MIT

Benchmark for Evaluation And Validation of Reactor Simulations

RELEASE rev. 1.0.1 MIT Computational Reactor Physics Group July 7, 2013

Authors Nicholas Horelik Bryan Herman

Advisors Benoit Forget Kord Smith

Acknowledgements We are extremely grateful for the detailed core specifications and measurement data provided to us by the utility, which will remain un-named. Without their generosity this benchmark would not be possible. We are also very grateful for the work of the Advanced Simulation and Design Integration team at the Knolls Atomic Power Laboratory, who contributed significantly to the development of this document by reviewing, beta-testing, and making important suggestions from the very beginning. We would also like to acknowledge the contributions of Koroush Shirvan for his extensive reviewing and quality assurance work. Finally we would like to thank Paul Romano for his help developing and debugging the OpenMC model of this benchmark. Partial funding for the development of this benchmark was provided by the Center for Exascale Simulation of Advanced Reactors, one of three exascale codesign centers funded by the Department of Energy’s Office of Advanced Scientific Computing Research.

Citation N. Horelik, B. Herman, B. Forget, and K. Smith. Benchmark for Evaluation and Validation of Reactor Simulations (BEAVRS), v1.0.1. Proc. Int. Conf. Mathematics and Computational Methods Applied to Nuc. Sci. & Eng., 2013. Sun Valley, Idaho

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Changelog 2/21/13 - 1.0.1 • Inconel was misreported as the grid material in Figure 17, changed to Zircaloy • Grid thickness reported in the caption of Figure 16 did not match figure • Grid thickness reported in the caption of Figure 17 did not match figure • Grid strap thickness reported in the caption of Figure 18 did not match figure

1/31/13 - 1.0 • Changed Mass density and composition of SS304

1/18/13 - 0.2.5 • Updated RPV thickness to accurate source • Updated inconel spring mass and dimension to approximate source • Changed top/bottom egg-crate dimensions to properly conserve inconel mass. Top/bottom grids now have different radial dimensions vs. intermediate grids for the egg-crate. • Hot Zero Power temperature was changed from 560 K to 560 F. • All Fuel material mass and number densities have been changed to reflect actual coreaveraged Uranium assembly loading for each enrichment. • Burnable absorber specification was changed so that the active poison extends from the top of the active fuel to 2 in. above the bottom of the active fuel. The blank pin above burnable absorbers was also changed from Zircaloy to Stainless Steel. • Added air gap to control rods • Changed Ag-In-Cd cladding material to SS304 • Changed water density to reflect boron in it (changed boron num dens) • Fixed Air mass density, factor of 10 lower • Changed RPV inner and outer radii

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12/17/12 - 0.2.4 • Revised instrument tube and burnable absorber tube pincell details above active fuel regions.

12/4/12 - 0.2.3 • Changed instrument tube and guide tube pincell details above and below active fuel regions.

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Contents 1 Introduction

1

2 Benchmark Specifications 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Radial Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Pin Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fuel Pin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Upper Fuel Pin Plenum . . . . . . . . . . . . . . . . . . . . . . . Empty Guide Tube Geometry above Dashpot . . . . . . . . . . Empty Guide Tube Geometry at Dashpot . . . . . . . . . . . . . Instrument Tube Pin Geometry . . . . . . . . . . . . . . . . . . . BP Geometry above Dashpot . . . . . . . . . . . . . . . . . . . . BP Geometry at Dashpot . . . . . . . . . . . . . . . . . . . . . . Control Rod Pin Geometry . . . . . . . . . . . . . . . . . . . . . 2.2.2 Fuel Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2.1 Burnable Absorber Configurations . . . . . . . . . . . 2.2.2.2 Radial Grid Spacer Specifications . . . . . . . . . . . . 2.2.3 Core Specification . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3.1 Enrichment Zones and Burnable Absorber Positions . 2.2.3.2 Control Rod Bank Positions . . . . . . . . . . . . . . . . 2.2.3.3 Instrument Tube Positions . . . . . . . . . . . . . . . . . 2.3 Axial Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Fuel Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Guide Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Instrument Tubes . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Burnable Absorbers . . . . . . . . . . . . . . . . . . . . . . . 2.3.5 Control Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.6 Aggregate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.6.1 Grid Spacers . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.6.2 Nozzles and Support Plate . . . . . . . . . . . . . . . . 2.3.6.3 Top and Bottom of the Core . . . . . . . . . . . . . . . 2.4 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fuel 1.6% Enriched . . . . . . . . . . . . . . . . . . . . . . . . . . . Fuel 2.4% Enriched . . . . . . . . . . . . . . . . . . . . . . . . . . . Fuel 3.1% Enriched . . . . . . . . . . . . . . . . . . . . . . . . . . . Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Borosilicate Glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ag-In-Cd Control Rods . . . . . . . . . . . . . . . . . . . . . . . . . Helium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inconel 718 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stainless Steel 304 . . . . . . . . . . . . . . . . . . . . . . . . . . . Zircaloy 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

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2 2 4 4 5 6 6 7 7 8 9 10 11 13 18 21 21 21 24 26 26 28 28 30 30 34 34 35 35 37 37 38 38 39 39 40 40 41 42 43

Borated Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Carbon Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3 Operating Data 3.1 Processing Measured In-Core Detector Data . . 3.1.1 Example – Hot Zero Power Measurements 3.2 Hot Zero Power Data Discussion . . . . . . . . . 3.3 Cycle 1 and 2 Available Data . . . . . . . . . . .

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References

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Source Details

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List of Figures 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

Core cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fuel Pin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Upper Fuel Pin Plenum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Empty Guide Tube Geometry above Dashpot . . . . . . . . . . . . . . . . Empty Guide Tube Geometry at Dashpot . . . . . . . . . . . . . . . . . . . Instrument Tube Pin Geometry . . . . . . . . . . . . . . . . . . . . . . . . . BP Geometry above Dashpot . . . . . . . . . . . . . . . . . . . . . . . . . . BP Geometry at Dashpot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control Rod Pin Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . Fuel assembly guide tube locations. . . . . . . . . . . . . . . . . . . . . . . The 6BA burnable absorber configuration. . . . . . . . . . . . . . . . . . . The 12BA burnable absorber configuration. . . . . . . . . . . . . . . . . . The 15BA burnable absorber configuration. . . . . . . . . . . . . . . . . . The 16BA burnable absorber configuration. . . . . . . . . . . . . . . . . . The 20BA burnable absorber configuration. . . . . . . . . . . . . . . . . . Fuel pincell geometry for the top/bottom grid spacer inner egg-crate . Fuel pincell geometry for the intermediate grid spacer inner egg-crate Schematic dimensions of stainless steel grid sleeve model . . . . . . . . Scale view of grid spacer model . . . . . . . . . . . . . . . . . . . . . . . . Core enrichment zones and burnable absorber positions . . . . . . . . . Detailed burnable absorber view . . . . . . . . . . . . . . . . . . . . . . . . Control rod and shutdown bank positions. . . . . . . . . . . . . . . . . . . Instrument tube positions. . . . . . . . . . . . . . . . . . . . . . . . . . . . Fuel rod pincell axial specification . . . . . . . . . . . . . . . . . . . . . . . Empty guide tube pincell axial specification . . . . . . . . . . . . . . . . . Instrument tube pincell axial specification . . . . . . . . . . . . . . . . . . Burnable absorber pincell axial specification . . . . . . . . . . . . . . . . Control rod pincell axial specification . . . . . . . . . . . . . . . . . . . . . Control rod insertion sequence and axial specification . . . . . . . . . . Scale view of all axial planes. . . . . . . . . . . . . . . . . . . . . . . . . . . Radial picture of nozzles and support plate in aggregate model . . . . Axial scale view of aggregate pincell model near core top and bottom . Initial Raw Detector Measurements (top to bottom). . . . . . . . . . . . Detector Measurements Corrected for Background (top to bottom). . Detector Measurements Gain Factors Applied (top to bottom). . . . . . Detector Measurements with Zero Points Removed (top to bottom). . Detector Measurements with in J10 Assembly (top to bottom). . . . . J10 Detector Measurements Divided by Core Power (top to bottom). . All Detector Signals Before Realignment. . . . . . . . . . . . . . . . . . . All Detector Signals After Realignment. . . . . . . . . . . . . . . . . . . . Multiple Detector Signals Averaged in J10 (top to bottom). . . . . . . . Application of Detector Normalization Factors for J10. . . . . . . . . . . Comparision of Splined Data for Assembly J10. . . . . . . . . . . . . . . vi

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Comparison of All Assemblies after Spline. . . . . . . . . . . . Final Processed Hot Zero Power (HZP) Measurement Data. . Radial detector measurements (axially integrated). . . . . . Quarter core (full core folded) radial measurements. . . . . Measured boron letdown curves for two cycles of operation. Power history of Cycle 1. . . . . . . . . . . . . . . . . . . . . . . Power history of Cycle 2. . . . . . . . . . . . . . . . . . . . . . .

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List of Tables 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Summary of key model parameters. . . . . . . Fuel assembly parameters. . . . . . . . . . . . . Structural component specifications. . . . . . . Fuel 1.6% Enriched . . . . . . . . . . . . . . . . . Fuel 2.4% Enriched . . . . . . . . . . . . . . . . . Fuel 3.1% Enriched . . . . . . . . . . . . . . . . . Air . . . . . . . . . . . . . . . . . . . . . . . . . . . Borosilicate Glass . . . . . . . . . . . . . . . . . . Ag-In-Cd Control Rods . . . . . . . . . . . . . . . Helium . . . . . . . . . . . . . . . . . . . . . . . . Inconel 718 . . . . . . . . . . . . . . . . . . . . . . Stainless Steel 304 . . . . . . . . . . . . . . . . . Zircaloy 4 . . . . . . . . . . . . . . . . . . . . . . . Borated Water . . . . . . . . . . . . . . . . . . . . Carbon Steel . . . . . . . . . . . . . . . . . . . . . Cycle 1 hot zero power physics configuration. Cycle 1 hot zero power physics data. . . . . . . Boron Letdown Curve Data for Cycles 1 and 2.

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List of Source References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

Core Arrangement of Fuel Assemblies . . . . . Fuel Assembly Loading . . . . . . . . . . . . . . Fuel Lattice Specifications . . . . . . . . . . . . Active Core Height . . . . . . . . . . . . . . . . Control Rod Composition . . . . . . . . . . . . Nominal Core Power . . . . . . . . . . . . . . . Core Mass Flow Rate . . . . . . . . . . . . . . . Fuel Pellet Radius . . . . . . . . . . . . . . . . . Fuel Cladding Inner Radius . . . . . . . . . . . Fuel Cladding Outer Radius . . . . . . . . . . . Plenum Spring Radius . . . . . . . . . . . . . . Guide Tube Inner Radius . . . . . . . . . . . . . Guide Tube Outer Radius . . . . . . . . . . . . Guide Tube Inner Radius at Dashpot . . . . . Guide Tube Outer Radius at Dashpot . . . . . Instrumentation Tube Thimble Inner Radius . Instrumentation Tube Thimble Outer Radius Inner Cladding Inner Radius of BP Pin . . . . Inner Cladding Outer Radius of BP Pin . . . . Inner Radius of Poison of BP Pin . . . . . . . . Outer Radius of Poison of BP Pin . . . . . . . . Outer Cladding Inner Radius of BP Pin . . . . Outer Cladding Outer Radius of BP Pin . . . . Control Rod Thimble Inner Radius . . . . . . . Control Rod Thimble Outer Radius . . . . . . Fuel Assembly Pitch . . . . . . . . . . . . . . . . Fuel Pin Pitch . . . . . . . . . . . . . . . . . . . Inconel Grid Weight . . . . . . . . . . . . . . . . Zircaloy Grid Weight . . . . . . . . . . . . . . . Burnable Poison Specifications . . . . . . . . . Grid Spacers . . . . . . . . . . . . . . . . . . . . Core Baffle Thickness . . . . . . . . . . . . . . . Core Barrel Inner Radius . . . . . . . . . . . . Core Barrel Outer Radius . . . . . . . . . . . . Core Barrel Material . . . . . . . . . . . . . . . Reactor Pressure Vessel . . . . . . . . . . . . . . Instrument Tube Axial Planes . . . . . . . . . . Burnable Absorber Axial Planes . . . . . . . . Guide Tube Axial Planes . . . . . . . . . . . . . Control Rod Axial Planes . . . . . . . . . . . . Assembly Nozzles and Fuel Rod Plenum . . . Location of Instrument Tubes . . . . . . . . . . 1.6% Enriched Fuel Composition . . . . . . . ix

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2.4% Enriched Fuel Composition . . . 3.1% Enriched Fuel Composition . . . Composition of Air . . . . . . . . . . . . Composition of Borosilicate Glass . . . Composition of Ag-In-Cd Control Rods Composition of Helium . . . . . . . . . . Composition of Inconel . . . . . . . . . Composition of Stainless Steel . . . . . Composition of Zircaloy . . . . . . . . . Composition of Borated Water . . . . . Composition of Carbon Steel . . . . . . Missing Data . . . . . . . . . . . . . . . . Isotopic Masses . . . . . . . . . . . . . . Isotopic Natural Abundances . . . . . . Elemental Masses . . . . . . . . . . . . . Assembly Loadings . . . . . . . . . . . .

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111 113 115 116 117 118 119 120 121 122 124 125 126 128 130 131

Definitions and Acronyms ARO

All Rods Out

BAF

Bottom of Active Fuel

BP

Burnable Poison

BOC

Beginning of Cycle

CASL

Consortium for Advanced Simulation of Light Water Reactors (LWRs)

CESAR

Center for Exascale Simulation of Advanced Reactors

EFPD

Effective Full Power Days

EPRI

Electric Power Research Institute

FFTF

Fast Flux Test Factility

HZP

Hot Zero Power

IR

Inner Radius

LMFR

Liquid Metal Fast Reactor

LWR

Light Water Reactor

MOX

Mixed Oxide

OR

Outer Radius

pcm

per cent mille

ppm

parts per million

PWR

Pressurized Water Reactor

SS304

Stainless Steel 304

TAF

Top of Active Fuel

xi

Section 1. Introduction

1

rev. 1.0.1

Introduction

Advances in computing capabilities are further improving the feasibility of fast-running highfidelity simulations of nuclear cores. Where current core simulations require a series of homogenization procedures to model reactors on a coarse-mesh in order to overcome memory and computer processing limitations [2], modern techniques aspire to provide solutions using fully-detailed geometries with far fewer approximations. For instance, recent research efforts improving the scalability and efficiency of Monte Carlo neutron transport algorithms have resulted in very accurate solutions to the well-known Hoogenboom-Martin problem [3] with the MC21 Monte Carlo code [4] [5], with statistical uncertainties approaching the 1% pin-power accuracy criterion proposed by Smith [6] for full-core Monte Carlo analysis. Likewise, modern deterministic approaches are targeting similar accuracy on some of the world’s largest supercomputers [7]. Indeed, the development of such high-fidelity full-core modelling capabilities for LWRs is the stated goal of several DOE projects such as CASL (Consortium for Advanced Simulation of LWRs) [8] and CESAR (Center for Exascale Simulation of Advanced Reactors) [9]. However, there is a lack of detailed and relevant benchmarks needed to validate these methods, and a more complete benchmark that includes measured reactor data is presented here. Nearly all non-proprietary benchmarks do not capture the detail of LWRs needed to validate high-fidelity methods being developed today. For instance, the OECD LWR and Pressurized Water Reactor (PWR) reactor benchmark specifications [10] mostly refer to simple lattice experiments, limited physics testing configurations, and small test reactors. Whereas several full-core LMFR models are available (FFTF, JOYO, etc.), LWRs are markedly under represented. This is particularly true for full-core benchmarks of most interest to the methods development and regulatory community: production reactors similar to operating and planned commercial units. Some recent publications come close to satisfying this need, but they ultimately fall short either in scope or applicability. For instance, a 2011 EPRI report [11] provides reactivity and depletion data with several benchmark specifications for PWR assembly lattices. These benchmarks, while using full-core simulations and measured data, take the approach of reducing the benchmark to single-assembly calculations and do not provide detailed full-core tests or measured reactor data. A distinction should be noted between the kind of data-backed benchmark being pursued here and the code-comparison benchmarks often used to evaluate methods. For instance, several newer and widely-used LWR benchmarking suites are not backed by measured data, such as the C5G7 MOX benchmarks [12], the Hoogenboom-Martin LWR Monte Carlo benchmark [4], and the approximate PWR specification by Douglas et al. [13]. Instead, comparisons are based on results submitted by many different parties using a variety of codes. Measured reactor data is required for a credible validation. This document introduces a new benchmark that addresses many of the shortcomings of previous LWR benchmarks by providing a highly-detailed PWR specification with two cycles of measured operational data that can be used to validate high-fidelity core analysis methods.

