... , 79, 80, 81, 82, 83, 84, 85, 86) only. For each assembly, an array of 15 × 15 relative pin powers is given. Pin powers are normalized so that the average of the fuel-pin powers (e.g., 204 per assembly) is 1.00. The pin powers are ordered in rows: the first value corresponds to the pin in the top left corner of the assembly, the last value in row 1 to the pin at the top right corner of the assembly, and the last value in row 15 to the pin at the bottom right corner of the assembly. The orientation of the assembly in the core is as shown in Fig. 3.1. The cycle-average pin powers were obtained by weighting the pin powers which were given at eight core burnup steps during the cycle. The weight assigned to the power distribution at the I-th burnup step was proportional to the burnup increment from the midpoint of the (I-1)-th and I-th burnup step and I-th and (I+1)-th burnup step.

For cycle 9, a low-leakage core loading pattern was used in which 12 previously burned fuel elements (i.e., elements number 1, 2, 3, 57, 71, 72, 86, 87, 101, 155, 156, and 157) were put on the core periphery. During cycle 9, the relative powers of the outer assemblies changed significantly. This effect, which is often referred to as power redistribution, is caused by the fuel burnout and gradual changes of the boron concentration in the coolant during the cycle. The power redistribution affects the core neutron leakage and consequently the dosimeter reaction rates. For this reason, the cycle-average core power distribution data, described previously, are supplemented by the power distribution data at several burnup steps during the cycle. At the core-average cycle burnups of 147, 417, 1632, 3363, 5257, 7595, 9293, and 10379 megawatt days per metric ton of uranium (MWd/MTU) the following information was provided: average assembly powers (FILE4.DAT, see Fig. 3.5), assembly burnups (FILE5.DAT, see Fig. 3.6), pin-power distributions for the assemblies in the upper left quadrant of the core (FILE6.DAT, see Fig. 3.7), and assembly-wise axial power distributions in 12 axial segments (FILE7.DAT,see Fig. 3.8).

The core power history for cycle 9 was given in the FILE8.DAT as is illustrated in Fig. 3.9.

Descriptions of the contents and formats of the files are given at the end of each file and are shown in Figs. 3.2-3.9.

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Fig. 3.2 Content and Format of the FILE1.DAT. (Beginning and end of the file are shown).

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4. DOSIMETRY MEASUREMENS

During cycle 9, comprehensive sets of dosimeters were irradiated in the surveillance capsule position and in several locations in the reactor cavity (Ref. 6). For the benchmark, a subset of the measurements was chosen. The selected subset consists of the threshold radiometric monitors from the surveillance capsule at the azimuthal angle of 20° and from the cavity dosimetry located at the azimuthal angle of 0°.

A specially built surveillance capsule containing no metallurgical specimens, but otherwise identical to a standard Westinghouse capsule, was placed in a previously used holder at the 20° azimuthal angle location in the downcomer. The region that usually contains metallurgical specimens was filled with carbon steel, and the dosimeters were installed in the holes drilled in the steel. Specific activities given in Table 4.1 are for the core-mid-plane set. (Dosimetry sets were installed in the capsule at the core mid-plane and approximately 28 cm (11 in.) above and below the mid-plane. The measured activities showed axial variations of only ~ 3%, which is not considered important, and therefore only the results for the mid-plane set were given. Radially, the dosimeters were installed at the capsule centerline at the radius of 191.15 cm (see Fig. 2.4). The specially built capsule was irradiated during cycle 9 only.

Specific activities of the cavity dosimeters irradiated at 0° azimuth, on the core mid-plane, are also given in Table 4.1. In the present benchmark, only the mid-plane measurements are available for comparison with calculation. However, at the 0° azimuth multiple dosimeter sets were irradiated at the mid-plane and at 213 cm ( 7 ft) and 107 cm (3.5 ft) above and below the mid-plane; and activities of the gradient wire [54_Fe(n,p)54_{Mn and}58_Ni(n,p)58_{Co reactions] were measured at several}

positions between the foil locations but these measurements were not added to the benchmark because the authors (I. Remec, F.B.K. Kam, etc.) would not enlarge the scope of the benchmark /1/ to include verification of the calculational methodology for off-mid-plane locations.

The dosimeters were irradiated in an aluminum 6061 holder 5.08 cm (2 in.) wide, 1.422 cm (0.56 in.) thick, and 15.240 cm (6 in.) long. Aluminum was selected as the holder material in order to minimize neutron flux perturbations at the dosimeter locations. The holder was supported by a 0.813-mm (0.032-in.)-diam. stainless steel gradient wire mounted vertically in the gap between the insulation and the biological shield at a radius of 238.02 cm (93.71 in.). The sketch of the 0° azimuth cavity dosimetry axial locations is given in Fig. 4.1.

Specific activities listed in Table 4.1 were as-measured with no corrections (e.g., for impurities or photo-fission). The corrections, which are suggested for comparison with calculation, are given in the footnotes to Table 4.1 /5/.

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Table 4.1 Measured Specific Activities of the Dosimeter from the Surveillance Capsule and from the Cavity in the Core Midplane at the End of Cycle 9 (26-01-1984).

(Specific activities (Bq/mg) are given per mg of Ni, Fe, Ti, and Cu material with

Naturally occurring isotopic composition, and per mg of 237_{Np and}238_{U isotopes).}

Surveillance capsule Cavity

(core midplane, _20°azimuth, (core midplane, 0° _azimuth, Dosimeter radius 191.15cm)* radius 238.02 cm) ✝

237_Np(n,f)137_Cs _3.671E+02 _2.236E+01

238_U(n,f)137_Cs _5.345E+01 _8.513E-01

58_Ni(n,p)58_Co _{1.786E+4 ‡} _1.959E+02

54_Fe(n,p)54_Mn _{9.342E+2 ‡} _8.711

46_Ti(n,p)46_Sc _{3.500E+2 **} _3.310

63_Cu(n,α)60_Co _{2.646E+1 **} _2.645E-01

* Dosimeters in the capsule were irradiated under 0.508 mm (0.020 in.) Gd cover,

except where noted differently. Ref. 5 estimates that in order to compensate for the photofission contribution, the 137_{Cs activity in}237_{Np and}238_{U should be reduced by}

2.5% and 5%, respectively, and 60_{Co activity in}63_{Cu should be reduced by 2.5% to}

compensate for the contribution from the 59_Co(n,γ)60_{Co reaction on the Co impurities}

in the Cu dosimeter.

† In the cavity, the 237_Np,238_{U and Ni dosimeters were irradiated under}

0.508 mm (0.020 in.) Cd cover. Ti and Fe dosimeters were irradiated bare. Activity of the Fe is an average of four measurements. The Cu activity is an average of one bare dosimeter and one dosimeter irradiated in Cd cover.

Ref. 5 estimates that in order to compensate for the photo-fission contribution, the 137_{Cs activity in}237_{Np and}238_{U should be reduced by 5.0% and 10.0%, respectively;}

and 60_{Co activity in}63_{Cu should be reduced by 2.5% to compensate for the contribution}

from the 59_Co(n,γ)60_{Co reaction on the Co impurities in the Cu dosimeter.}

‡ Average of five dosimeters, three inside Gd and two outside. **Average of two measurements.

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Fig. 4.1 Schematic Drawing of the Axial Positions of the Cavity Dosimeters*.