1

Section 2. Benchmark Specifications

2 2.1

rev. 1.0.1

Benchmark Specifications Overview

The core geometry specifications are described in 3 levels of increasing scope, detailing each of the hierarchical elements of the model. First the radial geometry is described, followed by a section detailing the axial parameters. At the lowest level, the radial geometry of each of the pincell types used throughout the core is described. Next, the fuel assembly design is detailed, including the possible configurations of burnable absorbers and the radial specification of the grid spacers. Finally, the greater core geometry is described, including the fuel assembly enrichment locations, the positions of burnable absorbers, instrument tubes, control rod banks, and shutdown banks, as well as the baffle that surrounds the fuel assemblies, the core barrel, four neutron shield panels, and the reactor pressure vessel. After the radial and axial geometry descriptions, a material specifications section lists the details of each of the materials referred to. Table 1 provides a summary of key model parameters that will be specified in greater detail in subsequent sections, and Figure 1 shows a core cross section indicating the radial structures and assembly loading pattern.

2

Section 2. Benchmark Specifications

rev. 1.0.1

Table 1: Summary of key model parameters. Core Lattice No. Fuel Assemblies

Source 193

1

w/o U235 1.60† 2.40† 3.10†

1 1 1

81.8 MT

2

17 × 17 365.76 cm 264 8

3 4 3 3

Ag-80%, In-15%, Cd-5% 57

5 1

1266 Borosilicate Glass, 12.5 w/o B2 O3

1 3

Loading Pattern Region 1 Region 2 Region 3 Cycle 1 Heavy Metal Loading Fuel Assemblies Pin Lattice Configuration Active Fuel Length No. Fuel Rods No. Grid Spacers Control Control Rod Material No. Control Rod Banks No. Burnable Poison Rods in Core Burnable Poison Material

Performance Core Power Operating Pressure Core Flow Rate † ‡

3411 MWth 2250 psia 6 61.5 × 10 kg/hr (5% bypass‡ )

Actual core-averaged enrichments calculated from detailed assembly loadings, see Source 59. It is assumed that 5% of core flow rate goes core into bypass region.

3

6 6 7

Section 2. Benchmark Specifications

rev. 1.0.1

Core Barrel Pressure Vessel

Neutron Shield Panel

Baffle

Figure 1: Core cross-section indicating radial structures and enrichment loading pattern. Black denote stainless steel, light blue denotes water, and red, yellow, and dark blue denote the 1.6, 2.4, and 3.1 w/o U235 regions, respectively.

2.2 2.2.1

Radial Geometry Pin Types

In this section the radial parameters of each of the pincell types used in the fuel assemblies are detailed. Each of these describes a complete pincell surrounded by the main coolant - in other words, the outer guide tube shell that surrounds instrument tubes, control rods, and burnable absorber rods is presented here as part of those pincells. While the following radial parameters are constant throughout the axial extent of the core of most pins, a distinction is made for the pins that have components below the control rod stop at the bottom of the core. This region, referred to as the “dashpot,” consists of a tapering of the guide tubes to a thinner radius that causes the constriction of flow to naturally prevent control rods from extending too far into the core. In this model, this is approximated by a region of thinner guide tubes (described further in later sections). Thus radial parameters are provided for pins for both regions where appropriate. 4

Section 2. Benchmark Specifications

rev. 1.0.1

For all figures in this section, dimensions and materials are specified in order starting from the inner region, through the outer rings. No thermal expansion was performed.

Figure 2 — Fuel Pin

1 2 3

Arrow Radius (cm) Material Source 1 2 3

5

0.39218 0.40005 0.45720

Fuel Helium Zircaloy

8 9 10

Section 2. Benchmark Specifications

rev. 1.0.1

Figure 3 — Upper Fuel Pin Plenum

2 1

3

Arrow Radius (cm) Material Source 1 2 3

0.06459 0.40005 0.45720

Inconel Helium Zircaloy

11 9 10

This shows the radial geometry used in the upper plenum region of the fuel pins, with a small mass of Inconel to approximate the spring.

Figure 4 — Empty Guide Tube Geometry above Dashpot

1 2

Arrow Radius (cm) Material Source 1 2

6

0.56134 0.60198

Water Zircaloy

12 13

Section 2. Benchmark Specifications

rev. 1.0.1

Figure 5 — Empty Guide Tube Geometry at Dashpot

1 2

Arrow Radius (cm) Material Source 1 2

0.50419 0.54610

Water Zircaloy

14 15

Figure 6 — Instrument Tube Pin Geometry

1 2 3 Arrow Radius (cm) Material Source

4

1 2

0.43688 0.48387

Air Zircaloy

16 17

3 4

0.56134 0.60198

Water Zircaloy

12 13

The thimble radii were chosen to be equivalent to the outer thimble radii of control rods and burnable absorber rods by assumption. Note that not all instrument tube positions contain the thimble defined by the first 2 radii in the diagram above, as discussed in Section 2.2.3.3.

7

Section 2. Benchmark Specifications

rev. 1.0.1

Figure 7 — BP Geometry above Dashpot

1

2 3 4 5

8 6

7

Arrow Radius (cm) 1 2 3 4 5 6 7 8

0.21400 0.23051 0.24130 0.42672 0.43688 0.48387 0.56134 0.60198

Material

Source

Air SS304 Air Borosilicate Glass Air SS304 Water Zircaloy

18 19 20 21 22 23 12 13

8

Section 2. Benchmark Specifications

rev. 1.0.1

Figure 8 — BP Geometry at Dashpot

1

2 3 4 5

8 6

7

Arrow Radius (cm) 1 2 3 4 5 6 7 8

0.21400 0.23051 0.24130 0.42672 0.43688 0.48387 0.50419 0.54610

Material

Source

Air SS304 Air Borosilicate Glass Air SS304 Water Zircaloy

18 19 20 21 22 23 14 15

9

Section 2. Benchmark Specifications

rev. 1.0.1

Figure 9 — Control Rod Pin Geometry

1 2 3

Arrow Radius (cm) Material Source 4

5

10

1

0.43310

Ag-In-Cd

24

2 3 4 5

0.43688 0.48387 0.56134 0.60198

Air SS304 Water Zircaloy

55 25 12 13

Section 2. Benchmark Specifications

2.2.2

rev. 1.0.1

Fuel Assemblies

Each of the assemblies in the core is made up of a 17 × 17 array of pins described in Section 2.2.1. Table 2 outlines the important parameters of each, and the positions of the guide tubes are shown in Figure 10. Assemblies are made up of one of three different enrichment fuel pins, and the guide tube positions can be filled with one of several different burnable absorber configurations described in Section 2.2.2.1. For any configuration, the center guide tube may contain an instrument tube. The details of the layout of these features throughout the core are described in Section 2.2.3. Table 2: Fuel assembly parameters. Source Fuel Assembly Lattice Pitch Pin Lattice Pitch Pin Lattice Configuration No. Fuel Rods No. Guide Tube Positions No. Instrument Tube Positions No. Grid Spacers Top/Bottom Grid Spacer Material Top/Bottom Grid Sleeve Material Intermediate Grid Spacer and Sleeve Material Weight of Inconcel per Top/Bottom Grid Weight of Stainless Steel per Top/Bottom Grid Weight of Zircaloy per intermediate Grid

11

21.50364 cm 1.25984 cm 17 × 17 264 24 1

26 27 3 3 3 3

8 Inconel 718 Stainless Steel 304 Zircaloy 390.136 g 80.0 g 1,169.23 g

3 3 3 3 28 55 29

Section 2. Benchmark Specifications

G

rev. 1.0.1

G

G

G

G

G

G

G

G

G

G

G

I

G

G

G

G

G

G

G

G

G G

G

G

Figure 10: Fuel assembly guide tube locations. Blank locations denote fuel rods, G denotes a guide tube location, and I denotes a guide tube position that might contain an instrument tube. Source: 30

12

Section 2. Benchmark Specifications

2.2.2.1

rev. 1.0.1

Burnable Absorber Configurations

Assemblies in the core that do not contain control rods may posses one of 5 burnable absorber configurations, or have none at all. Figures 11, 12, 13, 14, and 15 depict these configurations. Each configuration appears in all four quadrants of the core, and thus the 6BA and 5BA configurations need to be rotated as indicated. Core Center

B

G

B

B

B

B

G

G

G

B

G

G

I

G

G

G

G

G

G

G

G

G G

G

G

Figure 11: The 6BA burnable absorber configuration. Blank locations denote fuel rods, G denotes a guide tube location, B denotes a burnable absorber rod, and I denotes a guide tube position that might contain an instrument tube. Source: 30

13

Section 2. Benchmark Specifications

B

rev. 1.0.1

G

B

B

B

B

G

G

G

B

G

G

I

G

G

B

G

G

G

B

B

B B

G

B

Figure 12: The 12BA burnable absorber configuration. Blank locations denote fuel rods, G denotes a guide tube location, B denotes a burnable absorber rod, and I denotes a guide tube position that might contain an instrument tube. Source: 30

14

Section 2. Benchmark Specifications

rev. 1.0.1

Core Center

B

B

B G

B B

B

B

B

G

B

B

I

B

G

B

B

B

B

G

G

G G

G

G

Figure 13: The 15BA burnable absorber configuration. Blank locations denote fuel rods, G denotes a guide tube location, B denotes a burnable absorber rod, and I denotes a guide tube position that might contain an instrument tube. Source: 30

15

Section 2. Benchmark Specifications

B

rev. 1.0.1

B

B

B

B

B

G

G

G

B

B

G

I

G

B

B

G

G

G

B

B

B B

B

B

Figure 14: The 16BA burnable absorber configuration. Blank locations denote fuel rods, G denotes a guide tube location, B denotes a burnable absorber rod, and I denotes a guide tube position that might contain an instrument tube. Source: 30

16

Section 2. Benchmark Specifications

B

rev. 1.0.1

B

B

B

B

B

B

G

B

B

B

G

I

G

B

B

B

G

B

B

B

B B

B

B

Figure 15: The 20BA burnable absorber configuration. Blank locations denote fuel rods, G denotes a guide tube location, B denotes a burnable absorber rod, and I denotes a guide tube position that might contain an instrument tube. Source: 30

17

Section 2. Benchmark Specifications

2.2.2.2

rev. 1.0.1

Radial Grid Spacer Specifications

In axial regions containing spacers, dimensions are chosen to conserve the total weight of Inconel, Zircaloy, and stainless steel in each grid, as listed in Table 2. The present model creates an egg-crate structure around each pincell as well as a sleeve around assemblies. The middle six grid spacers consist entirely of Zircaloy while the top and bottom spacers consist of a Stainless Steel 304 (SS304) sleeve with Inconel internal structures. As described in Source 31, for the top/bottom grids the entire mass of the Inconel was distributed evenly among each of the 289 pincells in box of appropriate thickness inside the outer edges of the pincells. Additionally, the stainless steel mass of the grid sleeve was placed in a box of appropriate thickness around the outside of the assembly, fitting inside the region between assemblies. The 6 intermediate grids also consist of both these regions (outer grid sleeve and inner egg-crate), filled with Zircaloy. This was done for a top/bottom grid height of 1.65in and an intermediate grid height of 2.25in, with the same grid sleeve dimensions for each grid type. The inner egg-crate dimensions differ between each grid type. Figures 16 and 17 show the modified pincell geometry used for the inner grid structure around a fuel pin for each grid type, where the box thicknesses are chosen to conserve mass in the total grid. The same box is also placed around the guide tube pincells for each grid type.

1 2 3

Arrow Length (cm) Material Source

5 4

1 2 3

0.39218 0.40005 0.45720

Fuel Helium Zircaloy

8 9 10

4 5

0.62208 0.62992

Water Inconel

31 31

Figure 16: Fuel pincell geometry for the Inconel 718 top/bottom grid spacer inner egg-crate, chosen to have a thickness of 0.00784cm. Source: 31

Figure 18 shows the dimensions of the grid sleeve assemblies in all grid spacer regions. To see what this looks like in combination with the inner structural component in the pincells see Figure 19, which shows an image of what the aggregate grid spacer model looks like to scale.

18

Section 2. Benchmark Specifications

rev. 1.0.1

1 2 Arrow Length (cm) Material Source

3 5 4

1 2 3

0.39218 0.40005 0.45720

Fuel Helium Zircaloy

8 9 10

4 5

0.60978 0.62992

Water Zircaloy

31 31

Figure 17: Fuel pincell geometry for the Zircaloy intermediate grid spacer inner egg-crate, chosen to have a thickness of 0.02014cm. Source: 31

1 2 3

Arrow Length (cm)

Material

Source

1

10.70864

(Assembly)

31

2

10.73635

(Grid Sleeve)

31

3

10.75182

Water

26

Figure 18: Schematic dimensions of stainless steel grid sleeve. Arrow 1 is the half-width of 17 times the pin lattice pitch; arrow 2 is the outer grid sleeve box half-width; arrow 3 is the outer boundary of the assembly pitch in the overall fuel assembly layout. The grid sleeve thickness was chosen as 0.02771cm to conserve the estimated stainless steel mass. Source: 31

19

Section 2. Benchmark Specifications

rev. 1.0.1

Figure 19: Scale view of an intermediate grid spacer showing inter-assembly spacing at a corner of position J14. Grey is Zircaloy, black is stainless steel, light blue is water, green is burnable absorber, white is air, and dark blue, red and yellow are the three different fuel enrichments.

20

Section 2. Benchmark Specifications

2.2.3

rev. 1.0.1

Core Specification

The remainder of the radial specification is made up of the building blocks defined in the previous sections. Specifically, the main core lattice of fuel assemblies is made up of the previously described fuel assemblies, separated by the fuel assembly lattice pitch specified in Table 2. In addition, specifications for the structural components surrounding the fuel assembly lattice are given in Table 3. Table 3: Structural component specifications. Source Baffle Width Baffle Material

2.22250 cm Stainless Steel 304

32 55

Core Barrel IR Core Barrel OR Core Barrel Material

187.960 cm 193.675 cm Stainless Steel 304

33 34 35

199.39 cm Stainless Steel 304 30◦ at the 45◦ marks

55 55 55

230.0 cm 251.9 cm Carbon Steel

36 36 55

Neutron Shield Panel OR Neutron Shield Panel Material Neutron Shield Panel Width Pressure Vessel IR Pressure Vessel OR Pressure Vessel Material

2.2.3.1

Enrichment Zones and Burnable Absorber Positions

The initial fuel assembly loading pattern is shown in Figure 20, including the distribution of enrichments as well as burnable absorber locations. The burnable absorber configurations here are described in Section 2.2.2.1, rotated as appropriate for core symmetry. A scale view of burnable absorber pins depicting these rotations is shown in Figure 21.

2.2.3.2

Control Rod Bank Positions

Each of the four control rod banks - specified by the identifiers A, B, C, and D - are made up of several control rod clusters in multiple fuel assemblies. In control rod clusters, every guide tube is filled with the control rod pincell described in section 2.2.1, with the exception of the center tube. Each of the clusters in a given control rod bank move together. In addition to the control rod banks, 5 shutdown banks of control rod clusters are included above the core - specified by SA , SB , SC , SD , and SE . These clusters are not used in normal 21

Section 2. Benchmark Specifications

R

P

N M

L

1

15 16

4

16

5

16 6

7

11

12

16

6

12 12

16 20

6

12 12

16 16

12

16

13

15 16

14 15

20

16

12

12 16

6

3.1 w/o U235

6 20

16 16

16

6 16

16 16 15

16 20

6

16 12

12

6 20

12

12

12

16

A

16 16

12

12

12

16

12

16

12

B

16 16

12

16

12

16

12

16

12

16

12

16

C

16 15

16

12

12

D

16

12

12

E

6

16

12

F

20

12

16

G

6

16

16

20

9 10

H

20

16

3

8

J

K

6

2

6

rev. 1.0.1

16 6

2.4 w/o U235

1.6 w/o U235 Figure 20: Layout of fuel assemblies showing enrichment loading pattern and burnable absorber positions. Source: 1

22

Section 2. Benchmark Specifications

rev. 1.0.1

Figure 21: Detailed scale view of burnable absorber pins, showing proper rotations.

23

Section 2. Benchmark Specifications

rev. 1.0.1

operation, however, their reactivity worth was measured and reported in Table 17. Figure 22 shows the radial locations of control rod clusters belonging to each control rod and shutdown bank. The axial specifications of each are described later in Section 2.3.5. R

P

N M

L

K

J

H

G

F

E

D

C

B

A

1 SA

2

SD

3 4

SA

B SB

SE

A

D

SE

A

C

B

C

A

B SC

SD SA

C SB

SE

D SC

13 14

C

A

SB

11 12

SD C

C

SA

D

SB

9 10

SC

SB SE

D

B

7 8

SB

SA

B

SC

5 6

C

B

SA

SB

SB C

B

D

SA

SD B

SA

15

Figure 22: Control rod and shutdown bank positions. Source: 1

2.2.3.3

Instrument Tube Positions

The central guide tube for many fuel assemblies in the core is filled by an instrument tube, as described in Section 2.2.1. Figure 23 shows these positions. Where not indicated, the central guide tube is filled with water, as described in section 2.2.1. 24

Section 2. Benchmark Specifications

R

P

N M

L

rev. 1.0.1

K

J

H

◦

1 ◦

2

◦

◦

◦ ◦ ◦

8

◦

◦

◦ ◦

◦

14

◦

15

A

◦ ◦

◦

◦

◦

◦

◦ ◦

◦

◦

◦

◦

◦ ◦

◦ ◦

12 ◦

B

◦

◦

◦

13

C

◦ ◦

◦

10 11

◦

◦

9

◦ ◦

◦

7

D

◦

5 ◦

E

◦ ◦

4

F

◦

3

6

G

◦ ◦

◦

◦ ◦

◦ ◦

◦ ◦

◦

◦

◦

Figure 23: Instrument tube positions. Source: 42

25

Section 2. Benchmark Specifications

2.3

rev. 1.0.1

Axial Geometry

While some of the previously-described radial features are uniform along the entire height of the model, many have several different axial zones. For instance, the models of the baffle, core barrel, neutron shield panels, and reactor pressure vessel do not change axially, in contrast to the pincells that make up the fuel assemblies. As presented in the following sections, the axial zones are treated at the pincell level to faciliate easier modelling, since the boundaries for the axial zones for each pincell type are not all at the same planes. With this type of definition, the final aggregate geometry inside the core barrel need only consist of the fuel assemblies, which are made up of only the inter-assembly gridstraps and the pincells that are defined for the entire axial extent.

2.3.1

Fuel Rods

Figure 24 shows all different axial sections used in the fuel rod pincell occupying each fuel position in the assemblies. In most places the pincells described in Section 2.2.1 are used, however where indicated the pincell is filled either entirely with water, or with solid pins of either stainless steel or Zircaloy. These solid pins use the outer-most radius of the regular fuel rod pincell.

26

Section 2. Benchmark Specifications

rev. 1.0.1

Elevation (cm) 455.444 435.444 426.617 423.272 421.223 416.720 412.529 401.767 365.864 360.149 313.667 307.952 261.470 255.755 209.273 203.558 157.076 151.361 104.879 99.1640 42.0700 37.8790 36.0070 35.1600 20.0000 0.00000

Source Reference 55 41 41 41 41 31 41 4 31 4 31 4 31 4 31 4 31 4 31 4 31 4 41 55 55

Water Stainless Steel Pin Water Zircaloy Pin Fuel Rod Plenum Pincell Fuel Rod Plenum Pincell w/ Grid Fuel Rod Plenum Pincell Fuel Rod Pincell Fuel Rod Pincell w/ Grid Fuel Rod Pincell Fuel Rod Pincell w/ Grid Fuel Rod Pincell Fuel Rod Pincell w/ Grid Fuel Rod Pincell Fuel Rod Pincell w/ Grid Fuel Rod Pincell Fuel Rod Pincell w/ Grid Fuel Rod Pincell Fuel Rod Pincell w/ Grid Fuel Rod Pincell Fuel Rod Pincell w/ Grid Fuel Rod Pincell Zircaloy Pin Stainless Steel Pin Water

Description Highest Extent Top of Upper Nozzle Bottom of Upper Nozzle Top of Fuel Rod Bottom of Top End Plug Grid 8 Top Grid 8 Bottom Top of Active Fuel Grid 7 Top Grid 7 Bottom Grid 6 Top Grid 6 Bottom Grid 5 Top Grid 5 Bottom Grid 4 Top Grid 4 Bottom Grid 3 Top Grid 3 Bottom Grid 2 Top Grid 2 Bottom Grid 1 Top Grid 1 Bottom Bottom of Active Fuel Bottom of Fuel Rod Bottom of Support Plate Lowest Extent

Figure 24: Fuel rod pincell axial specification.

27

Section 2. Benchmark Specifications

2.3.2

rev. 1.0.1

Guide Tubes

Figure 25 shows the empty guide tube axial differentiation, referring to the pincells described in Section 2.2.1. As with the fuel rods, the pincell is replaced by water below the fuel region. Elevation (cm) Description

Source Reference 55

Water

39

Guide Tube Pincell

31

Guide Tube Pincell w/ Grid

39

Guide Tube Pincell

31

Guide Tube Pincell w/ Grid

39

Guide Tube Pincell

31

Guide Tube Pincell w/ Grid

39

Guide Tube Pincell

31

Guide Tube Pincell w/ Grid

39

Guide Tube Pincell

31

Guide Tube Pincell w/ Grid

39

Guide Tube Pincell

31

Guide Tube Pincell w/ Grid

39

Guide Tube Pincell

31

Guide Tube Pincell w/ Grid

39 39

Guide Tube Pincell Dashpot Guide Tube

31

Dashpot Guide Tube w/ Grid

39

Dashpot Guide Tube

55

Water

455.444

Highest Extent

426.617

Bottom of Upper Nozzle

416.720

Grid 8 Top

412.529 365.864

Grid 8 Bottom Grid 7 Top

360.149 313.667

Grid 7 Bottom Grid 6 Top

307.952 261.470

Grid 6 Bottom Grid 5 Top

255.755 209.273

Grid 5 Bottom Grid 4 Top

203.558 157.076

Grid 4 Bottom Grid 3 Top

151.361 104.879

Grid 3 Bottom Grid 2 Top

99.1640 45.0790

Grid 2 Bottom Control Rod Step 0

42.0700

Grid 1 Top

37.8790

Grid 1 Bottom

35.1600

Bottom of Fuel Rod

0.00000

Lowest Extent

Figure 25: Empty guide tube pincell axial specification.

2.3.3

Instrument Tubes

Figure 26 shows the instrument tube axial differentiation, referring to the pincells described in Section 2.2.1. This follows the same pattern as the guide tube axial specification, with the caveat that below the fuel region the inner section of the instrument tubes (that is, without the surrounding guide tube) is used through the lowest extent of the geometry. Also note that regardless of whether or not the central instrument tube contains the inner instrument thimble, the outer guide tube does not shrink for the dashpot. 28

Section 2. Benchmark Specifications

rev. 1.0.1

Elevation (cm) Description

Source Reference 55

Water

37

Instr. Tube Pincell

31

Instr. Tube Pincell w/ Grid

37

Instr. Tube Pincell

31

Instr. Tube Pincell w/ Grid

37

Instr. Tube Pincell

31

Instr. Tube Pincell w/ Grid

37

Instr. Tube Pincell

31

Instr. Tube Pincell w/ Grid

37

Instr. Tube Pincell

31

Instr. Tube Pincell w/ Grid

37

Instr. Tube Pincell

31

Instr. Tube Pincell w/ Grid

37

Instr. Tube Pincell

31

Instr. Tube Pincell w/ Grid

37

Instr. Tube Pincell

31

Instr. Tube Pincell w/ Grid

37

Instr. Tube Pincell

37

Bare Instr. Tube

455.444

Highest Extent

426.617

Bottom of Upper Nozzle

416.720

Grid 8 Top

412.529

Grid 8 Bottom

365.864

Grid 7 Top

360.149

Grid 7 Bottom

313.667

Grid 6 Top

307.952

Grid 6 Bottom

261.470

Grid 5 Top

255.755

Grid 5 Bottom

209.273

Grid 4 Top

203.558

Grid 4 Bottom

157.076

Grid 3 Top

151.361

Grid 3 Bottom

104.879

Grid 2 Top

99.1640

Grid 2 Bottom

42.0700

Grid 1 Top

37.8790

Grid 1 Bottom

35.1600

Bottom of Fuel Rod

0.00000

Lowest Extent

Figure 26: Instrument tube pincell axial specification.

29

Section 2. Benchmark Specifications

2.3.4

rev. 1.0.1

Burnable Absorbers

Figure 27 shows the axial regions of the burnable absorber pincells. Here, the active region of burnable absorber rods as presented in Section 2.2.1 extend from a plane 2 inches above the bottom of the active fuel through the top of the active fuel. Above there, the outermost inner radius of the burnable absorber rods (or arrow 6 in Figure 7) is used to create a solid stainless steel pin tube through the top of the upper nozzle, inside the guide tube where appropriate. Elevation (cm) Description

Source Reference 55 38 38 31 38 38 31 38 31 38 31 38 31 38 31 38 31 38 38 38 31 39 55

455.444 435.444 426.617 416.720 412.529 401.767 365.864 360.149 313.667 307.952 261.470 255.755 209.273 203.558 157.076 151.361 104.879 99.1640 45.0790 42.0700 41.0870 37.8790 20.0000 0.00000

Water Stainless Steel Pin Stainless Steel Pin in GT Stainless Steel Pin in GT w/ Grid Stainless Steel Pin in GT Burnable Absorber Pincell Burnable Absorber Pincell w/ Grid Burnable Absorber Pincell Burnable Absorber Pincell w/ Grid Burnable Absorber Pincell Burnable Absorber Pincell w/ Grid Burnable Absorber Pincell Burnable Absorber Pincell w/ Grid Burnable Absorber Pincell Burnable Absorber Pincell w/ Grid Burnable Absorber Pincell Burnable Absorber Pincell w/ Grid Burnable Absorber Pincell Dashpot Burnable Absorber Dashpot Burnable Absorber w/ Grid Dashpot Guide Tube w/ Grid Dashpot Guide Tube Water

Highest Extent Top of Upper Nozzle Bottom of Upper Nozzle Grid 8 Top Grid 8 Bottom Top of Active Fuel Grid 7 Top Grid 7 Bottom Grid 6 Top Grid 6 Bottom Grid 5 Top Grid 5 Bottom Grid 4 Top Grid 4 Bottom Grid 3 Top Grid 3 Bottom Grid 2 Top Grid 2 Bottom Control Rod Step 0 Grid 1 Top Bot. of Burnable Absorbers Grid 1 Bottom Bottom of Support Plate Lowest Extent

Figure 27: Burnable absorber pincell axial specification.

2.3.5

Control Rods

Figure 28 shows the control rod axial layout, which depending on the degree of insertion can either be occupied by the empty guide tube pincell or the control rod pincell described in

30

Section 2. Benchmark Specifications

rev. 1.0.1

Section 2.2.1. The details of insertion depend on the radial location of the specific control rod cluster, i.e. which control or shutdown bank it belongs to. Control rods are considered to move in "steps," or units of 1.5817 cm, and are modelled to contain exactly 228 steps (360.634 cm) of the control rod pincell from the bottom tip of the rod. Above this region, a solid Zircaloy pin is used inside the guide tubes, similar to the region above burnable absorbers. The actual axial planes used for the top and bottom of this active region depend on the number of steps of insertion of the rod, and may be superceded by the highest axial plane when appropriate. For instance, the bottom and top axial planes used for the active region of a fully-inserted control rod, respectively, are the step 0 and step 228 planes indicated in Figure 28, with a Zircaloy pin inside the guide tube above that region. Alternatively, a fully withdrawn control rod will have empty guide tubes below the step 228 axial plane, and the active control rod pincell from there through the highest extent of the geometry. The control rods in the shutdown banks are all fully-withdrawn, but control rod banks A, B, C, and D, can have any level of partial insertion, where the bottom tips of the control rods can be at any axial step level between step 0 and step 228. While each of these banks move their control rod clusters together, their movement is often staggered with the other control rod banks, described in Figure 29 with an insertion sequence example. However, insertion levels for each individual bank are provided for most of the data presented in this benchmark, so the algorithm in Figure 29 may not be needed.

31

Section 2. Benchmark Specifications

rev. 1.0.1

Elevation (cm) Description

Source Reference 40

Control Rod or Zircaloy pin in GT

31

Control Rod or Zircaloy pin in GT w/ Grid

40

Control Rod or Zircaloy pin in GT

40

Guide Tube or CR Pincell

31

Guide Tube or CR Pincell w/ Grid

40

Guide Tube or CR Pincell

31

Guide Tube or CR Pincell w/ Grid

40

Guide Tube or CR Pincell

31

Guide Tube or CR Pincell w/ Grid

40

Guide Tube or CR Pincell

31

Guide Tube or CR Pincell w/ Grid

40

Guide Tube or CR Pincell

31

Guide Tube or CR Pincell w/ Grid

40

Guide Tube or CR Pincell

31

Guide Tube or CR Pincell w/ Grid

40 39

Guide Tube or CR Pincell Dashpot Guide Tube

31

Dashpot Guide Tube w/ Grid

39

Dashpot Guide Tube

55

Water

455.444

Highest Extent

416.720

Grid 8 Top

412.529 405.713

Grid 8 Bottom Control Rod Step 228

365.864

Grid 7 Top

360.149 313.667

Grid 7 Bottom Grid 6 Top

307.952 261.470

Grid 6 Bottom Grid 5 Top

255.755 209.273

Grid 5 Bottom Grid 4 Top

203.558 157.076

Grid 4 Bottom Grid 3 Top

151.361 104.879

Grid 3 Bottom Grid 2 Top

99.1640 45.0790

Grid 2 Bottom Control Rod Step 0

42.0700

Grid 1 Top

37.8790 20.0000

Grid 1 Bottom Bottom of Support Plate

0.00000

Lowest Extent

Figure 28: Control rod pincell axial specification.