* At each marked locations a multiple dosimeter set was irradiated. Data in Table 4.1 are for the set

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5 CROSS SECTION LIBRARIES AND NUCLEAR DATA IN TRANSPORT CALCULTIONS The BUGLE-96 /8/, BUGJEFF311.BOLIB /9/, BUGENDF70.BOLIB /10/ and BUGLE-B7 /11/ group working cross section libraries were used in the present deterministic transport analysis. The ENEA-Bologna BUGJEFF311.BOLIB and BUGENDF70.BOLIB libraries and the ORNL BUGLE-B7 and BUGLE-96 libraries adopt the same neutron (Table. 5.1) and photon (Table. 5.2) group structure and are briefly described in this chapter.

5.1 BUGJEFF311.BOLIB Cross Section Library

BUGJEFF311.BOLIB /9/ is an ENEA-Bologna broad-group (47 neutron groups + 20 photon groups) coupled neutron and photon working cross section library in FIDO-ANISN format, generated in the same energy group structure of the ORNL BUGLE-96 similar library and based on the OECD-NEADB JEFF-3.1.1 /12/ /13/ evaluated nuclear data library. This broad-group library was obtained through problem-dependent cross section collapsing and self-shielding from the ENEA-Bologna VITJEFF311.BOLIB /14/ fine-group coupled neutron and photon pseudo-problem-independent library in AMPX format for nuclear fission applications. VITJEFF311.BOLIB adopts the same energy group structure (199 neutron groups + 42 photon groups) of the ORNL VITAMIN-B6 /8/ library and it is based on the Bondarenko /15/ (f-factor) neutron resonance self-shielding method.

BUGJEFF311.BOLIB, dedicated to LWR shielding and pressure vessel dosimetry applications, was generated using the ENEA-Bologna 2007 Revision /16/ of the ORNL SCAMPI /17/ nuclear data processing system, able to treat double precision data and freely released at OECD-NEADB and ORNL-RSICC.

The BUGJEFF311.BOLIB library was freely released at OECD-NEADB in 2011, assuming the designation NEA-1866 ZZ BUGJEFF311.BOLIB.

5.2 BUGENDF70.BOLIB Cross Section Library

BUGENDF70.BOLIB /10/ is an ENEA-Bologna broad-group (47 neutron groups + 20 photon groups) coupled neutron and photon working cross section library in FIDO-ANISN format, generated in the same energy group structure of the ORNL BUGLE-96 similar library and based on the US ENDF/B-VII.0 /18/ evaluated nuclear data library. BUGENDF70.BOLIB is exactly the twin library of BUGJEFF311.BOLIB, the former based on ENDF/B-VII.0, the latter on JEFF-3.1.1. This broad-group library was obtained through problem-dependent cross section collapsing and self-shielding from the ENEA-Bologna VITENDF70.BOLIB /19/ fine-group coupled neutron and photon pseudo-problem-independent library in AMPX format for nuclear fission applications. VITENDF70.BOLIB adopts the same energy group structure (199 neutron groups + 42 photon groups) of the ORNL VITAMIN-B6 library and it is based on the Bondarenko (f-factor) neutron resonance self-shielding method.

Also BUGENDF70.BOLIB was generated using the ENEA-Bologna 2007 Revision of the ORNL SCAMPI nuclear data processing system. The BUGENDF70.BOLIB library was freely released at OECD-NEADB in 2013, assuming the designation NEA-1872 ZZ BUGENDF70.BOLIB.

5.3 BUGLE-B7 Cross Section Library

BUGLE-B7 /11/ is an ORNL broad-group (47 neutron groups + 20 photon groups) coupled neutron and photon working cross section library in FIDO-ANISN format, based on the US ENDF/B-VII.0 evaluated nuclear data library. BUGLE-B7 was obtained through problem-dependent cross section

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collapsing and self-shielding from the ORNL VITAMIN-B7 /11/ fine-group (199 neutron groups + 42 photon groups) coupled neutron and photon pseudo-problem-independent library in AMPX format for nuclear fission applications. VITAMIN-B7 is based on the Bondarenko (f-factor) neutron resonance self-shielding method.

BUGLE-B7, dedicated to LWR shielding and pressure vessel dosimetry applications, was generated using the ORNL AMPX-6 /20/ nuclear data processing system.

5.4 BUGLE-96 Cross Section Library

BUGLE-96 /8/ is an ORNL broad-group (47 neutron groups + 20 photon groups) coupled neutron and photon working cross section library in FIDO-ANISN format, based on the US ENDF/B-VI.3 /21/ evaluated nuclear data library. BUGLE-96 was obtained through problem-dependent cross section collapsing and self-shielding from the ORNL VITAMIN-B6 fine-group (199 neutron groups + 42 photon groups) coupled neutron and photon pseudo-problem-independent library in AMPX format for nuclear fission applications. VITAMIN-B6 is based on the Bondarenko (f-factor) neutron resonance self-shielding method.

BUGLE-96, dedicated to LWR shielding and pressure vessel dosimetry applications, was generated using the ORNL SCAMPI nuclear data processing system and was freely released to OECD-NEADB in 1996 where assumed the designation DLC-0185 ZZ BUGLE-96.

Both BUGLE-96 and VITAMIN-B6 became reference standards (see /22/,ANSI/ANS-6.1.2-1999 (R2009)) as multi-group libraries for shielding applications and were successfully used all over the world.

5.5 IRDF-2002 Dosimeter Cross Sections

The dosimeter cross sections used in the transport calculations /23/ were all derived from the IAEA International Reactor Dosimetry File 2002 /24/ (IRDF-2002). A major objective of this data development project was to prepare and distribute a standardized, updated and tested reactor dosimetry cross section library accompanied by uncertainty information for use in service life assessments of nuclear power reactors.

The 237_Np(n,f),238_U(n,f),58_Ni(n,p)58_Co,54_Fe(n,p)54_Mn,46_Ti(n,p)46_{Sc and}63_Cu(n,α)60_{Co dosimeter}

cross sections needed in the HBR-2 transport analyses with the BUGJEFF311.BOLIB, BUGENDF70.BOLIB, BUGLE-b7 and BUGLE-96 cross section libraries were derived from the IRDF-2002 set of point-wise dosimetry cross sections through data processing with the GROUPIE program of the PREPRO 2007 /25/ nuclear data processing system into the 47-group neutron energy structure of the ORNL BUGLE-96 cross section library, using flat cross section weighting. Since flat weighting was adopted, the dosimeter cross sections in the 47-group neutron energy structure were the same for all the 4 cross section libraries in transport calculations.

The flat weighting 47-group cross sections are reported in Table 5.3, and their corresponding graphical representations are respectively shown from Fig. 5.1 to Fig. 5.6.

In particular Table 5.3, Fig. 5.1 and Fig. 5.2 report the 237_{Np and the}238_{U dosimeter fission cross}

section values. The 237_Np(n,f)137_Cs,238_U(n,f)137_{Cs values can be obtained by multiplying the}

dosimeter fission cross section by the corresponding cumulative 137_{Cs fission yield for one fast}

fission. The following values, taken from the “Live Chart of Nuclides” of the International Atomic Energy Agency (IAEA) web site, based on JEFF-3.1.1 data, were used for all libraries in calculations:

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5.6 Fission Neutron Spectra

The fission neutron spectrum used in calculation was taken as the average of 235_{U and}239_{Pu in order}

to account for the contribution of 235_{U and}239_{Pu to the fission neutron source, as reccomended in}

ref. /1/, pag 27.