32

Section 2. Benchmark Specifications

rev. 1.0.1

Control Rod Insertion Sequence Starting from all rods fully withdrawn: • First D moves in alone, until it gets to 113 steps withdrawn • Now D and C move together until C gets to 113 steps withdrawn (D is all the way in when C is at 115) • Now C and B move together until B gets to 113 steps withdrawn (C is all the way in when B is at 115) • Now B and A move together until A gets to 0 steps withdrawn (B is all the way in when A is at 115) Assuming only movement of each control rod bank by one step at a time, in total this sequence yields 574 unique positions, which we denote with integer S steps withdrawn. If S = 0 all control rods are out of the core, and if S = 574 all rods are fully inserted. For example for normal operation with the D bank at the bite position of S D = 213 steps withdrawn, S = 228 − 213 = 15. With this notation, the following algorithm provides the elevation of the top axial planes of the active region in each control rod bank (sibot and si ) for a given S with the fully inserted elevation s0 and step width δ. S D = max(0, 228 − S) SC = (S D < 113) ? max(0, 228 − S + 113 + 3) : 228 SB = (SC < 113) ? max(0, 228 − S + 113 × 2 + 5) : 228 SA = (SB < 113) ? max(0, 228 − S + 113 × 3 + 7) : 228 sAbot = s0 + δ × SA sBbot = s0 + δ × SB sCbot = s0 + δ × SC sbot = s0 + δ × S D D top

sA = sAbot + δ × 228 top

sB = sBbot + δ × 228 top

sC = sCbot + δ × 228 top

s D = sbot + δ × 228 D

Figure 29: Control rod insertion sequence and axial specification [14].

33

Section 2. Benchmark Specifications

2.3.6

rev. 1.0.1

Aggregate

By defining the full extent of the axial geometry in the pincells, several features remain to be described or examined in the final combination of each element of the model. In aggregate it is useful to see an exhaustive list of all axial planes used in the model, as presented in Figure 30. Control rod insertions are treated separately, as discussed in Section 2.3.5. Elevation (cm) 455.444 435.444 426.617 423.272 421.223 416.720 412.529 405.713 401.767 365.864 360.149 313.667 307.952 261.470 255.755 209.273 203.558 157.076 151.361 104.879 99.1640 45.0790 42.0700 41.0870 37.8790 36.0070 35.1600 20.0000 0.00000

Description Highest Extent Top of Upper Nozzle Bottom of Upper Nozzle Top of Fuel Rod Bottom of Top End Plug Grid 8 Top Grid 8 Bottom Control Rod Step 228 Top of Active Fuel Grid 7 Top Grid 7 Bottom Grid 6 Top Grid 6 Bottom Grid 5 Top Grid 5 Bottom Grid 4 Top Grid 4 Bottom Grid 3 Top Grid 3 Bottom Grid 2 Top Grid 2 Bottom Control Rod Step 0 Grid 1 Top Bot. of Burnable Absorbers Grid 1 Bottom Bottom of Active Fuel Bottom of Fuel Rod Bottom of Support Plate Lowest Extent

Figure 30: Left: Scale view of row 8 axial cross section, with highlighted grid spacers and partial insertion of control rod bank D to the bite position. Right: exhaustive list of all axial planes used in the model, excluding partial control rod insertion planes.

2.3.6.1

Grid Spacers

Nearly all axial features of the model are captured in the axial pincell specifications. However, the stainless steel grid sleeve described in Section 2.2.2.2 for each of the 8 grid spacers needs to be defined on the assembly level, as it is not contained within any of the pincell elements. The axial planes used for the grid sleeves are the same as those used for the grids in the pincells, as listed in Figure 30.

34

Section 2. Benchmark Specifications

2.3.6.2

rev. 1.0.1

Nozzles and Support Plate

By defining pincells as completely water or as solid material pins below and above the fuel rod regions, the model implicitly approximates the nozzle and support plate regions as depicted in Figure 31. While the axial planes used here were taken from Source 41, this does not necessarily conserve the mass of stainless steel in these regions. Note that since the bottom nozzle and support plate are both stainless steel, no distinction is made between the two regions.

Figure 31: Radial picture of nozzles and support plate in aggregate model

2.3.6.3

Top and Bottom of the Core

For verification, Figure 32 shows scale views close to the bottom and top regions of the core resulting from the aggregate pincell specification as defined previously.

35

Section 2. Benchmark Specifications

rev. 1.0.1

Top of Upper Nozzle

Bottom of Upper Nozzle Instrument Tube Empty Guide Tube Top of Fuel Rods Fuel Rod End Plug Top of Plenum Fuel Rod Plenum Inconel Spring Approx. Grid 8 Top Burnable Absorber Rod Grid 8 Bottom

.. . Dashpot Boundary (Control Rod Step 0) Grid 1 Top Bottom of Burnable Absorbers Fuel Grid 1 Bottom Bottom of Active Fuel Bottom of Fuel Rod

Fuel Rod End Plug

Bottom of Support Plate

Figure 32: Axial scale view of the model near the top and bottom of the fuel rods in the center of position J8, showing pin plenums, approximated springs, and fuel rod end plugs. Blue: water; orange: helium; black: stainless steel; light grey: Zircaloy; dark grey Inconel; white: air; green: borosilicate glass; yellow: fuel.

36

Section 2. Benchmark Specifications

2.4

rev. 1.0.1

Materials

Table 4 — Fuel 1.6% Enriched Density (g/cc)

10.31362

Isotope

Number Density (atom/b-cm)

U-234 U-235 U-238 O-16 O-17 O-18

3.0131e-06 3.7503e-04 2.2626e-02 4.5896e-02 1.7483e-05 9.4315e-05

Source: 43

37

Section 2. Benchmark Specifications

rev. 1.0.1

Table 5 — Fuel 2.4% Enriched Density (g/cc)

10.29769

Isotope

Number Density (atom/b-cm)

U-234 U-235 U-238 O-16 O-17 O-18

4.4843e-06 5.5815e-04 2.2408e-02 4.5829e-02 1.7457e-05 9.4178e-05

Source: 44

Table 6 — Fuel 3.1% Enriched Density (g/cc)

10.301870

Isotope

Number Density (atom/b-cm)

U-234 U-235 U-238 O-16 O-17 O-18

5.7988e-06 7.2176e-04 2.2254e-02 4.5851e-02 1.7466e-05 9.4224e-05

Source: 45

38

Section 2. Benchmark Specifications

rev. 1.0.1

Table 7 — Air Density (g/cc) Isotope

0.000616 Atom Density (atom-b/cm)

C-12 C-13 O-16 O-17 O-18 N-14 N-15 Ar-36 Ar-38 Ar-40

6.7565e-09 7.3076e-11 5.2864e-06 2.0137e-09 1.0863e-08 1.9681e-05 7.1900e-08 7.9414e-10 1.4915e-10 2.3506e-07

Source: 46

Table 8 — Borosilicate Glass Density (g/cc) Isotope

2.260000 Atom Density (atom/b-cm)

B-10 B-11 O-16 O-17 O-18 Al-27 Si-28 Si-29 Si-30

9.6506e-04 3.9189e-03 4.6511e-02 1.7717e-05 9.5581e-05 1.7352e-03 1.6924e-02 8.5977e-04 5.6743e-04

Source: 47

39

Section 2. Benchmark Specifications

rev. 1.0.1

Table 9 — Ag-In-Cd Control Rods Density (g/cc)

10.160000

Isotope

Atom Density (atom/b-cm)

Ag-107 Ag-109 In-113 In-115 Cd-106 Cd-108 Cd-110 Cd-111 Cd-112 Cd-113 Cd-114 Cd-116

2.3523e-02 2.1854e-02 3.4291e-04 7.6504e-03 3.4019e-05 2.4221e-05 3.3991e-04 3.4835e-04 6.5669e-04 3.3257e-04 7.8188e-04 2.0384e-04

Source: 48

Table 10 — Helium Density (g/cc) Isotope

0.001598 Atom Density (atom/b-cm)

He-4

2.4044e-04

Source: 49

40

Section 2. Benchmark Specifications

rev. 1.0.1

Table 11 — Inconel 718 Density (g/cc)

8.2000

Isotope

Atom Density (atom/b-cm)

Si-28 Si-29 Si-30 Cr-50 Cr-52 Cr-53 Cr-54 Mn-55 Fe-54 Fe-56 Fe-57 Fe-58 Ni-58 Ni-60 Ni-61 Ni-62 Ni-64

5.6753e-04 2.8831e-05 1.9028e-05 7.8239e-04 1.5088e-02 1.7108e-03 4.2586e-04 7.8201e-04 1.4797e-03 2.3229e-02 5.3645e-04 7.1392e-05 2.9320e-02 1.1294e-02 4.9094e-04 1.5653e-03 3.9864e-04

Source: 50

41

Section 2. Benchmark Specifications

rev. 1.0.1

Table 12 — Stainless Steel 304 Density (g/cc)

8.03

Isotope

Atom Density (atom/b-cm)

Si-28 Si-29 Si-30 Cr-50 Cr-52 Cr-53 Cr-54 Mn-55 Fe-54 Fe-56 Fe-57 Fe-58 Ni-58 Ni-60 Ni-61 Ni-62 Ni-64

9.5274e-04 4.8400e-05 3.1943e-05 7.6778e-04 1.4806e-02 1.6789e-03 4.1791e-04 1.7604e-03 3.4620e-03 5.4345e-02 1.2551e-03 1.6703e-04 5.6089e-03 2.1605e-03 9.3917e-05 2.9945e-04 7.6261e-05

Source: 51

42

Section 2. Benchmark Specifications

rev. 1.0.1

Table 13 — Zircaloy 4 Density (g/cc)

6.55

Isotope

Atom Density (atom/b-cm)

O-16 O-17 O-18 Cr-50 Cr-52 Cr-53 Cr-54 Fe-54 Fe-56 Fe-57 Fe-58 Zr-90 Zr-91 Zr-92 Zr-94 Zr-96 Sn-112 Sn-114 Sn-115 Sn-116 Sn-117 Sn-118 Sn-119 Sn-120 Sn-122 Sn-124

3.0743e-04 1.1711e-07 6.3176e-07 3.2962e-06 6.3564e-05 7.2076e-06 1.7941e-06 8.6699e-06 1.3610e-04 3.1431e-06 4.1829e-07 2.1827e-02 4.7600e-03 7.2758e-03 7.3734e-03 1.1879e-03 4.6735e-06 3.1799e-06 1.6381e-06 7.0055e-05 3.7003e-05 1.1669e-04 4.1387e-05 1.5697e-04 2.2308e-05 2.7897e-05

Source: 52

43

Section 2. Benchmark Specifications

rev. 1.0.1

Table 14 — Borated Water Density (g/cc) Isotope

0.740582 Number Density (atom/b-cm)

B-10 B-11 H-1 H-2 O-16 O-17 O-18

8.0042e-06 3.2218e-05 4.9457e-02 7.4196e-06 2.4672e-02 9.3982e-06 5.0701e-05

Source: 53

44

Section 2. Benchmark Specifications

rev. 1.0.1

Table 15 — Carbon Steel Density (g/cc)

7.800

Isotope

Atom Density (atom/b-cm)

C-12 C-13 Si-28 Si-29 Si-30 Mn-55 P-31 Mo-92 Mo-94 Mo-96 Mo-97 Mo-98 Mo-100 Fe-54 Fe-56 Fe-57 Fe-58 Ni-58 Ni-60 Ni-61 Ni-62 Ni-64

9.6726e-04 1.0462e-05 4.2417e-04 2.1548e-05 1.4221e-05 1.1329e-03 3.7913e-05 3.7965e-05 2.3725e-05 4.2875e-05 2.4573e-05 6.2179e-05 2.4856e-05 4.7714e-03 7.4900e-02 1.7298e-03 2.3020e-04 2.9965e-04 1.1543e-04 5.0175e-06 1.5998e-05 4.0742e-06

Source: 54

45

Section 3. Operating Data

3

rev. 1.0.1

Operating Data

3.1

Processing Measured In-Core Detector Data

In this reactor plant, there are 58 assemblies that contain in-core detectors. This layout of in-core detectors is shown in Figure 23. These detectors are typically U-235 fission chambers varying in mass of U-235. Although there are 58 locations, there are usually only a few detectors (6-10). When measurements are being taken, multiple passes are performed to adequately measure all 58 assemblies. Each detector will, however, pass through one common assembly. This becomes important in the normalization process of detector signals. Before a measurement is taken, detectors are inserted into the core through instrumentation tubes in assemblies until the top of the assembly is hit. Detector measurements are then taken as the detectors are pulled back through the core at a constant speed. Thus, each measurement reported is an integral of the signal over the recording time. Also, axial locations of where data is recorded may be slightly skewed. In these measurements, 61 axial data points were collected and processed with a Python script.

3.1.1

Example – Hot Zero Power Measurements

This section will go through the process of filtering measured data for HZP. The core power for these measurements is approximately 25 MWth. Raw data was processed by first organizing it in Python objects. Each collection of measurements contain detector information for multiple passes through the core in various assemblies. Raw data for HZP is shown in Figure 33. In order to show all detector signals on one plot, each raw data signal was normalized to a sum of unity. The first step in this process is to remove any detector background signal. This information was supplied with the raw data and can be subtracted from each detector measurement pass. The corrected data for background is shown in Figure 34. Depending on the strength of the signal being measured, the signal can be amplified by adjusting the gain on the detectors. Gain factors are also reported with the raw data. When processing, these gain factors are multiplied by the measured data. For HZP, all of the gain factors are unity. Figure 35 shows the measured data after gain factors are applied. In some of the detector signals, zero points exist where the detector failed. These zero points are removed by performing a linear interpolation/extrapolation between/from the nearest two points. The corrected data is shown in Figure 36. As explained above, there is one common assembly where all detectors will pass. This is needed for normalization of detector signals. In this plant, assembly J10 was chosen as the common assembly. Figure 37 shows the measurements taken in assembly J10.

46

Section 3. Operating Data

rev. 1.0.1

0.03

Detector Signal [-]

0.025 0.02

0.015

0.01 0.005

0

0

10

20

30

40

50

60

70

Measurement Location (top to bottom) [-]

Figure 33: Initial Raw Detector Measurements (top to bottom).

0.03

Detector Signal [-]

0.025 0.02 0.015 0.01 0.005 0 -0.005

0

10

20

30

40

50

60

70

Measurement Location (top to bottom) [-]

Figure 34: Detector Measurements Corrected for Background (top to bottom).

47

Section 3. Operating Data

rev. 1.0.1

0.03

Detector Signal [-]

0.025 0.02 0.015 0.01 0.005 0 -0.005

0

10

20

30

40

50

60

70

Measurement Location (top to bottom) [-]

Figure 35: Detector Measurements Gain Factors Applied (top to bottom).

0.03

Detector Signal [-]

0.025 0.02

0.015

0.01 0.005

0

0

10

20

30

40

50

60

70

Measurement Location (top to bottom) [-]

Figure 36: Detector Measurements with Zero Points Removed (top to bottom).