The fission spectra used in trasport calculations for BUGJEFF311.BOLIB, BUGENDF70.BOLIB, BUGLE-B7 and BUGLE-96 are reported in Table 5.4.

Tables 5.5, 5.6, 5.7 and 5.8 report the fission neutron spectrum values for 235_{U and}239_{Pu for}

BUGJEFF311.BOLIB, BUGENDF70.BOLIB, BUGLE-B7 and BUGLE-96, respectively. It is worth while saying that BUGJEFF311.BOLIB and BUGENDF70.BOLIB include both contribution of prompt and delayed neutrons, whereas BUGLE-B7 and BUGLE-96 only of the prompt ones. Obtaining in both BUGJEFF311.BOLIB and BUGENDF70.BOLIB total fission spectra for all fissionable isotopes was made possible through the use of the ENEA-Bologna 2007 Revision of the ORNL SCAMPI nuclear data processing system.

Fig. 5.7 plots the fission spectrum of all the four libraries.

Figs. 5.8, 5.9, 5.10 and 5.11 report on the same plot the fission spectrum used in the calculations and the correspondig 238_{U and}239_{Pu spectra for BUGJEFF311.BOLIB, BUGENDF70.BOLIB,}

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Table 5.1 Neutron Group Energy and Lethargy Boundaries for the BUGJEFF311.BOLIB, BUGENDF70.BOLIB, BUGLE-B7 and BUGLE-96 Libraries.

Group Upper Energy Upper Lethargy [eV] 1 1.7332E+07 -5.4997E-01 2 1.4191E+07 -3.5002E-01 3 1.2214E+07 -2.0000E-01 4 1.0000E+07 0. 5 8.6071E+06 1.5000E-01 6 7.4082E+06 3.0000E-01 7 6.0653E+06 5.0000E-01 8 4.9659E+06 7.0000E-01 9 3.6788E+06 1.0000E-00 10 3.0119E+06 1.2000E+00 11 2.7253E+06 1.3000E+00 12 2.4660E+06 1.4000E+00 13 2.3653E+06 1.4417E+00 14 2.3457E+06 1.4500E+00 15 2.2313E+06 1.5000E+00 16 1.9205E+06 1.6500E+00 17 1.6530E+06 1.8000E+00 18 1.3534E+06 2.0000E+00 19 1.0026E+06 2.3000E+00 20 8.2085E+05 2.5000E+00 21 7.4274E+05 2.6000E+00 22 6.0810E+05 2.8000E+00 23 4.9787E+05 3.0000E+00 24 3.6883E+05 3.3000E+00 25 2.9721E+05 3.5159E+00 26 1.8316E+05 4.0000E+00 27 1.1109E+05 4.5000E+00 28 6.7379E+04 5.0000E+00 29 4.0868E+04 5.5000E+00 30 3.1828E+04 5.7500E+00 31 2.6058E+04 5.9500E+00 32 2.4176E+04 6.0250E+00 33 2.1875E+04 6.1250E+00 34 1.5034E+04 6.5000E+00 35 7.1017E+03 7.2500E+00 36 3.3546E+03 8.0000E+00 37 1.5846E+03 8.7500E+00 38 4.5400E+02 1.0000E+01 39 2.1445E+02 1.0750E+01 40 1.0130E+02 1.1500E+01 41 3.7266E+01 1.2500E+01 42 1.0677E+01 1.3750E+01 43 5.0435E+00 1.4500E+01 44 1.8554E+00 1.5500E+01 45 8.7643E-01 1.6250E+01 46 4.1399E-01 1.7000E+01 47 1.0000E-01 1.8421E+01 1.0000E-05 2.7631E+01

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Table 5.2 Photon Group Energy Boundaries for the BUGJEFF311.BOLIB, BUGENDF70.BOLIB, BUGLE-B7 and BUGLE-96 Libraries.

Group Upper Energy [eV] 1 1.4000E+07 2 1.0000E+07 3 8.0000E+06 4 7.0000E+06 5 6.0000E+06 6 5.0000E+06 7 4.0000E+06 8 3.0000E+06 9 2.0000E+06 10 1.5000E+06 11 1.0000E+06 12 8.0000E+05 13 7.0000E+05 14 6.0000E+05 15 4.0000E+05 16 2.0000E+05 17 1.0000E+05 18 6.0000E+04 19 3.0000E+04 20 2.0000E+04 1.0000E+04

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Table 5.3 IRDF-2002 Flat Weighting Neutron Dosimeter Cross Sections [barns] Used in the TORT-3.2 Calculations with BUGJEFF311.BOLIB, BUGENDF70.BOLIB, BUGLE-B7 and BUGLE-96.

Group Upper Energy Np-237 U-238 Ni-58 Fe-54 Ti-46 Cu-63 [Mev] (n,f) (n,f) (n,p) (n,p) (n,p) (n,α) 1 1.7332e+01 2.2071e+00 1.2190e+00 2.2132e-01 2.3634e-01 1.9614e-01 3.4460e-02 2 1.4191e+01 2.1063e+00 1.0428e+00 4.4874e-01 3.9357e-01 2.8124e-01 4.6786e-02 3 1.2214e+01 2.0841e+00 9.7830e-01 6.0075e-01 4.6624e-01 2.9804e-01 3.8885e-02 4 1.0000e+01 2.1774e+00 9.8793e-01 6.3861e-01 4.8169e-01 2.6868e-01 2.6939e-02 5 8.6071e+00 2.2235e+00 9.9636e-01 6.4484e-01 4.8240e-01 2.3930e-01 1.8860e-02 6 7.4082e+00 1.9547e+00 8.6164e-01 6.2243e-01 4.7885e-01 1.8477e-01 1.0688e-02 7 6.0653e+00 1.5224e+00 5.4549e-01 5.4560e-01 4.3669e-01 9.7292e-02 3.6481e-03 8 4.9659e+00 1.5290e+00 5.5498e-01 4.0492e-01 3.1544e-01 4.0127e-02 6.1452e-04 9 3.6788e+00 1.6280e+00 5.3415e-01 2.5204e-01 1.9564e-01 5.3275e-03 4.2940e-05 10 3.0119e+00 1.6660e+00 5.3271e-01 1.6817e-01 1.3414e-01 5.7867e-04 4.6929e-06 11 2.7253e+00 1.6804e+00 5.4403e-01 1.2162e-01 7.8808e-02 7.3689e-05 1.3682e-06 12 2.4660e+00 1.6855e+00 5.4972e-01 9.3475e-02 5.6762e-02 2.1604e-05 7.4165e-07 13 2.3653e+00 1.6868e+00 5.5067e-01 8.4827e-02 5.1203e-02 1.7487e-05 4.7235e-07 14 2.3457e+00 1.6875e+00 5.5129e-01 7.5697e-02 4.5047e-02 1.2901e-05 1.7922e-07 15 2.2313e+00 1.6832e+00 5.4443e-01 5.0849e-02 2.9403e-02 1.8982e-06 0. 16 1.9205e+00 1.6656e+00 4.8376e-01 2.5952e-02 9.5530e-03 0. 0. 17 1.6530e+00 1.6260e+00 3.2313e-01 1.1677e-02 2.9684e-03 0. 0. 18 1.3534e+00 1.5299e+00 4.4018e-02 3.7988e-03 7.8514e-04 0. 0. 19 1.0026e+00 1.4011e+00 1.2809e-02 4.8761e-04 9.0118e-05 0. 0. 20 8.2085e-01 1.2445e+00 3.7983e-03 1.5596e-04 6.6796e-06 0. 0. 21 7.4274e-01 1.0224e+00 1.4955e-03 4.1887e-05 3.9326e-07 0. 0. 22 6.0810e-01 6.5194e-01 5.9988e-04 3.3813e-06 0. 0. 0. 23 4.9787e-01 2.8178e-01 2.8527e-04 2.9075e-07 0. 0. 0. 24 3.6883e-01 9.8144e-02 1.5015e-04 0. 0. 0. 0. 25 2.9721e-01 4.5283e-02 9.3264e-05 0. 0. 0. 0. 26 1.8316e-01 2.6086e-02 6.8791e-05 0. 0. 0. 0. 27 1.1109e-01 1.6780e-02 3.8553e-05 0. 0. 0. 0. 28 6.7379e-02 1.5320e-02 8.4376e-05 0. 0. 0. 0. 29 4.0868e-02 1.5819e-02 3.6056e-05 0. 0. 0. 0. 30 3.1828e-02 1.6263e-02 5.9821e-05 0. 0. 0. 0. 31 2.6058e-02 1.6493e-02 8.4858e-05 0. 0. 0. 0. 32 2.4176e-02 1.6618e-02 9.5280e-05 0. 0. 0. 0. 33 2.1875e-02 1.7580e-02 1.1676e-04 0. 0. 0. 0. 34 1.5034e-02 2.0739e-02 1.1372e-04 0. 0. 0. 0. 35 7.1017e-03 2.5089e-02 1.6682e-05 0. 0. 0. 0. 36 3.3546e-03 3.3672e-02 4.4890e-09 0. 0. 0. 0. 37 1.5846e-03 4.5093e-02 1.0089e-03 0. 0. 0. 0. 38 4.5400e-04 6.2187e-02 1.0793e-05 0. 0. 0. 0. 39 2.1445e-04 1.0463e-01 1.9529e-05 0. 0. 0. 0. 40 1.0130e-04 1.6104e-01 3.0217e-05 0. 0. 0. 0. 41 3.7266e-05 9.3968e-02 1.4925e-04 0. 0. 0. 0. 42 1.0677e-05 2.0404e-02 6.7098e-05 0. 0. 0. 0. 43 5.0435e-06 8.9537e-03 1.7685e-06 0. 0. 0. 0. 44 1.8554e-06 1.9759e-02 1.8697e-06 0. 0. 0. 0. 45 8.7643e-07 1.1841e-02 2.5136e-06 0. 0. 0. 0. 46 4.1399e-07 6.6293e-03 3.9826e-06 0. 0. 0. 0. 47 1.0000e-07 2.1237e-02 1.1744e-05 0. 0. 0. 0. 1.0000e-11

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Fig. 5.1 IRDF-2002 Flat Weighting 237_{Np(n,f) Dosimeter Cross Section}

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Fig. 5.2 IRDF-2002 Flat Weighting 238_{U(n,f) Dosimeter Cross Section}

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Fig. 5.3 IRDF-2002 Flat Weighting 58_Ni(n,p)58_{Co Dosimeter Cross Section}

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Fig. 5.4 IRDF-2002 Flat Weighting 54_Fe(n,p)54_{Mn Dosimeter Cross Section}

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Fig. 5.5 IRDF-2002 Flat Weighting 46_Ti(n,p)46_{Sc Dosimeter Cross Section}

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Fig. 5.6 IRDF-2002 Flat Weighting 63_Cu(n,α)60_{Co Dosimeter Cross Section}

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Table 5.4 Total or Prompt ½(235_U+239_{Pu) Fission Neutron Spectra (χ) in the TORT-3.2 Calculations}

Using the BUGJEFF311.BOLIB, BUGENDF70.BOLIB, BUGLE-B7 and BUGLE-96 Libraries

Total (χ) Total (χ) Prompt (χ) Prompt (χ) Group Upper Energy BUGJEFF311.BOLIB BUGENDF70.BOLIB BUGLE-B7 BUGLE-96 [MeV]

1 1.7332e+01 2 1.4191e+01 3 1.2214e+01 4 1.0000e+01 5 8.6071e+00 6 7.4082e+00 7 6.0653e+00 8 4.9659e+00 9 3.6788e+00 10 3.0119e+00 11 2.7253e+00 12 2.4660e+00 13 2.3653e+00 14 2.3457e+00 15 2.2313e+00 16 1.9205e+00 17 1.6530e+00 18 1.3534e+00 19 1.0026e+00 20 8.2085e-01 21 7.4274e-01 22 6.0810e-01 23 4.9787e-01 24 3.6883e-01 25 2.9721e-01 26 1.8316e-01 27 1.1109e-01 28 6.7379e-02 29 4.0868e-02 30 3.1828e-02 31 2.6058e-02 32 2.4176e-02 33 2.1875e-02 34 1.5034e-02 35 7.1017e-03 36 3.3546e-03 37 1.5846e-03 38 4.5400e-04 39 2.1445e-04 40 1.0130e-04 41 3.7266e-05 42 1.0677e-05 43 5.0435e-06 44 1.8554e-06 45 8.7643e-07 46 4.1399e-07 47 1.0000e-07 1.0000e-11 6.2600e-05 6.4498e-05 6.4080e-05 5.3193e-05 2.4009e-04 2.4711e-04 2.4810e-04 2.1421e-04 1.3098e-03 1.3425e-03 1.3480e-03 1.2191e-03 2.8557e-03 2.8587e-03 2.8706e-03 2.7308e-03 6.2344e-03 6.2368e-03 6.2630e-03 6.0634e-03 1.7340e-02 1.7350e-02 1.7423e-02 1.7128e-02 3.2309e-02 3.2321e-02 3.2460e-02 3.2364e-02 8.3028e-02 8.2983e-02 8.3342e-02 8.4152e-02 7.7838e-02 7.7788e-02 7.8128e-02 7.8994e-02 4.4239e-02 4.4223e-02 4.4414e-02 4.4785e-02 4.6701e-02 4.6691e-02 4.6892e-02 4.7170e-02 1.9977e-02 1.9975e-02 2.0060e-02 2.0150e-02 4.0122e-03 4.0120e-03 4.0289e-03 4.0368e-03 2.4236e-02 2.4235e-02 2.4337e-02 2.4434e-02 7.3020e-02 7.3019e-02 7.3320e-02 7.3494e-02 7.1213e-02 7.1215e-02 7.1494e-02 7.1590e-02 8.8385e-02 8.8392e-02 8.8676e-02 8.8754e-02 1.1336e-01 1.1336e-01 1.1356e-01 1.1330e-01 6.1702e-02 6.1716e-02 6.1680e-02 6.1273e-02 2.6816e-02 2.6815e-02 2.6754e-02 2.6507e-02 4.6107e-02 4.6128e-02 4.5945e-02 4.5390e-02 3.7063e-02 3.7101e-02 3.6812e-02 3.6283e-02 4.1258e-02 4.1267e-02 4.0804e-02 4.0306e-02 2.1161e-02 2.1165e-02 2.0880e-02 2.0795e-02 2.9834e-02 2.9823e-02 2.9326e-02 2.9357e-02 1.5378e-02 1.5387e-02 1.5040e-02 1.5228e-02 7.4605e-03 7.4459e-03 7.2493e-03 7.4611e-03 3.5675e-03 3.5622e-03 3.4628e-03 3.5486e-03 1.0074e-03 1.0071e-03 9.7473e-04 9.9750e-04 5.8095e-04 5.7935e-04 5.5648e-04 5.6678e-04 1.7767e-04 1.7716e-04 1.6933e-04 1.7373e-04 2.0862e-04 2.0794e-04 1.9833e-04 2.0795e-04 5.6369e-04 5.5924e-04 5.2782e-04 5.3524e-04 5.0701e-04 5.0365e-04 4.7296e-04 5.0178e-04 1.6210e-04 1.6245e-04 1.5382e-04 1.5762e-04 5.3918e-05 5.4153e-05 4.9973e-05 5.2233e-05 2.2995e-05 2.3067e-05 1.4174e-05 2.1404e-05 3.0664e-06 3.0743e-06 0. 2.5992e-06 1.0837e-06 1.0860e-06 0. 8.4503e-07 4.5980e-07 4.5977e-07 0. 3.1159e-07 1.3907e-07 1.3920e-07 0. 6.0722e-08 1.9053e-08 2.1959e-08 0. 1.3585e-11 9.5788e-09 9.9079e-09 0. 4.1453e-12 2.7569e-09 2.6753e-09 0. 3.4287e-13 1.2484e-09 1.2038e-09 0. 0. 8.2184e-10 7.9541e-10 0. 0. 2.5500e-10 2.4960e-10 0. 0.