48

Section 3. Operating Data

rev. 1.0.1

0.5

Detector Detector Detector Detector Detector Detector

0.45

Detector Signal [-]

0.4 0.35

1 2 3 4 6 4

0.3 0.25 0.2 0.15 0.1 0.05 0

0

10

20

30

40

50

60

70

Measurement Location (top to bottom) [-]

Figure 37: Detector Measurements with in J10 Assembly (top to bottom). Each detector measurement represents a different measurement pass. The core power during one pass may not be the same as the others. There is typically a small fluctuation present in the core power. To account for this, each signal is divided by the core power reported during that measurement pass. The resulting detector signals are shown in Figure 38 for assembly J10. The next step in the process is to make sure that all detector signals line up with one another. We can verify this by plotting all 58 detector signals on top of each other. This is the same as plot as Figure 38, except all assemblies are plotted here with signals normalized for shape comparison. This is shown in Figure 39. It is observed that not all of the signals are aligned with each other. Luckily, signals can be aligned to a single grid depression. Here, we align to the grid depression between measurements 20 and 30, however any grid depression could be used. The first step in this process is to find the measurement index corresponding to a local minimum between 20 and 30. The alignment index is then taken as the most reoccurring local minimum index. All grids not having a local minimum occurring at this alignment index are then shifted either left or right. Depending on the shift direction, one end will lose a point and the other will gain one. The data point that is lost is just deleted from the data array, while the point that is gained is determined by a simple linear extrapolation from the nearest two points. The resulting realignment is shown in Figure 40. Results show that all detector signals are more consistently aligned, however still not perfect. The span of these signals can also be attributed to measurement uncertainty as the should all have the same shape once normalized here. There is one signal that is an outlier is observed between measurements 0 and 5. This assembly location corresponds to where control rod bank D is slightly inserted. Therefore, we should expect this depression in the signal toward the top of the core. The next step in the process is to average detector signals that were measured from the same detector. It is important to look at the raw signals before performing this step since measurements may be poor. If this is observed, the poor measurement is commented out in the 49

Section 3. Operating Data

rev. 1.0.1

0.02

Detector Detector Detector Detector Detector Detector

0.018

Detector Signal [-]

0.016 0.014

1 2 3 4 6 4

0.012 0.01 0.008 0.006 0.004 0.002 0

0

10

20

30

40

50

60

70

Measurement Location (top to bottom) [-]

Figure 38: J10 Detector Measurements Divided by Core Power (top to bottom).

0.03

Detector Signal [-]

0.025 0.02

0.015

0.01 0.005

0

0

10

20

30

40

50

60

Measurement Location (top to bottom) [-]

Figure 39: All Detector Signals Before Realignment.

50

70

Section 3. Operating Data

rev. 1.0.1

0.03

Detector Signal [-]

0.025 0.02

0.015

0.01 0.005

0

0

10

20

30

40

50

60

70

Measurement Location (top to bottom) [-]

Figure 40: All Detector Signals After Realignment. data file. In Figure 38 the two signals from detector 4 are close to each other and should be averaged. The resulting signals for assembly J10 are shown in Figure 41. Each fission chamber detector contains a different amount of U-235. Therefore, some normalization process is needed to account for this mass difference. To get these normalization factors, the average of all detector signals is determined first. Then, normalization factors are computed by taking the ratio of the integral of each individual detector signal to the integral of the mean of all detector signals. For example, for HZP the normalization factors for each detector are: • Detector 1: 0.922 • Detector 2: 0.901 • Detector 3: 1.272 • Detector 4: 1.002 • Detector 6: 0.903 These normalization factors are then multiplied to each corresponding detector signal in the core. The resulting signals are now very close to each other as shown in Figure 42 for assembly J10. Lastly, detector signals need to be put on an axial coordinate grid corresponding to points that range from the bottom to top of active fuel. To do this we use the same grid point as before since we know that the centerline location of this grid is at 222.6 cm above bottom of active fuel. The distance between axial measurement locations is assumed uniform and is equal to active core height divided by 60 intervals. A 2nd order spline fit is then used to map from 51

Section 3. Operating Data

rev. 1.0.1

0.02

Detector Detector Detector Detector Detector

0.018

Detector Signal [-]

0.016 0.014

1 2 3 4 6

0.012 0.01 0.008 0.006 0.004 0.002 0

0

10

20

30

40

50

60

70

Measurement Location (top to bottom) [-]

Figure 41: Multiple Detector Signals Averaged in J10 (top to bottom).

0.016

Detector Detector Detector Detector Detector

0.014

Detector Signal [-]

0.012

1 2 3 4 6

0.01 0.008 0.006 0.004 0.002 0

0

10

20

30

40

50

60

Measurement Location (top to bottom) [-]

Figure 42: Application of Detector Normalization Factors for J10.

52

70

Section 3. Operating Data

rev. 1.0.1

measured data axial locations to a axial map has equal data points exactly at the Top of Active Fuel (TAF) and Bottom of Active Fuel (BAF). A comparison of applying this spline is shown in Figure 43. The spline fit does well for this data, however grid depressions are now less since 0.025

Original Spline

Detector Signal [-]

0.02

0.015

0.01

0.005

0

0

50

100

150

200

250

300

350

400

Measurement Location (relative to BAF) [cm]

Figure 43: Comparision of Splined Data for Assembly J10. the grid centerline does not match up with the final axial grid. Before the spline, all detector signals were averaged such that there is only one signal per assembly. All splined signals are shown in Figure 44. There is some spread in the data when they are all normalized to one another. There is one detector signal that seems to not follow the same shape at the top of the core. That measurement corresponds to assembly D12 where control rod bank D is slightly inserted and thus there is a depression in the measurement signal. A separate Excel sheet contains all of the processed data organized by measurement data file and by assembly. A plot of the final measurements (not all normalized to sum of unity) is shown in Figure 45.

53

Section 3. Operating Data

rev. 1.0.1

0.03

Detector Signal [-]

0.025 0.02

0.015

0.01 0.005

0

0

50

100

150

200

250

300

350

400

Measurement Location (relative to BAF) [cm]

Figure 44: Comparison of All Assemblies after Spline.

0.04 0.035

Detector Signal [-]

0.03 0.025 0.02 0.015 0.01 0.005 0

0

50

100

150

200

250

300

350

Measurement Location (relative to BAF) [cm]

Figure 45: Final Processed HZP Measurement Data.

54

400

Section 3. Operating Data

3.2

rev. 1.0.1

Hot Zero Power Data Discussion

Table 16 lists the thermal power of the reactor during initial physics testing the first available detector maps. Also included are the rod bank positions and critical boron concentration. This data can be used to evaluate how far off reactor models are from critical at HZP conditions. Table 16: Cycle 1 hot zero power physics configuration. Core Power Core Flow Rate Inlet Coolant Temperature Rod Bank A Position Rod Bank B Position Rod Bank C Position Rod Bank D Position Boron Concentration

25 MWth 61.5 × 106 kg/hr 560◦ F Step 228 Step 228 Step 228 Step 213 975 ppm

Radial maps were also created to view the average relative power produced per assembly. These were obtained by renormalizing the signals in Figure 45 such that their total sum is the number of detector locations (in this case 58). Each measurement in an assembly was then axially averaged to produce a relative radial peaking factor. In Figure 46, this factor is presented on each assembly where a measurement was taken. Results show that measurement locations are consistent with the reported instrumentation diagram shown in Figure 23. Since the reactor is quarter-core symmetric (disregarding perturbations from instrument tubes), measurements can be compared. For example, assemblies H13, C8, H3 and N8 are located in symmetric positions. The measured values in these locations should be close. It is observed that the measurements are on the same order, but not all that close. This can happen at low powers and gives us an indication of measurement uncertainty. Another way to look at the data is to collapse it to quarter core. We can compare rotational quarter core positions. If more than one radial power is available, the mean and standard deviation are reported. Otherwise, the result from Figure 46 is listed without a standard deviation. This is shown in Figure 47. In each assembly, three values are reported. From top to bottom they are: average of radial (axially averaged) signals, standard deviation of average and number of measurements that were averaged. The standard deviations give us some idea on the uncertainty in these measured values. They can range all the way up to 5.4%. A weighted average of the standard deviation was computed to get an idea of the overall measurement uncertainty. This was determined by multiplying each uncertainty by the number of radial powers and then dividing by 58. For HZP, this uncertainty is 3.7%. This is rather high since we really would like to see values below 1%. However, when the power is very low, power tilting can occur which contributes to this high uncertainty. To compare simulation values to these measured data, axial edits of a tally such as U235 fission 55

Section 3. Operating Data

rev. 1.0.1

R

P

N

M

L

J

K

1 1.171

0.645

0.875 1.115

0.920

9

0.899

11

0.918

1.204

0.774

1.088

1.175 0.966 1.295

14

0.700

1.330 1.034

1.339

0.846 1.291

1.223

13

1.175

0.968

1.263

0.857

1.320

0.892

0.920

0.964 0.576

A

1.239

1.017

12

15

1.247

1.008

0.837

10

B

0.689

1.042

1.102 0.924

0.730

C

1.171

0.965

1.129

1.165

7

D

1.115

5 0.670

E

0.699

0.898

4

F

1.223

3

8

G

0.777

2

6

H

0.631 1.438

0.984 0.919

0.792 1.357

1.050

0.837

0.602

Figure 46: Radial detector measurements (axially integrated).

56

Section 3. Operating Data

rev. 1.0.1 H

8

G

F

E

D

C

B

A

0.774 —– 1

1.065 0.023 2

0.943 0.025 2

1.145 0.030 2

0.937 0.039 4

1.259 0.036 2

0.784 0.053 2

1.152 0.023 2

0.924 —– 1

0.919 —– 1

0.846 —– 1

9

0.774 —– 1

1.013 0.004 2

0.920 —– 1

10

1.065 0.023 2

0.892 —– 1

1.102 —– 1

11

0.943 0.025 2

12

1.145 0.030 2

1.034 —– 1

13

0.937 0.039 4

1.204 —– 1

14

1.259 0.036 2

0.837 —– 1

15

0.784 0.053 2

0.777 —– 1

0.964 —– 1

1.257 0.034 2 1.251 0.059 4 1.438 —– 1 1.320 —– 1

1.256 0.077 3

1.050 —– 1

0.942 0.023 2

0.685 0.014 2

1.339 —– 1

0.616 0.014 2

1.143 0.028 2

0.875 —– 1

0.857 —– 1

0.746 0.046 2

0.667 0.022 2

0.576 —– 1

Figure 47: Quarter core (full core folded) radial measurements. rate must be applied to each instrumented assembly in the core. To be fully consistent with the data a constant width 60 interval mesh (61 points) from bottom of active fuel to top of active fuel should be applied. All signals should be renormalized such that their average is 1.0 (or sum of all signals is 58). Table 17 presents measured data for control rod bank worths and isothermal temperature coefficients for HZP conditions. Also provided are the critical boron concentrations for each configuration. Table 17: Cycle 1 hot zero power physics data, including critical boron concentrations, control rod bank worths for the full insertion sequence, and isothermal temperature coefficients. Crit. Boron Concentrations (ppm) All Rods Out (ARO) D in C, D in

975 902 810

A, B, C, D in

686

A, B, C, D, SE, SD, SC in

508

Control Rod Bank Worths (pcm) D in C with D in B with D, C in A with D, C, B in SE with D, C, B, A in SD with D, C, B, A, SE in SC with D, C, B, A, SE, SD in

57

788 1203 1171 548 461 772 1099

Temp. Coeffs. (pcm/◦ F) ARO D in C, D in

-1.75 -2.75 -8.01

Section 3. Operating Data

3.3

rev. 1.0.1

Cycle 1 and 2 Available Data

For Cycle 1 and 2 operation of this reactor, there are detector measurement maps available at various times during operation. For each measurement file, data is given for core power, critical boron concentration and rod bank configuration. Although these are not described here, each measurement file has been processed according to the methodology described in Section 3.1. These are available online at the MIT-CRPG website. Also available is the boron letdown curve during Cycle 1 and Cycle 2 operation. Figure 48 and corresponding Table 18 presents the boron letdown data. Finally, the power history reference from Beginning of Cycle (BOC) for Cycle 1 operation is presented in Figure 49. Power history data is also available online at the MIT-CRPG website. In Figure 49, locations of where detector maps are available are also shown. Note, the powers shown in Figure 49 are 24-hr averages, whereas, in detector measurement files, powers reported are instantaneous at the time of measurement. In the plot they are shown to be coincident with the power history, however, in the files they may be slightly different. Similarly, Figure 50 shows the power history of Cycle 2. 1000

Cycle 1 Cycle 2

900 800

Boron [ppm]

700 600 500 400 300 200 100 0

0

50

100

150

200

250

300

350

EFPD

Figure 48: Measured boron letdown curves for two cycles of operation.

58

Section 3. Operating Data

rev. 1.0.1

Table 18: Boron Letdown Curve Data for Cycles 1 and 2. Cycle 1 EFPD 4 11 16 22 31 36 52 69 85 96 110 124 141 144 152 164 174 177 180 190 204 214 219 225 228 248 271 295 326

Cycle 2

Boron [ppm] 599 610 614 621 638 610 623 598 569 559 533 506 471 461 457 415 394 384 384 367 322 296 286 270 270 207 149 72 0

EFPD 13 23 43 63 84 103 129 150 176 202 234 257

59

Boron [ppm] 918 882 832 764 687 623 538 466 376 292 184 104

Section 3. Operating Data

Detector Map Positions

60

Percent Rated Power [%]

100

80

60

40

20

0

0

100

200

300

400

500

Calendar Days From BOC rev. 1.0.1

Figure 49: Power history of Cycle 1.

61

Percent Rated Power [%]

Section 3. Operating Data

Detector Map Positions

100

80

60

40

20

0

0

50

100

150

200

250

Calendar Days From BOC rev. 1.0.1

Figure 50: Power history of Cycle 2.

References [1] N. Horelik, B. Herman, B. Forget, and K. Smith. Benchmark for Evaluation and Validation of Reactor Simulations (BEAVRS), v1.0.1. Proc. Int. Conf. Mathematics and Computational Methods Applied to Nuc. Sci. & Eng., 2013. Sun Valley, Idaho. [2] K.S. Smith. Assembly homogenization techniques for light water reactor analysis. Progress in Nuclear Energy, 17(3):303 – 335, 1986. [3] J. E. Hoogenboom and W. R. Martin. A Proposal for a Benchmark to Monitor the Performance of Detailed Monte Carlo Calculation of Power Densities in a Full Size Reactor Core. Proc. Int. Conf. Mathematics, Computational Methods, and Reactor Physics, 2009. Saratoga Springs, New York. [4] D. Kelly, T. Sutton, T. Trumbull, and P. Dobreff. MC21 Monte Carlo Analysis of the Hoogenboom-Martin Full-Core PWR Benchmark Problem. Proc. PHYSOR 2010, Adv. in Reac. Phys. to Power the Nuc. Renaissance, Pittsburgh, Pennsylvania, USA, May 9-14, on CD-ROM(2010), May 2010. [5] D. Kelly, T. Sutton, and S. Wilson. MC21 Analysis of the Nuclear Energy Agency Monte Carlo Performance Benchmark Problem. Proc. PHYSOR 2012, Adv. in Reac. Phys., Knoxville, Tennessee, USA April 15-20, on CD-ROM(2010), April 2012. [6] K. Smith. Reactor Core Methods, 2003. Invited lecture at the M&C2003 International Conference, April 6-10, 2003, Gatlinburg, TN, USA (http://wwwtest.iri.tudelft.nl/˜jhoogenb). [7] J. J. Jarrell, A. T. Godfrey, T. M. Evans, and G. G. Davidson. Full Core Reactor Analysis: Running Denovo on Jaguar. Proc. PHYSOR 2012, Adv. in Reac. Phys., Knoxville, Tennessee, USA April 15-20, on CD-ROM(2010), April 2012. [8] USDOE. Consortium for Advanced Simulation of Light Water Reactors (CASL), 2012. http://www.casl.gov/goals.shtml. [9] USDOE. About CESAR | Center for Exascale Simulation of Advanced Reactors, 2012. http://cesar.mcs.anl.gov/content/about-cesar. [10] OECD/NEA. International Reactor Physics Benchmark Experiments (IRPhE), May 2012. ISBN 978-92-64-99168-2. [11] K.S. Smith, S. Tarves, T. Bahadir, and R. Ferrer. Benchmarks for Quantifying Fuel Reactivity Depletion Uncertainty. Technical Report 1022909, Electric Power Research Institute, 2011. [12] Benchmark on Deterministic Transport Calculations Without Spatial Homogenisation. Technical Report NEA/NSC/DOC(2005)16, NEA No. 5420, 2005. ISBN 92-64-01069-6. [13] S. Douglass, F. Rahnema, and J. Margulies. A stylized three dimensional PWR whole-core benchmark problem with Gadolinium. Annals of Nuclear Energy, 37(10):1384 – 1403, 2010. 62

[14] K. Smith. Personal communication on control rod sequence, May 2012. [15] PWR Utility. Specifications and Measured Data from PWR Plant. 2012. [16] Studsvik Scandpower. CASMO-4: A Fuel Assembly Burnup Program, University edition, 2009. [17] Global Data. Power eTrack, Catawba 1 http://www.poweretrack.com.libproxy.mit.edu/.