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Table 5.5 Total ½(235_U+239_{Pu) Fission Neutron Spectra (χ) in the TORT-3.2 Calculations Using}

the BUGJEFF311.BOLIB Library

Group Upper Energy Total(χ) Total(χ) U-235 Total(χ) Pu-239 [MeV] ½(U-235+Pu-235) BUGJEFF311.BOLIB BUGJEFF311.BOLIB 1 1.7332e+01 6.2600e-05 4.9847e-05 7.5353e-05 2 1.4191e+01 2.4009e-04 2.0032e-04 2.7986e-04 3 1.2214e+01 1.3098e-03 1.1384e-03 1.4812e-03 4 1.0000e+01 2.8557e-03 2.5055e-03 3.2059e-03 5 8.6071e+00 6.2344e-03 5.6193e-03 6.8496e-03 6 7.4082e+00 1.7340e-02 1.6040e-02 1.8640e-02 7 6.0653e+00 3.2309e-02 3.0508e-02 3.4110e-02 8 4.9659e+00 8.3028e-02 7.9978e-02 8.6077e-02 9 3.6788e+00 7.7838e-02 7.6252e-02 7.9423e-02 10 3.0119e+00 4.4239e-02 4.3722e-02 4.4756e-02 11 2.7253e+00 4.6701e-02 4.6381e-02 4.7021e-02 12 2.4660e+00 1.9977e-02 1.9899e-02 2.0055e-02 13 2.3653e+00 4.0122e-03 4.0004e-03 4.0240e-03 14 2.3457e+00 2.4236e-02 2.4188e-02 2.4284e-02 15 2.2313e+00 7.3020e-02 7.3086e-02 7.2954e-02 16 1.9205e+00 7.1213e-02 7.1516e-02 7.0910e-02 17 1.6530e+00 8.8385e-02 8.9032e-02 8.7737e-02 18 1.3534e+00 1.1336e-01 1.1467e-01 1.1205e-01 19 1.0026e+00 6.1702e-02 6.2706e-02 6.0698e-02 20 8.2085e-01 2.6816e-02 2.7337e-02 2.6294e-02 21 7.4274e-01 4.6107e-02 4.7125e-02 4.5089e-02 22 6.0810e-01 3.7063e-02 3.8049e-02 3.6078e-02 23 4.9787e-01 4.1258e-02 4.2477e-02 4.0038e-02 24 3.6883e-01 2.1161e-02 2.1827e-02 2.0495e-02 25 2.9721e-01 2.9834e-02 3.0837e-02 2.8832e-02 26 1.8316e-01 1.5378e-02 1.5950e-02 1.4806e-02 27 1.1109e-01 7.4605e-03 7.7421e-03 7.1788e-03 28 6.7379e-02 3.5675e-03 3.7043e-03 3.4308e-03 29 4.0868e-02 1.0074e-03 1.0482e-03 9.6653e-04 30 3.1828e-02 5.8095e-04 6.0737e-04 5.5452e-04 31 2.6058e-02 1.7767e-04 1.8654e-04 1.6879e-04 32 2.4176e-02 2.0862e-04 2.1922e-04 1.9803e-04 33 2.1875e-02 5.6369e-04 5.9716e-04 5.3022e-04 34 1.5034e-02 5.0701e-04 5.3875e-04 4.7527e-04 35 7.1017e-03 1.6210e-04 1.7068e-04 1.5351e-04 36 3.3546e-03 5.3918e-05 5.7556e-05 5.0281e-05 37 1.5846e-03 2.2995e-05 2.4994e-05 2.0996e-05 38 4.5400e-04 3.0664e-06 3.4437e-06 2.6892e-06 39 2.1445e-04 1.0837e-06 1.2527e-06 9.1480e-07 40 1.0130e-04 4.5980e-07 5.5078e-07 3.6881e-07 41 3.7266e-05 1.3907e-07 1.7589e-07 1.0226e-07 42 1.0677e-05 1.9053e-08 2.2718e-08 1.5389e-08 43 5.0435e-06 9.5788e-09 1.2140e-08 7.0172e-09 44 1.8554e-06 2.7569e-09 3.7279e-09 1.7859e-09 45 8.7643e-07 1.2484e-09 1.7610e-09 7.3581e-10 46 4.1399e-07 8.2184e-10 1.1957e-09 4.4801e-10 47 1.0000e-07 2.5500e-10 3.8080e-10 1.2919e-10 1.0000e-11

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Table 5.6 Total ½(235_U+239_{Pu) Fission Neutron Spectra (χ) in the TORT-3.2 Calculations Using}

the BUGENDF70.BOLIB Library

Group Upper Energy Total(χ) Total(χ) U-235 Total(χ) Pu-239 [MeV] ½(U-235+Pu-235) BUGENDF70.BOLIB BUGENDF70.BOLIB 1 1.7332e+01 6.4498e-05 4.9839e-05 7.9158e-05 2 1.4191e+01 2.4711e-04 2.0031e-04 2.9392e-04 3 1.2214e+01 1.3425e-03 1.1384e-03 1.5465e-03 4 1.0000e+01 2.8587e-03 2.5055e-03 3.2119e-03 5 8.6071e+00 6.2368e-03 5.6195e-03 6.8541e-03 6 7.4082e+00 1.7350e-02 1.6041e-02 1.8658e-02 7 6.0653e+00 3.2321e-02 3.0511e-02 3.4131e-02 8 4.9659e+00 8.2983e-02 7.9986e-02 8.5979e-02 9 3.6788e+00 7.7788e-02 7.6258e-02 7.9318e-02 10 3.0119e+00 4.4223e-02 4.3728e-02 4.4717e-02 11 2.7253e+00 4.6691e-02 4.6388e-02 4.6993e-02 12 2.4660e+00 1.9975e-02 1.9903e-02 2.0047e-02 13 2.3653e+00 4.0120e-03 4.0013e-03 4.0228e-03 14 2.3457e+00 2.4235e-02 2.4193e-02 2.4276e-02 15 2.2313e+00 7.3019e-02 7.3105e-02 7.2934e-02 16 1.9205e+00 7.1215e-02 7.1538e-02 7.0893e-02 17 1.6530e+00 8.8392e-02 8.9083e-02 8.7701e-02 18 1.3534e+00 1.1336e-01 1.1474e-01 1.1198e-01 19 1.0026e+00 6.1716e-02 6.2734e-02 6.0697e-02 20 8.2085e-01 2.6815e-02 2.7329e-02 2.6301e-02 21 7.4274e-01 4.6128e-02 4.7130e-02 4.5125e-02 22 6.0810e-01 3.7101e-02 3.8038e-02 3.6164e-02 23 4.9787e-01 4.1267e-02 4.2436e-02 4.0098e-02 24 3.6883e-01 2.1165e-02 2.1807e-02 2.0523e-02 25 2.9721e-01 2.9823e-02 3.0779e-02 2.8868e-02 26 1.8316e-01 1.5387e-02 1.5922e-02 1.4852e-02 27 1.1109e-01 7.4459e-03 7.7147e-03 7.1771e-03 28 6.7379e-02 3.5622e-03 3.6943e-03 3.4301e-03 29 4.0868e-02 1.0071e-03 1.0459e-03 9.6819e-04 30 3.1828e-02 5.7935e-04 6.0374e-04 5.5497e-04 31 2.6058e-02 1.7716e-04 1.8501e-04 1.6930e-04 32 2.4176e-02 2.0794e-04 2.1735e-04 1.9853e-04 33 2.1875e-02 5.5924e-04 5.8781e-04 5.3068e-04 34 1.5034e-02 5.0365e-04 5.3054e-04 4.7675e-04 35 7.1017e-03 1.6245e-04 1.7033e-04 1.5458e-04 36 3.3546e-03 5.4153e-05 5.7386e-05 5.0921e-05 37 1.5846e-03 2.3067e-05 2.4884e-05 2.1251e-05 38 4.5400e-04 3.0743e-06 3.4200e-06 2.7285e-06 39 2.1445e-04 1.0860e-06 1.2414e-06 9.3057e-07 40 1.0130e-04 4.5977e-07 5.4440e-07 3.7515e-07 41 3.7266e-05 1.3920e-07 1.7323e-07 1.0518e-07 42 1.0677e-05 2.1959e-08 2.9006e-08 1.4912e-08 43 5.0435e-06 9.9079e-09 1.3842e-08 5.9741e-09 44 1.8554e-06 2.6753e-09 3.8754e-09 1.4753e-09 45 8.7643e-07 1.2038e-09 1.7694e-09 6.3819e-10 46 4.1399e-07 7.9541e-10 1.1790e-09 4.1186e-10 47 1.0000e-07 2.4960e-10 3.7167e-10 1.2752e-10 1.0000e-11

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Table 5.7 Prompt ½(235_U+239_{Pu) Fission Neutron Spectra (χ) in the TORT-3.2 Calculations Using}

the BUGLE-B7 Library

Group Upper Energy Prompt(χ) Prompt(χ) U-235 Prompt(χ) Pu-239 [MeV] ½(U-235+Pu-235) BUGLE-B7 BUGLE-B7 1 1.7332e+01 6.4080e-05 4.8822e-05 7.9337e-05 2 1.4191e+01 2.4810e-04 2.0162e-04 2.9458e-04 3 1.2214e+01 1.3480e-03 1.1459e-03 1.5500e-03 4 1.0000e+01 2.8706e-03 2.5220e-03 3.2192e-03 5 8.6071e+00 6.2630e-03 5.6564e-03 6.8696e-03 6 7.4082e+00 1.7423e-02 1.6146e-02 1.8700e-02 7 6.0653e+00 3.2460e-02 3.0711e-02 3.4208e-02 8 4.9659e+00 8.3342e-02 8.0511e-02 8.6173e-02 9 3.6788e+00 7.8128e-02 7.6758e-02 7.9497e-02 10 3.0119e+00 4.4414e-02 4.4010e-02 4.4817e-02 11 2.7253e+00 4.6892e-02 4.6685e-02 4.7098e-02 12 2.4660e+00 2.0060e-02 2.0029e-02 2.0091e-02 13 2.3653e+00 4.0289e-03 4.0263e-03 4.0316e-03 14 2.3457e+00 2.4337e-02 2.4344e-02 2.4329e-02 15 2.2313e+00 7.3320e-02 7.3548e-02 7.3091e-02 16 1.9205e+00 7.1494e-02 7.1947e-02 7.1040e-02 17 1.6530e+00 8.8676e-02 8.9497e-02 8.7856e-02 18 1.3534e+00 1.1356e-01 1.1503e-01 1.1209e-01 19 1.0026e+00 6.1680e-02 6.2687e-02 6.0674e-02 20 8.2085e-01 2.6754e-02 2.7240e-02 2.6268e-02 21 7.4274e-01 4.5945e-02 4.6852e-02 4.5038e-02 22 6.0810e-01 3.6812e-02 3.7617e-02 3.6007e-02 23 4.9787e-01 4.0804e-02 4.1772e-02 3.9836e-02 24 3.6883e-01 2.0880e-02 2.1390e-02 2.0369e-02 25 2.9721e-01 2.9326e-02 3.0048e-02 2.8605e-02 26 1.8316e-01 1.5040e-02 1.5408e-02 1.4672e-02 27 1.1109e-01 7.2493e-03 7.4253e-03 7.0734e-03 28 6.7379e-02 3.4628e-03 3.5462e-03 3.3794e-03 29 4.0868e-02 9.7473e-04 9.9809e-04 9.5137e-04 30 3.1828e-02 5.5648e-04 5.6978e-04 5.4317e-04 31 2.6058e-02 1.6933e-04 1.7337e-04 1.6528e-04 32 2.4176e-02 1.9833e-04 2.0306e-04 1.9359e-04 33 2.1875e-02 5.2782e-04 5.4039e-04 5.1524e-04 34 1.5034e-02 4.7296e-04 4.8421e-04 4.6172e-04 35 7.1017e-03 1.5382e-04 1.5747e-04 1.5017e-04 36 3.3546e-03 4.9973e-05 5.1157e-05 4.8789e-05 37 1.5846e-03 1.4174e-05 1.4763e-05 1.3585e-05 38 4.5400e-04 0. 0. 0. 39 2.1445e-04 0. 0. 0. 40 1.0130e-04 0. 0. 0. 41 3.7266e-05 0. 0. 0. 42 1.0677e-05 0. 0. 0. 43 5.0435e-06 0. 0. 0. 44 1.8554e-06 0. 0. 0. 45 8.7643e-07 0. 0. 0. 46 4.1399e-07 0. 0. 0. 47 1.0000e-07 0. 0. 0.