Nuclear

Power

Plant,

2013.

[18] Engineer at Utility. Additional PWR Plant Specifications, October 2012. [19] K. J. Geelhood, W. G. Luscher, and C. E. Beyer. FRAPCON-3.4: Integral Assessment. Technical Report NUREG/CR-7022, Vol. 2; PNNL-19418, Vol. 2, Pacific Northwest National Laboratory; USNRC, March 2011. http://frapcon.labworks.org/. [20] Public Service Enterprise Group. SALEM, UNITS 1 AND 2 - UPDATED FINAL SAFETY ANALYSIS REPORT, REVISION 18. Technical Report ML003712110, USNRC, 2000. [21] Course 0519 R304P. Westinghouse Technology 3.1 Reactor Vessel and Internals. Technical Report ML11223A212, Nuclear Regulatory Commission, August 2009. [22] Tennessee Valley Authority. Watts Bar, Unit 2 - Amendment 98 to Final Safety Analysis Report, Section 4, Reactor. Technical Report ML101370397, USNRC, May 2010. [23] PWR Utility. Data Measurements from PWR Plant for Cycles 1 and 2. 2012. Air Properties. Electronic, [24] Engineering Toolbox. http://www.engineeringtoolbox.com/air-properties-d_156.html.

January

2013.

[25] National Institute of Standards and Technology. Isothermal Properties for Helium. Electronic, January 2013. [26] AK Steel. 304/304L Stainless Steel Product Data Sheet, January 2013. UNS S30400. [27] National Institute of Standards and Technology. Isothermal Properties for Water. Electronic, January 2013. [28] American Society for Testing and Materials. Standard Specification for Pressure Vessel Plates, Alloy Steel, Quenched and Tempered, Manganese-Molybdenum and ManganeseMolybdenum-Nickel – A533 , September 2012. [29] E. M. Baum, M. C. Ernesti, H. D. Knox, T. R. Miller, and A. M. Watson. Nuclides and Isotopes. Chart of the Nuclides. Knolls Atomic Power Laboratory, 17 edition, 2009.

63

Source Details Source 1 — Core Arrangement of Fuel Assemblies This information is reported on the Core Arrangement worksheet.

References [15]

Pages 3, 22, 24

64

Source 2 — Fuel Assembly Loading This information is reported on the Assembly Loading worksheet.

References [15]

Pages 3

65

Source 3 — Fuel Lattice Specifications This information is reported on the Fuel Lattice worksheet.

References [15]

Pages 3, 11

66

Source 4 — Active Core Height This information is reported on the Fuel Lattice worksheet. The active fuel length is L f = 144 in · 2.54

cm in

References [15]

Value 365.76

Units cm

Pages 3, 27

67

= 365.76 cm

Source 5 — Control Rod Composition This composition of Control Rods is found in Example 3.1 in Section 2.10.3 in the CASMO manual.

References [16]

Pages 3

68

Source 6 — Nominal Core Power Nominal Core Power is taken to be that for Catawba, which is available online from Power etrack.

References [17]

Value 3411

Units MWth

Pages 3

69

Source 7 — Core Mass Flow Rate From an email communication with the utility, the total pump flow rate is 61.5 × 106 kg/hr. Normally, about 5% of the flow goes into the bypass region, so 95% of flow is through the core area, and the flow in the guide tubes is very low. It is assumed that this has no impact on active cooling flow. It is common to take 5% for the flow fraction through the bypass region although it is not known precisely.

References [18]

Value 61.5 × 106

Units kg/hr

Pages 3

70

Source 8 — Fuel Pellet Radius This information is reported on the Fuel Lattice worksheet. The fuel pellet radius is calculated in the spreadsheet with the following forumla: Rf =

0.3088 in 2

· 2.54

cm in

= 0.39218 cm

It can be inferred that the diameter of the fuel pellet that this radius was derived as was 0.3088 in.

References [15]

Value 0.39218

Units cm

Pages 5, 18, 19

71

Source 9 — Fuel Cladding Inner Radius This information is reported on the Fuel Lattice worksheet. The fuel rod inner radius is calculated in the spreadsheet with the following forumla: R IR =

0.36 in − 0.0225 in · 2 2

· 2.54

cm in

= 0.40005 cm

It can be inferred that the cladding thickness is 0.0225 in.

References [15]

Value 0.40005

Units cm

Pages 5, 6, 18, 19

72

Source 10 — Fuel Cladding Outer Radius This information is reported on the Fuel Lattice worksheet. The fuel rod outer radius given is calculated in the spreadsheet with the following forumla: ROR =

0.36 in 2

· 2.54

cm in

= 0.45720 cm

It can be inferred that the diameter of the fuel rod is 0.36 in.

References [15]

Value 0.45720

Units cm

Pages 5, 6, 18, 19

73

Source 11 — Plenum Spring Radius The radius for the mass of Inconel approximating the plenum spring is chosen to be the equivalent radius for the volume of an approximate helical spring. The spring wire diameter dsp g w and number of turns vs for the helical spring are taken from the FRAPCON3 Integral Assessment Document in the appendix regarding the Westinghouse BR-3 fuel rods, which are assumed to be similar to the fuel rods in this plant. The helix diameter dsp g was chosen such that the ratio of the outer fuel rod cladding diameter dco to the helix diameter was the same. vs = 8 turns dco,BR−3 = 0.422 in dsp g,BR−3 = 0.37 in

dsp g = dco

dspg,BR−3 dco,BR−3

= 0.3156 in

From here volume of the helical spring is calculated as ‚ Vspr ing = vs π Vspr ing = 8π Vspr ing



dspgw

Œ2

2 0.055 in

2 = 0.01556 in3

€ Š π ddspg − dspgw 2

π(0.3156 in − 0.055 in)

Finally, the equivalent radius re is found with the plenum height h pl = 7.66 in as È re =

πh pl r

re =

Vspr ing 0.01556 in3

π7.66 in re = 0.02543 in re = 0.06459 cm

74

References [19]

Value 0.06459

Units cm

Pages 6

75

Source 12 — Guide Tube Inner Radius This information is reported on the Fuel Lattice worksheet. The guide tube inner radius is calculated in the spreadsheet with the following forumla: R IR =

0.442 in 2

· 2.54

cm in

= 0.56134 cm

It can be inferred that the inner diameter of the guide tube is 0.442 in. Note that this dimension is also used for instrumentation tubes.

References [15]

Value 0.56134

Units cm

Pages 6, 7, 8, 10

76

Source 13 — Guide Tube Outer Radius This information is reported on the Fuel Lattice worksheet. The guide tube outer radius is calculated in the spreadsheet with the following forumla: ROR =

0.474 in 2

· 2.54

cm in

= 0.60198 cm

It can be inferred that the outer diameter of the guide tube is 0.474 in. Note that this dimension is also used for instrumentation tubes.

References [15]

Value 0.60198

Units cm

Pages 6, 7, 8, 10

77

Source 14 — Guide Tube Inner Radius at Dashpot This information is reported on the Fuel Lattice worksheet. The guide tube inner radius is calculated in the spreadsheet with the following forumla: R IR =

0.397 in 2

· 2.54

cm in

= 0.50419 cm

It can be inferred that the inner diameter of the guide tube is 0.397 in.

References [15]

Value 0.50419

Units cm

Pages 7, 9

78

Source 15 — Guide Tube Outer Radius at Dashpot This information is reported on the Fuel Lattice worksheet. The guide tube outer radius is calculated in the spreadsheet with the following forumla: R IR =

0.43 in 2

· 2.54

cm in

= 0.54610 cm

It can be inferred that the outer diameter of the guide tube at dashpot is 0.43 in.

References [15]

Value 0.54610

Units cm

Pages 7, 9

79

Source 16 — Instrumentation Tube Thimble Inner Radius The instrumentation tube thimble inner radius was not reported in the spreadsheet. It is assumed that this dimension is the same as the burnable poison outer cladding inner radius (Source 22).

References [15]

Value 0.43688

Units cm

Pages 7

80

Source 17 — Instrumentation Tube Thimble Outer Radius The instrumentation tube thimble outer radius is not reported in the spreadsheet. It is assumed that this dimension is the same as the burnable poison outer cladding inner radius (Source 23).

References [15]

Value 0.48387

Units cm

Pages 7

81

Source 18 — Inner Cladding Inner Radius of BP Pin The dimensions of the Burnable Poison (BP) inner cladding inner radius is reported in the Fuel Lattice worksheet. This number was calculated with the following formula: R I C IR = 0.08425 in · 2.54

References [15]

Value 0.21400

Units cm

Pages 8, 9

82

cm in

= 0.21400 cm

Source 19 — Inner Cladding Outer Radius of BP Pin The dimensions of BP the inner cladding outer radius is reported in the Fuel Lattice worksheet. This number was calculated with the following formula: R I COR = 0.1905 in · 2.54

References [15]

Value 0.23051

Units cm

Pages 8, 9

83

cm in

= 0.23051 cm

Source 20 — Inner Radius of Poison of BP Pin The dimensions of the poison inner radius is reported in the Fuel Lattice worksheet. This number was calculated with the following formula: R P IR = 0.095 in · 2.54

References [15]

Value 0.24130

Units cm

Pages 8, 9

84

cm in

= 0.24130 cm

Source 21 — Outer Radius of Poison of BP Pin The dimensions of the poison outer radius is reported in the Fuel Lattice worksheet. This number was calculated with the following formula: R POR = 0.168 in · 2.54

References [15]

Value 0.42672

Units cm

Pages 8, 9

85

cm in

= 0.42672 cm

Source 22 — Outer Cladding Inner Radius of BP Pin The dimensions of the BP outer cladding inner radius is reported in the Fuel Lattice worksheet. This number was calculated with the following formula: ROC IR = 0.172 in · 2.54

References [15]

Value 0.43688

Units cm

Pages 8, 9, 80

86

cm in

= 0.43688 cm

Source 23 — Outer Cladding Outer Radius of BP Pin The dimensions of the BP outer cladding outer radius is reported in the Fuel Lattice worksheet. This number was calculated with the following formula: ROCOR = 0.09075 in · 2.54

References [15]

Value 0.48387

Units cm

Pages 8, 9, 81

87

cm in

= 0.48387 cm

Source 24 — Control Rod Thimble Inner Radius The control rod thimble inner radius was not reported in the spreadsheet. It is assumed that this dimension is the same as the burnable poison outer cladding inner radius (Source 22).

References [15]

Value 0.43688

Units cm

Pages 10

88

Source 25 — Control Rod Thimble Outer Radius The control rod thimble outer radius is not reported in the spreadsheet. It is assumed that this dimension is the same as the burnable poison outer cladding outer radius (Source 23).

References [15]

Value 0.48387

Units cm

Pages 10

89

Source 26 — Fuel Assembly Pitch The fuel assembly pitch is taken from the Fuel Lattice worksheet. The formula for calculating this parameter is Sa = 8.466 in · 2.54

cm in

References [15]

Value 21.50364

Units cm

Pages 11, 19

90

= 21.50364 cm

Source 27 — Fuel Pin Pitch The fuel pin pitch is taken from the Fuel Lattice worksheet. The formula for calculating this parameter is cm S p = 0.496 in · 2.54 = 1.25984 cm in References [15]

Value 1.25984

Units cm

Pages 11

91

Source 28 — Inconel Grid Weight Taken from email correspondence with an engineer at the utility. The weight of Inconel718 for the grid spacers is 332 lbs. The following formula is used to calculate the weight of Inconel per top/bottom grid: Win = 332 lb · 453.59237

g

1

·

·

1

lb 193 assemblies 2 grids

References [18]

Value 390.136

Units g

Pages 11

92

= 390.136 g.

Source 29 — Zircaloy Grid Weight Taken from email correspondence with an engineer at the utility. The weight of Zircaloy-4 for the grid spacers is 2985 lbs. The following formula is used to calculate the weight of Zircaloy-4 per intermediate grid: Wz r = 2985 lb · 453.59237

g

1

·

·

1

lb 193 assemblies 6 grids

References [18]

Value 1,169.23

Units g

Pages 11

93

= 1, 169.23 g.

Source 30 — Burnable Poison Specifications Taken from the data spreadsheet provided by the utility, on the sheet named BP Arrangement.

References [15]

Pages 12, 13, 14, 15, 16, 17

94

Source 31 — Grid Spacers The axial positioning of the grid centers was taken from the Fuel Lattice worksheet. Upper and lower planes for each grid were found using the following approximated grid geometry. The masses for determining radial grid spacer dimensions are taken from Sources 28 and 29, with the exception of the wieght of SS304 in the grid sleeve of the top/bottom grids. This number was not provided, and is estimated as Wss304 = 80 g per grid for this calculation. Grid spacer heights were also not provided, and are estimated as h t b = 1.65 in and hint = 2.25 in for the top/bottom and intermediate grids, respectively. Top/Bottom Grid Sleeve As shown in Figure 18, the grid sleeve is a box shell defined by inner and outer square pitch parameters Pi and Po , where Pi is found using the pin pitch as 17 × S p . Using the density of SS304 ρSS304 , the estimated mass for each grid Wss304 , and the height of the grid, the outer pitch is found as: È Po =

Pi2 +

WSS304 /ρSS304 ht b

s =

g

(17 × 1.25984 cm)2 +

80 g/8.03 cm3 1.65 in × 2.54 cm in

= 21.47270 cm This fits between assemblies, as Po is less than the assembly pitch (21.50364 cm). The square radius reported in Figure 18 is half of Po , or 10.73681 cm. Top/Bottom Egg-Crate As shown in Figure 16, the egg-crate is defined by a box shell defined by inner and outer square pitch parameters pi and po , where po is simply the outer pincell pitch S p . It is assumed that the entire mass of Inconel reported from Source 28 is uniformly distributed between all pincells in an assembly. Thus the mass of Inconel per pincell is Win w in = 17×17 = 1.34995 g. Using this with the density of Inconel ρin and the height of the grid, the inner pitch is found as: È pi =

po2

−

w in /ρin ht b

s =

g

(1.25984 cm) − 2

1.34995 g/8.2 cm3 1.65 in × 2.54 cm in

= 1.24415 cm This fits between the pin and outer pincell pitch for all pincell types, as pi is greater than the guide tube diameter (1.20396 cm). The square radius reported in Figure 16 is half of 95

pi , or 0.62208 cm. Intermediate Grid Sleeve The dimensions for the intermediate grid sleeves are taken to be identical to those for the top/bottom grid sleeves. Intermediate Egg-Crate The intermediate grid egg-crate dimensions are found in the same way as the top/bottom grids, using the appropriate Zircaloy masses and densities. Here, the weight of Zircaloy wz r,e g g used to calculate the egg-crate dimensions is the total grid weight of Zircaloy Wz r from Source 29, less the weight of Zircaloy in the intermediate grid sleeve wzr,sleeve , divided by the number of pincells. The weight in the sleeve is found using the density of Zircaloy and the volume of the sleeve from the intermediate grid height and the previosuly-calculated grid sleeve pitch parameters. € Š wzr,sl eeve = ρz r hint Po2 − Pi2 Š cm € g (21.47270 cm)2 − (21.41728 cm)2 = 6.55 3 × 2.25 in × 2.54 cm in = 88.98 g wz r,e g g = wz r,e g g = wz r,e g g

1

€ Š Wz r − wzr,sleeve

17 × 17 1

17 × 17 = 3.7379 g È

pi =

po2 −


1169.23 g − 88.98 g

wz r,e g g /ρzr hint

s =

g

(1.25984 cm)2 −

3.7379 g/6.55 cm3 2.25 in × 2.54 cm in

= 1.21957 cm This fits between the pin and outer pincell pitch for all pincell types, as pi is greater than the guide tube diameter (1.20396 cm). The square radius reported in Figure 17 is half of pi , or 0.60978 cm.