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Table 5.8 Prompt ½(235_U+239_{Pu) Fission Neutron Spectra (χ) in the TORT-3.2 Calculations Using}

the BUGLE-96 Library

Group Upper Energy Prompt(χ) Prompt(χ) U-235 Prompt(χ) Pu-239 [MeV] ½(U-235+Pu-235) BUGLE-96 BUGLE-96 1 1.7332e+01 5.3193e-05 5.0179e-05 5.6208e-05 2 1.4191e+01 2.1421e-04 2.0166e-04 2.2677e-04 3 1.2214e+01 1.2191e-03 1.1460e-03 1.2921e-03 4 1.0000e+01 2.7308e-03 2.5222e-03 2.9394e-03 5 8.6071e+00 6.0634e-03 5.6568e-03 6.4700e-03 6 7.4082e+00 1.7128e-02 1.6147e-02 1.8109e-02 7 6.0653e+00 3.2364e-02 3.0712e-02 3.4016e-02 8 4.9659e+00 8.4152e-02 8.0512e-02 8.7792e-02 9 3.6788e+00 7.8994e-02 7.6758e-02 8.1231e-02 10 3.0119e+00 4.4785e-02 4.4010e-02 4.5561e-02 11 2.7253e+00 4.7170e-02 4.6685e-02 4.7656e-02 12 2.4660e+00 2.0150e-02 2.0028e-02 2.0272e-02 13 2.3653e+00 4.0368e-03 4.0262e-03 4.0474e-03 14 2.3457e+00 2.4434e-02 2.4344e-02 2.4523e-02 15 2.2313e+00 7.3494e-02 7.3547e-02 7.3440e-02 16 1.9205e+00 7.1590e-02 7.1946e-02 7.1233e-02 17 1.6530e+00 8.8754e-02 8.9495e-02 8.8012e-02 18 1.3534e+00 1.1330e-01 1.1503e-01 1.1158e-01 19 1.0026e+00 6.1273e-02 6.2685e-02 5.9861e-02 20 8.2085e-01 2.6507e-02 2.7239e-02 2.5776e-02 21 7.4274e-01 4.5390e-02 4.6851e-02 4.3929e-02 22 6.0810e-01 3.6283e-02 3.7615e-02 3.4950e-02 23 4.9787e-01 4.0306e-02 4.1771e-02 3.8841e-02 24 3.6883e-01 2.0795e-02 2.1390e-02 2.0200e-02 25 2.9721e-01 2.9357e-02 3.0048e-02 2.8665e-02 26 1.8316e-01 1.5228e-02 1.5408e-02 1.5048e-02 27 1.1109e-01 7.4611e-03 7.4251e-03 7.4971e-03 28 6.7379e-02 3.5486e-03 3.5461e-03 3.5511e-03 29 4.0868e-02 9.9750e-04 9.9806e-04 9.9694e-04 30 3.1828e-02 5.6678e-04 5.6977e-04 5.6378e-04 31 2.6058e-02 1.7373e-04 1.7337e-04 1.7409e-04 32 2.4176e-02 2.0795e-04 2.0305e-04 2.1284e-04 33 2.1875e-02 5.3524e-04 5.4037e-04 5.3012e-04 34 1.5034e-02 5.0178e-04 4.8419e-04 5.1937e-04 35 7.1017e-03 1.5762e-04 1.5746e-04 1.5779e-04 36 3.3546e-03 5.2233e-05 5.1156e-05 5.3309e-05 37 1.5846e-03 2.1404e-05 2.0827e-05 2.1981e-05 38 4.5400e-04 2.5992e-06 2.5484e-06 2.6501e-06 39 2.1445e-04 8.4503e-07 8.2729e-07 8.6276e-07 40 1.0130e-04 3.1159e-07 3.0900e-07 3.1417e-07 41 3.7266e-05 6.0722e-08 5.9997e-08 6.1447e-08 42 1.0677e-05 1.3585e-11 5.4050e-12 2.1765e-11 43 5.0435e-06 4.1453e-12 0. 8.2907e-12 44 1.8554e-06 3.4287e-13 0. 6.8575e-13 45 8.7643e-07 0. 0. 0. 46 4.1399e-07 0. 0. 0. 47 1.0000e-07 0. 0. 0. 1.0000e-11

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Fi g. 5.7 C om pa ris on o f th e Fi ss ion N eut ron S pe ct ra us ed in 3D T ra ns por t C al cul at ions w ith t he BUGJ EF F3 11 .B OL IB , B UGE NDF 70 .B OL IB , B UGL E-B7 a nd BU G LE -96 L ibr ar ie s.

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Fi g. 5.8 B U G JE FF 311.B O LI B L ibr ar y: F iss ion N eut ron S pe ct ra o f 23 5 U, 23 9 Pu a nd F iss ion N eut ron Sp ect ru m U sed in the 3D T ra ns por t C al cu la tions ½( 23 5 U+ 23 9 Pu ).

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Fi g. 5.9 B UGE NDF 70 .B OL IB L ib ra ry : F iss ion N eut ron S pe ct ra o f 23 5 U, 23 9 Pu a nd F iss ion N eut ron Sp ect ru m U sed in the 3D T ra ns por t C al cu la tions ½( 23 5U+ 23 9Pu ).

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Fi g. 5. 10 B UGL E-B7 L ib ra ry : F iss ion N eut ron S pe ct ra o f 23 5 U, 23 9 Pu a nd F iss ion N eut ron S pe ct rum U se d in t he 3D T ra ns por t C al cul at ions ½( 23 5 U+ 23 9 Pu ).

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Fi g. 5. 11 B UGL E-96 Li bra ry : F iss ion N eut ron S pe ct ra o f 23 5 U, 23 9 Pu a nd F iss ion N eut ron S pe ct rum U se d in the 3D T ra ns por t C al cul at ions ½( 23 5 U+ 23 9 Pu ).

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6 TRANSPORT CALCULATIONS 6.1 Transport Calculation General Features

This section describes the analysis of the HBR-2 benchmark. Fixed source transport calculations were performed using the TORT-3.2 /26/ three-dimensional (3D) discrete ordinates (SN) code

included in the ORNL DOORS-3.2a /27/ system of deterministic transport codes. Thus the analysis is completely different with respect to the one performed and described in ref /1/, consisting in the use of the DORT-2.12.14 /27/ two-dimensional (2D) discrete ordinates code, also included in the ORNL DOORS-3.2a system, and of the flux synthesis method /1//5/. That method results are full reliable only at the core mid-plane, whereas a 3D transport calculation permits to have a “reliable” 3D result distribution.

The TORT-3.2 code was used on a personal computer (CPU: INTEL PENTIUM D 3.40 GHz, 3.10 GB of RAM) under Linux openSUSE 10.2 (i586) operating system with FORTRAN-77 compiler g77, version 3.3.5-38.

The ENEA-Bologna BUGJEFF311.BOLIB, BUGENDF70.BOLIB and the ORNL BUGLE-B7, BUGLE-96 working libraries were alternatively used in the transport calculations with TORT-3.2. The calculations were performed by including all the 47 neutron energy groups. It was not possible to use the same set of atomic densities in all the calculations with all libraries because both BUGJEFF311.BOLIB and BUGENDF70.BOLIB include all the needed processed cross sections for all the isotopes of each natural element in the HBR-2 compositional model whereas this is not always the case both in BUGLE-B7 and in BUGLE-96. In fact, some needed processed cross sections are only available as natural element cross section files in BUGLE-B7 (Tinat and Sinat in

Inconel-718 and Snnat in Zircalloy-4) and in BUGLE-96 (Tinat and Sinat in Inconel-718; Snnat in

Zircalloy-4; Sinat , Canat, Knat and Mgnat in Concrete)

Both infinite dilution and self-shielded neutron cross sections were selected. Self-shielded cross sections from the BUGJEFF311.BOLIB, BUGENDF70.BOLIB, BUGLE-B7 and BUGLE-96 packages were used when available and applicable (for example for the reactor pressure vessel, biological shield, etc.). Group-organized files of macroscopic cross sections, requested by TORT and derived from BUGJEFF311.BOLIB, BUGENDF70.BOLIB, BUGLE-B7 and BUGLE-96 in FIDO-ANISN format, were prepared through the ORNL GIP /27/ program of the DOORS system, specifically dedicated to the discrete ordinates transport codes such as TORT.