References [15]

96

Pages 18, 19, 27, 28, 29, 30, 32

97

Source 32 — Core Baffle Thickness Taken from email correspondence with an engineer at the utility. The core baffle is 7/8 inches thick. Converting this to centimeters: Tba f =

7 8

in · 2.54

cm in

References [18]

Value 2.22250

Units cm

Pages 21

98

= 2.22250 cm

Source 33 — Core Barrel Inner Radius Taken from email corresponding with an engineer at the utility. The inner diameter of the core barrel is 148.0 inches. The inner radius of the core barrel is calculated to be R bar =

148.0 in 2

· 2.54

References [18]

Value 187.96

Units cm

Pages 21

99

cm in

= 187.96 cm

Source 34 — Core Barrel Outer Radius Taken from email correspondence with an engineer at the utility. The outer diameter of the core barrel is 152.5 inches. The outer radius of the core barrel is calculated to be R bar =

152.5 in 2

· 2.54

References [18]

Value 193.675

Units cm

Pages 21

100

cm in

= 193.675 cm

Source 35 — Core Barrel Material From email correspondence with the utility, the core barrel is made out of Stainless Steel 304.

References [18]

Pages 21

101

Source 36 — Reactor Pressure Vessel Power eTrack contains details about the reactor that is modeled in this document. It states that the Vessel Inner Diameter is 4.6m and the Vessel Wall Thick is 219mm. Therefore, the inner radius of the vessel is 230cm and outer radius is 251.9cm.

References [17]

Pages 21

102

Source 37 — Instrument Tube Axial Planes The instrument tube thimble penetrates the bottom of the reactor vessel and extends to the end of guide tubes at the bottom of the upper nozzle. The source for these planes is described in Source 41.

Pages 29

103

Source 38 — Burnable Absorber Axial Planes Burnable absorbers are inserted from the top of assemblies with a spider assembly similar to those that hold control rods. The axial specifications for the burnable absorber rods for this plant were not provided, so they were estimated from the final safety report for the Salem Nuclear Generating Station Figure 4.2-17. Here, they consist of a blank stainless steel pin above an active poison length of 142 in. (two inches less than the active fuel length). Thus, the active poison of burnable absorbers in this model are estimated to extend from the top of the active fuel to a plane 2 in. above the bottom of the active fuel.

References [20]

Pages 30

104

Source 39 — Guide Tube Axial Planes The guide tubes are the structural components of the assemblies, connecting the top of the lower nozzle to the bottom of the upper nozzle. The source for these planes is described in 41. The dashpot axial plane is placed at the control rod step 0, which was found as described in Source 40.

Pages 28, 30, 32

105

Source 40 — Control Rod Axial Planes The actual control rod axial specification for this plant was not provided, but it can be estimated from the grid spacer centerlines provided on the Fuel Lattice worksheet combined with the knowledge that the active region for control rods is typically 142 in. (found in [21]), and that control rods in this type of plant can move to a total of 228 different axial positions (or steps). From this information the step size is calculated as 1.582 cm. This is confirmed by noting that typically the axial centerlines of the intermediate grid spacers align with the bottom tip of the control rods for many of these steps. For the grid spacer centerlines provided, we see that with this step size the intermediate grids are exactly 33 steps apart each. To determine the fully withdrawn (step 228) and fully inserted (step 0) axial planes, it was assumed that step 228 was between 2 and 3 step lengths above the active fuel region. This is consistent with experience from other plants of similar design. From there, the step 0 axial plane was calculated with the length of the absorbing section of the rod (142 in.).

References [15] [21]

Pages 32, 105

106

Source 41 — Assembly Nozzles and Fuel Rod Plenum Fuel rod plenum and end plug axial dimensions were estimated from the Watts Bar Unit 2 Safety Analysis Report, Section 4, Figure 4.2-3. Figure 4.2-2 also informed estimates for upper nozzle and water gap axial spacings.

References [22]

Pages 27, 35, 103, 105

107

Source 42 — Location of Instrument Tubes The locations of the instrumentation tubes were inferred from HZP detector measurement files. There are 58 locations in various locations around the core.

References [23]

Pages 25

108

Source 43 — 1.6% Enriched Fuel Composition Provided in the spreadsheet sent by the utility the initial Uranium heavy metal mass and U-235 mass are detailed for each assembly under the worksheet, Assembly Loading. These allow us to calculate U-235 enrichments and fuel density. To limit the number of materials, the average values for the enrichments were calculated. Using the detailed assembly loadings, the actual core-averaged enrichment for the lowenriched bundles is χ25 = 1.61006% (see Source 59). It assumed that the enrichment of U-234 is 0.8% of this, χ24 = 0.008 · 1.61006% = 0.01288048%. The rest of the heavy metal in the initial fuel loading is made up of U-238 calculated as χ28 = 100% − 1.61006% + 0.01288048% = 98.37705952%. From these weight percents of Uranium isotopes in Uranium, the mass of atomic mass of Uranium can be calculated. The isotopic masses are taken from Source 56. The mass of Uranium is calculated as   χ25 χ28 −1 χ24 MU = + + = 238.001241552877 amu. M24 M25 M28 The weight fractions of Uranium in Uranium Dioxide and Oxygen in Uranium Dioxide can be determine by the following two expressions: ωU =

MU MU + 2 · MO

= 0.8814859441139345

and ωO = 1 − ωU = 0.118514055886065. From the Uranium heavy metal weight percent, and detailed heavy metal loadings reported in the spreadsheet, the average density can be calculated. The total Uranium heavy metal mass for low enriched bundles is m f = 27.570971 MT (see Source 59). If there are 65 low enriched bundles, the volume can be calculated with Vf = π · R2f · H · Nass y · Npins Vf = π · 0.392182 · 365.76 · 65 · 264 = 3032671.6413 cm3 . See Sources 8, 4 and Figures 10 and 20.

109

The fuel density can be calculated by computing the Uranium heavy metal density and dividing by its fractional weight ρf =

mf Vf · ω U

= 10.31362

g cm3

.

Isotopic number densities for Uranium are then calculated with N=

e·A ρ M

.

om e is the isotopic The parameter A is Avagadro’s number = 0.60221415 · 1024 atmol and ρ mass density. The isotopic mass density is calculated by multiplying the weight fraction of
the element by the weight fraction of the isotopic in that element ω · χ multiplied by the fuel mass density, e = ρ f · ω · χ. ρ

For oxygen, the total number density of oxygen is calculated with NO =

ρ f · ωO · A MO

.

Isotopic number densities are then determined by multiplying by fractional abundances provided in Source 57.

References [15]

Pages 37

110

Source 44 — 2.4% Enriched Fuel Composition Provided in the spreadsheet sent by the utility the initial Uranium heavy metal mass and U-235 mass are detailed for each assembly under the worksheet, Assembly Loading. These allow us to calculate U-235 enrichments and fuel density. To limit the number of materials, the average values for the enrichments were calculated. Using the detailed assembly loadings, the actual core-averaged enrichment for the mediumenriched bundles is χ25 = 2.39993% (see Source 59). It assumed that the enrichment of U-234 is 0.8% of this, χ24 = 0.008 · 2.39993% = 0.01919944%. The rest of the heavy metal in the initial fuel loading is made up of U-238 calculated as χ28 = 100% − 2.39993% + 0.01919944% = 97.58087056%. From these weight percents of Uranium isotopes in Uranium, the mass of atomic mass of Uranium can be calculated. The isotopic masses are taken from Source 56. The mass of Uranium is calculated as   χ25 χ28 −1 χ24 MU = + + = 237.9769423150815 amu. M24 M25 M28 The weight fractions of Uranium in Uranium Dioxide and Oxygen in Uranium Dioxide can be determine by the following two expressions: ωU =

MU MU + 2 · MO

= 0.8814752772323609

and ωO = 1 − ωU = 0.1185247227676391. From the Uranium heavy metal weight percent, and detailed heavy metal loadings reported in the spreadsheet, the average density can be calculated. The total Uranium heavy metal mass for medium enriched bundles is m f = 27.104522 MT (see Source 59). If there are 64 medium enriched bundles, the volume can be calculated with Vf = π · R2f · H · Nass y · Npins Vf = π · 0.392182 · 365.76 · 64 · 264 = 2986015.15 cm3 . See Sources 8, 4 and Figures 10 and 20.

111

The fuel density can be calculated by computing the Uranium heavy metal density and dividing by its fractional weight ρf =

mf Vf · ω U

10.29769

g cm3

..

Isotopic number densities for Uranium are then calculated with N=

e·A ρ M

.

om e is the isotopic The parameter A is Avagadro’s number = 0.60221415 · 1024 atmol and ρ mass density. The isotopic mass density is calculated by multiplying the weight fraction of
the element by the weight fraction of the isotopic in that element ω · χ multiplied by the fuel mass density, e = ρ f · ω · χ. ρ

For oxygen, the total number density of oxygen is calculated with NO =

ρ f · ωO · A MO

.

Isotopic number densities are then determined by multiplying by fractional abundances provided in Source 57.

References [15]

Pages 38

112

Source 45 — 3.1% Enriched Fuel Composition Provided in the spreadsheet sent by the utility the initial Uranium heavy metal mass and U-235 mass are detailed for each assembly under the worksheet, Assembly Loading. These allow us to calculate U-235 enrichments and fuel density. To limit the number of materials, the average values for the enrichments were calculated. Using the detailed assembly loadings, the actual core-averaged enrichment for the highenriched bundles is χ25 = 3.10221% (see Source 59). It assumed that the enrichment of U-234 is 0.8% of this, χ24 = 0.008 · 3.10221% = 0.02481768%. The rest of the heavy metal in the initial fuel loading is made up of U-238 calculated as χ28 = 100% − 3.10221% + 0.02481768% = 96.87297232%. From these weight percents of Uranium isotopes in Uranium, the mass of atomic mass of Uranium can be calculated. The isotopic masses are taken from Source 56. The mass of Uranium is calculated as   χ25 χ28 −1 χ24 MU = + + = 237.9553417272953 amu. M24 M25 M28 The weight fractions of Uranium in Uranium Dioxide and Oxygen in Uranium Dioxide can be determine by the following two expressions: ωU =

MU MU + 2 · MO

= 0.8814657934358563

and ωO = 1 − ωU = 0.1185342065641437. From the Uranium heavy metal weight percent, and detailed heavy metal loadings reported in the spreadsheet, the average density can be calculated. The total Uranium heavy metal mass for high enriched bundles is m f = 27.115256 MT (see Source 59). If there are 64 high enriched bundles, the volume can be calculated with Vf = π · R2f · H · Nass y · Npins Vf = π · 0.392182 · 365.76 · 64 · 264 = 2986015.15 cm3 . See Sources 8, 4 and Figures 10 and 20.

113

The fuel density can be calculated by computing the Uranium heavy metal density and dividing by its fractional weight ρf =

mf Vf · ω U

10.30187

g cm3

..

Isotopic number densities for Uranium are then calculated with N=

e·A ρ M

.

om e is the isotopic The parameter A is Avagadro’s number = 0.60221415 · 1024 atmol and ρ mass density. The isotopic mass density is calculated by multiplying the weight fraction of
the element by the weight fraction of the isotopic in that element ω · χ multiplied by the fuel mass density, e = ρ f · ω · χ. ρ

For oxygen, the total number density of oxygen is calculated with NO =

ρ f · ωO · A MO

.

Isotopic number densities are then determined by multiplying by fractional abundances provided in Source 57.

References [15]

Pages 38

114

Source 46 — Composition of Air The density of air was referenced from Engineering toolbox at 300 C to be ρair = 0.000616 g/cc. The composition of air included here contains Oxygen, Nitrogen, Argon and Carbon. Note that Hydrogen, Neon, Helium, Krypton and Xenon were all neglected as they contribute very little. Abundances were gathered from Engineering Toolbox and are listed below. Element

Fractional Abundance

O Ar

0.2095 0.00933

Element

Fractional Abundance

N C

0.7809 0.00027†

† Carbon adjusted slightly so sum is unity. Using these abundances and elemental masses in Source 58, the mass of air can be calculated with X αi Mi = 14.665664059 amu, Mai r = i

where α represents the abundance fraction. The total number density of air can be calculated with Nai r =

ρai r · A Mai r

= 2.529472343752123e − 04

atom barn · cm

.

om The parameter A is Avagadro’s number = 0.60221415 · 1024 atmol . Elemental number densities can be calculated by multiplying the number density of air by their respective abundances, Ni = αi · Nair .

Similarly, the isotopic number densities can be calculated by multiplying the elemental number densities by isotopic abundances reported in Source 57.

References [24]

Pages 39

115

Source 47 — Composition of Borosilicate Glass The density of Borosilicate glass was referenced from the CASMO-4 manual to be ρ bp = 2.26 g/cc. The composition, according to the manual is Element/Isotope

Weight Fraction

O Si B-11

0.5481 0.3787 0.0317

Element/Isotope

Weight Fraction

Al B-10

0.0344 0.0071

The relative weight fractions of B-10 and B-11 in Boron can be calculated using the absolute weight fractions above, χ50 =

ω50

χ50 =

ω50 + ω51

ω51 ω50 + ω51

.

The elemental mass of Boron can be done using isotopic masses in Source 56, MB =



χ50 M50

+

χ51 M51

−1

= 10.812422457829642 amu.

To compute the number densities of the elements/isotopes listed in the table above, the following formula can be used: ωi · ρ bp · A . Ni = Mi om The parameter A is Avagadro’s number = 0.60221415 · 1024 atmol . The isotopic number densities of the elements listed in the table can be calculated by multiplying the elemental number densities by isotopic abundances reported in Source 57.