The ENEA-Bologna ADEFTA-4.1 /28/ program was employed in the calculation of the atomic densities of the isotopes involved in the compositional model on the basis of the atomic abundances reported in the BNL-NNDC database /29/ included in ADEFTA. The input to ADEFTA was based on the materials of the components and regions reported in Table 2.2 and on densities and chemical compositions of Table 2.3. Component and region geometry is reported in Figs. 2.1, 2.2 and 2.3 and in Table 2.1. ADEFTA-4.1 was used not only to calculate the atomic densities for the benchmark experiment compositional model but also to handle them properly in order to automatically prepare the macroscopic cross section sets of the compositional model material mixtures in the format required by GIP. The automatic generation of the 3D mesh grids for both Cartesian (X,Y,Z) and cylindrical (R,θ,Z) geometries of the HBR-2 benchmark geometrical model for TORT-3.2 were performed through the ENEA-Bologna BOT3P-5.3 /30/ /31/ pre/post-processor system.

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The co-ordinete origin is at the centre of the core mid-plane. The global Z axis is normal to the core mid-plane. The X global axis is in the core mid-plane and crosses the cavity where dosimeters are located (θ =0°). The global Y axis is in the core mid-plane and is normal to the X global axis.

The geometrical model in calculations reproduced one quarter of the HBR-2 reactor up to the biological shield due to symmetry conditions. A 3D view of the compositional and geometrical TORT (X,Y,Z) model is reported in Fig. 6.1. Figs 6.2 to 6.4 show sections at Z=0. cm (core mid-plane), at X = 0. cm and Y = 0. cm, respectively.

Fig. 6.5 zooms the capsule area at the core mid-plane in the TORT (X,Y,Z) model. The geometrical domain in the TORT (X,Y,Z) model was:

0. cm ≤ X ≤ 348. cm; 0. cm ≤ Y ≤ 348. cm; -213.526 cm ≤ Z ≤ 212.410 cm. Fig. 6.6 shows a 3D view of the whole compositional and geometrical TORT (R,θ,Z) model.

Figs. 6.7 and 6.8 are also 3D views focused on the vessel and the biological shield upper parts, respectively, as from the core mid-plane.

Figs. 6.9 → 6.12 show sections at Z=0. cm (core mid-plane), θ=0°, θ=20° and θ=90°, respectively. Fig. 6.13 zooms the capsule area at the core mid-plane in the TORT (R,θ,Z) model

The geometrical domain in the TORT (R,θ,Z) model was:

0. cm ≤ R ≤ 348. cm; 0° ≤ θ ≤ 90°; -213.526 cm ≤ Z ≤ 212.410 cm.

Fixed source transport calculations with one source (outer) iteration were performed using fully symmetrical discrete ordinates directional quadrature sets for the flux solution.

The P3-S8 approximation was adopted as the standard reference. PN corresponds to the order of the

expansion in Legendre polynomials of the scattering cross section matrix and SN represents the

order of the flux angular discretization. It is worth underlining that the P3-S8 approximation is the

most widely used option in the fixed source calculations dedicated to LWR safety analyses. The theta-weighted difference approximation was selected for the flux extrapolation model.

In all the calculations the same numerical value (5.E-04) for the point-wise flux convergence criterion was employed with a maximum of 40 flux iterations per group.

The IRDF-2002 derived flat weighting neutron dosimeter cross sections in the BUGLE-96 47-group neutron energy structure for all the involved nuclear reactions (237_Np(n,f),238_U(n,f),58_Ni(n,p)58_Co, 54_Fe(n,p)54_Mn, 46_Ti(n,p)46_Sc, 63_Cu(n,α)60_{Co) were used in the calculations with all libraries}

(BUGJEFF311.BOLIB, BUGENDF70.BOLIB, BUGLE-B7 and BUGLE-96) to obtain the corresponding reaction rates in capsule and cavity positions.

The input files to ADEFTA-4.1 and partially those to BOT3P-5.3 used in this analysis are reported in Appendixes A, B. In particular:

APPENDIX A.1 Input File to ADEFTA-4.1 - Generation of the Compositional Model Used in the Calculations with the BUGJEFF311.BOLIB Library.

APPENDIX A.2 Input File to ADEFTA-4.1 - Generation of the Compositional Model Used in the Calculations with the BUGENDF70.BOLIB Library.

APPENDIX A.3 Input File to ADEFTA-4.1 - Generation of the Compositional Model Used in the Calculations with the BUGLE-B7 Library.

APPENDIX A.4 Input File to ADEFTA-4.1 - Generation of the Compositional Model Used in the Calculations with the BUGLE-96 Library.

APPENDIX B.1 Partial Input File to BOT3P-5.3 - Generation of the (X-Y-Z) Geometrical Model Used in the Transport Calculations with the BUGJEFF311.BOLIB BUGENDF70.BOLIB, BUGLE-B7 and BUGLE-96 Libraries.

APPENDIX B.2 Partial Input File to BOT3P-5.3 - Generation of the (R-θ-Z) Geometrical Model Used in the Transport Calculations with the BUGJEFF311.BOLIB, BUGENDF70.BOLIB, BUGLE-B7 and BUGLE-96 Libraries.

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Fig. 6.1 3D View of the Compositional and Geometrical Model in the HBR-2 TORT-3.2 (X,Y,Z) Calculations.

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Fig. 6.2 Compositional and Geometrical Model in the HBR-2 TORT-3.2 (X,Y,Z) Calculations. Section at the Core Mid-Plane (Z = 0. cm)

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Fig. 6.3 Compositional and Geometrical Model in the HBR-2 TORT-3.2 (X,Y,Z) Calculations. Section at X = 0. cm

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Fig. 6.4 Compositional and Geometrical Model in the HBR-2 TORT-3.2 (X,Y,Z) Calculations. Section at Y = 0. cm

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Fig. 6.5 Zoom on the Capsule Area in the HBR-2 TORT-3.2 (X,Y,Z) Model. Section at the Core Mid-Plane (Z = 0. cm)

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Fig. 6.6 3D View of the Compositional and Geometrical Model in the HBR-2 TORT-3.2 (R,θ,Z) Calculations.

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Fig. 6.9 Compositional and Geometrical Model in the HBR-2 TORT-3.2 (R,θ,Z) Calculations. Section at the Core Mid-Plane (Z = 0. cm)

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Fig. 6.10 Compositional and Geometrical Model in the HBR-2 TORT-3.2 (R,θ,Z) Calculations. Section at θ = 0°.

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Fig. 6.13 Zoom on the Capsule Area in the HBR-2 TORT-3.2 (R,θ,Z) Model. Section at the Core Mid-Plane (Z = 0. cm)