References [16]

Pages 39

116

Source 48 — Composition of Ag-In-Cd Control Rods The density of Ag-In-Cd control rods was referenced from the CASMO-4 manual to be ρc r = 10.16 g/cc. The composition, is given in the manual is 80% Ag, 15% In and 5% Cd. Using these weight percents and elemental masses from Source 58, the number densities of each element can be calculated with. Ni =

ωi · ρcr · A Mi

.

om The parameter A is Avagadro’s number = 0.60221415 · 1024 atmol . The isotopic number densities of the elements listed in the table can be calculated by multiplying the elemental number densities by isotopic abundances reported in Source 57.

References [16]

Pages 40

117

Source 49 — Composition of Helium The density of Helium gas was retrieved from NIST from a pressure of 2 MPa and temperature of 600 K. The density was given as ρH e = 0.0015981 g/cc. The number density can be computed along with the element mass from Source 58, NH e =

ρH e · A MH e

.

The parameter A is Avagadro’s number = 0.60221415 · 1024

References [25]

Pages 40

118

at om . mol

Source 50 — Composition of Inconel The density of Inconel-718 was referenced from the CASMO-4 manual to be ρin = 8.2 g/cc. The composition, according to the manual is Element/Isotope Si Mn Ni

Weight Fraction 0.0035 0.0087 0.5119

†

Element/Isotope

Weight Fraction

Cr Fe

0.1896 0.2863†

weight fraction adjust such that sum is unity

To compute the number densities of the elements/isotopes listed in the table above, the following formula can be used: ωi · ρin · A . Ni = Mi om The parameter A is Avagadro’s number = 0.60221415 · 1024 atmol . The isotopic number densities of the elements listed in the table can be calculated by multiplying the elemental number densities by isotopic abundances reported in Source 57.

References [16]

Pages 41

119

Source 51 — Composition of Stainless Steel The density of Stainless Steel-304 was referenced from AK Steel Product Data Sheet to be ρss = 8.03 g/cc. The composition, according to the data sheet is Element/Isotope Si Mn Ni

Weight Fraction 0.0060 0.0200 0.1000

†

Element/Isotope

Weight Fraction

Cr Fe

0.1900 0.6840†

weight fraction adjust such that sum is unity

To compute the number densities of the elements/isotopes listed in the table above, the following formula can be used: ωi · ρss · A Ni = . Mi om The parameter A is Avagadro’s number = 0.60221415 · 1024 atmol . The isotopic number densities of the elements listed in the table can be calculated by multiplying the elemental number densities by isotopic abundances reported in Source 57.

References [26]

Pages 42

120

Source 52 — Composition of Zircaloy The density of Zircaloy 4 was referenced from the CASMO-4 manual to be ρzr = 6.55 g/cc. The composition, according to the manual is Element/Isotope O Fe Sn

Weight Fraction 0.00125 0.0021 0.0145

†

Element/Isotope

Weight Fraction

Cr Zr

0.0010 0.98115†

weight fraction adjust such that sum is unity

To compute the number densities of the elements/isotopes listed in the table above, the following formula can be used: ωi · ρzr · A . Ni = Mi om The parameter A is Avagadro’s number = 0.60221415 · 1024 atmol . The isotopic number densities of the elements listed in the table can be calculated by multiplying the elemental number densities by isotopic abundances reported in Source 57.

Pages 43

121

Source 53 — Composition of Borated Water This source block describes how to compute the number density of isotopes in borated water. This block will show the necessary formulas, but the density and concentration of boron may change depending on cycle time. For a given reactor pressure and temperature, density of water is obtained from NIST. From the water density and boron weight percent, the density of borated water will be obtained. For a given concentration of boron, the weight percent of boron in water is  −1 ωB = CB ppm × 10−6 . The molecular mass of water can be determined from elemental masses in Source 58 as MH2 O = 2 · MH + MO . The number density of water can then be computed as NH2 O =

ρH2 O · A MH2 O

.

The parameter A is Avagadro’s number = 0.60221415 · 1024 hydrogen and oxygen are given as: NH = 2 · NH2 O

at om . mol

The number density of

NO = NH2 O .

The density of borated water can be computed from the density of water and the weight percent of boron, ρH2 O ρBW = ωB To compute the number density of boron, the following expression is used: NB =

ωB · ρBW · A MB

.

The isotopic number densities of the elements can be calculated by multiplying the elemental number densities by isotopic abundances reported in Source 57.

References [27]

122

Pages 44

123

Source 54 — Composition of Carbon Steel The density of Carbon Steel was assumed to be ρzr = 7.8 g/cc. The composition, according to the ranges in an ASTM datasheet is Element/Isotope C P Mo Fe

Weight Fraction 0.00250 0.00025 0.00525 0.97050

Element/Isotope Mn Si Ni

Weight Fraction 0.01325 0.00275 0.00550

To compute the number densities of the elements/isotopes listed in the table above, the following formula can be used: ωi · ρzr · A . Ni = Mi om The parameter A is Avagadro’s number = 0.60221415 · 1024 atmol . The isotopic number densities of the elements listed in the table can be calculated by multiplying the elemental number densities by isotopic abundances reported in Source 57.

References [28]

Pages 45

124

Source 55 — Missing Data This reference box lists all of the values that were estimated: • Baffle Material is assumed to be Stainless Steel 304 • Neutron Shield Panel outer radius is assumed to be 199.39 cm • Neutron Shield Panel Material is assumed to be Stainless Steel 304 • It is assumed that the center of each shield panel is at 45 degrees and wraps 15 degrees on either side • Top/Bottom grid sleeve SS304 mass is estimated to be 80 g • Top/Bottom grid height is estimated to be 1.65 in • Intermediate grid height is estimated to be 2.25 in • Control rod gap width is estimated

Pages 10, 11, 21, 27, 28, 29, 30, 32

125

Source 56 — Isotopic Masses

Isotope

Mass [amu]

Isotope

Mass [amu]

H-1 He-4 B-11 C-13 O-17 N-14 Si-28 Si-30 Al-27 Ar-38 Cr-50 Cr-53 Mn-55 Fe-56 Fe-58 Ni-60 Ni-62 Zr-90 Zr-92 Zr-96 Mo-94 Mo-96 Mo-98 Ag-107 Cd-106 Cd-110 Cd-112 Cd-114 In-113 Sn-112 Sn-115 Sn-117 Sn-119 Sn-122 U-234 U-238

1.0078250 4.0026032542 11.0093054 13.003354838 16.9991317 14.003074005 27.976926532 29.97377017 26.9815386 37.9627324 49.946044 52.940649 54.938045 55.934937 57.933276 59.930786 61.928345 89.904704 91.905041 95.908273 93.905088 95.904679 97.905408 106.905097 105.90646 109.903002 111.902758 113.903359 112.904058 111.904818 114.903342 116.902952 118.903308 121.903439 234.040952 238.050788

H-2 B-10 C-12 O-16 O-18 N-15 Si-29 P-31 Ar-36 Ar-40 Cr-52 Cr-54 Fe-54 Fe-57 Ni-58 Ni-61 Ni-64 Zr-91 Zr-94 Mo-92 Mo-95 Mo-97 Mo-100 Ag-109 Cd-108 Cd-111 Cd-113 Cd-116 In-115 Sn-114 Sn-116 Sn-118 Sn-120 Sn-124 U-235

2.0141018 10.0129370 12.0000000 15.9949146196 17.999161 15.000108898 28.97649470 30.9737616 35.96754511 39.962383123 51.940507 53.938880 53.939611 56.935394 57.935343 60.931056 63.927966 90.905646 93.906315 91.906811 94.905842 96.906021 99.90748 108.904752 107.90418 110.904178 112.904402 115.904756 114.903878 113.902779 115.901741 117.901603 119.902195 123.905274 235.043930

126

References [29]

Pages 109, 111, 113, 116

127

Source 57 — Isotopic Natural Abundances

Isotope

Fractional Abundance

Isotope

Fractional Abundance

H-1 He-4 B-11 C-13 O-17 N-14 Si-28 Si-30 Al-27 Ar-38 Cr-50 Cr-53 Mn-55 Fe-56 Fe-58 Ni-60 Ni-62 Zr-90 Zr-92 Zr-96 Mo-94 Mo-96 Mo-98 Ag-107 Cd-106 Cd-110 Cd-112 Cd-114 In-113 Sn-112 Sn-115 Sn-117 Sn-119 Sn-122

0.99985 1.0 0.801 0.0107 0.00038 0.99636 0.92223 0.03092 1.0 0.000632 0.04345 0.09501 1.0 0.91754 0.00282 0.262231 0.036345 0.5145 0.1715 0.0280 0.0923 0.1668 0.2419 0.51839 0.0125 0.1249 0.2413 0.2873 0.0429 0.0097 0.0034 0.0768 0.0859 0.0463

H-2 B-10 C-12 O-16 O-18 N-15 Si-29 P-31 Ar-36 Ar-40 Cr-52 Cr-54 Fe-54 Fe-57 Ni-58 Ni-61 Ni-64 Zr-91 Zr-94 Mo-92 Mo-95 Mo-97 Mo-100 Ag-109 Cd-108 Cd-111 Cd-113 Cd-116 In-115 Sn-114 Sn-116 Sn-118 Sn-120 Sn-124

0.00015 0.199 0.9893 0.99757 0.00205 0.00364 0.04685 1.0 0.003365 0.996003 0.83789 0.02365 0.05845 0.02119 0.680769 0.011399 0.009256 0.1122 0.1738 0.1477 0.1590 0.0956 0.0967 0.48161 0.0089 0.1280 0.1222 0.0749 0.9571 0.0066 0.1454 0.2422 0.3258 0.0579

128

References [29]

Pages 110, 112, 114, 115, 116, 117, 119, 120, 121, 122, 124

129

Source 58 — Elemental Masses

Element H B O P Si Cr Fe Zr Ag In

Mass 1.00794 10.811 15.9994 30.973762 28.0855 51.9961 55.845 91.224 107.8682 114.818

Element

Mass [amu]

He C N Al Ar Mn Ni Mo Cd Sn

4.002602 12.0107 14.0067 26.9815386 39.948 54.938045 58.6934 95.94 112.411 118.710

References [29]

Pages 115, 117, 118, 122

130

Source 59 — Assembly Loadings

Assembly ID

Uranium [g]

U-235 [g]

Enrichment [%]

A05 A06 A07 A08 A09 A10 A11 B03 B04 B05 B06 B07 B08 B09 B10 B11 B12 B13 C02 C03 C04 C05 C06 C07 C08 C09 C10 C11 C12 C13 C14 D02 D03 D04 D05 D06 D07

424944 420716 426067 424475 425874 425803 420801 424193 422216 420894 425287 425899 423432 425449 424324 424062 422104 423343 424937 424170 421871 424615 423086 422483 424345 424595 424891 424941 421583 423048 421975 424800 424180 424406 424911 424399 424181

13162 13030 13160 13142 13192 13186 13069 13136 13097 13253 6846 13198 6792 13182 6852 13129 13159 13140 13163 13119 10124 6829 10146 6783 10192 6849 10221 6844 10130 13127 13192 13159 10156 10169 10202 6848 10210

3.0973492978 3.0971011324 3.0887160939 3.0960598386 3.0976298154 3.0967372236 3.10574357 3.0967036231 3.1019667658 3.1487738005 1.6097364838 3.0988567712 1.6040355949 3.0983737181 1.614803782 3.0960095458 3.117478157 3.1038661322 3.0976356495 3.0928637103 2.3997857165 1.6082804423 2.3980940045 1.6055083873 2.4018192744 1.6130665693 2.4055581314 1.6105765271 2.4028483122 3.102957584 3.1262515552 3.097693032 2.3942665849 2.3960547212 2.4009733803 1.6135759038 2.4069913551

131

D08 D09 D10 D11 D12 D13 D14 E01 E02 E03 E04 E05 E06 E07 E08 E09 E10 E11 E12 E13 E14 E15 F01 F02 F03 F04 F05 F06 F07 F08 F09 F10 F11 F12 F13 F14 F15 G01 G02 G03 G04 G05 G06 G07

425152 422222 424412 424304 423100 424783 424281 423404 420730 424543 421801 424255 423596 421655 423553 423530 423784 426061 420485 423910 424243 423782 421004 424776 423535 423810 423695 424865 421380 421443 423216 424117 424105 425283 421755 424904 424964 423798 425033 424241 423025 423622 424373 424759

6833 10147 6847 10181 10150 10202 13124 13084 13039 6843 10123 6837 10170 6786 10191 6836 10167 6882 10097 6809 13137 13111 13280 6817 10162 6823 10149 6872 10157 6782 10180 6837 10174 6862 10118 6840 13164 13121 13158 6834 10162 6839 10207 6831

132

1.6071898991 2.403238107 1.6132908589 2.3994588785 2.3989600567 2.4016968664 3.0932330225 3.0901928182 3.0991372139 1.6118508608 2.3999468944 1.6115308011 2.4008725295 1.6093725913 2.4060743284 1.6140533138 2.3990995413 1.6152616644 2.4012747185 1.606237173 3.0965743689 3.0938076653 3.1543643291 1.6048458482 2.3993294533 1.6099195394 2.3953551493 1.6174549563 2.4104134036 1.6092330398 2.4053911005 1.612055164 2.3989342262 1.6135138249 2.3990231295 1.6097753846 3.0976741559 3.0960504769 3.0957596234 1.6108768365 2.4022220909 1.6144109607 2.4051954295 1.6082060651

G08 G09 G10 G11 G12 G13 G14 G15 H01 H02 H03 H04 H05 H06 H07 H08 H09 H10 H11 H12 H13 H14 H15 J01 J02 J03 J04 J05 J06 J07 J08 J09 J10 J11 J12 J13 J14 J15 K01 K02 K03 K04 K05 K06

423952 421474 423211 425181 424361 424788 426234 423030 424112 423343 423810 422511 423653 424642 421497 423849 422875 424615 424072 425265 422934 424688 425788 420911 425904 424409 424468 425512 424294 423432 423016 424375 424281 424993 424165 421347 424730 421853 422860 424618 421148 424555 421432 423746

10177 6782 10156 6847 10148 6847 13199 13097 13134 6793 10136 6778 10164 6822 10187 6823 10143 6825 10157 6865 10150 6836 13194 13082 13192 6824 10163 6859 10208 6834 10153 6824 10221 6847 10176 6753 13157 13063 13118 6826 10132 6819 10140 6824

133

2.4005076046 1.6091146785 2.3997485888 1.6103729941 2.3913601863 1.6118628586 3.0966558276 3.0959979198 3.0968234806 1.6046090286 2.3916377622 1.6042185884 2.3991332529 1.6065297356 2.4168618045 1.6097714044 2.398581141 1.6073384124 2.3951121508 1.6142875619 2.3999016395 1.6096522624 3.0987251872 3.1080204604 3.0974116233 1.607882962 2.3942912069 1.6119404388 2.4058789424 1.6139545429 2.400145621 1.608011782 2.4090166658 1.6110853591 2.399066401 1.6027170005 3.0977326772 3.0965762955 3.1022087689 1.6075625621 2.4058050851 1.6061523242 2.40608212 1.6103986822

K07 K08 K09 K10 K11 K12 K13 K14 K15 L01 L02 L03 L04 L05 L06 L07 L08 L09 L10 L11 L12 L13 L14 L15 M02 M03 M04 M05 M06 M07 M08 M09 M10 M11 M12 M13 M14 N02 N03 N04 N05 N06 N07 N08

424555 424044 422699 424649 423288 424956 423244 422255 424116 422352 420794 425338 424261 424742 424150 423764 424256 425410 424950 421625 423639 424023 424050 424459 425885 424014 421257 425262 423693 423907 424198 424072 425652 422201 424551 425089 425657 421693 422588 421881 423101 424140 425284 424883

10169 6818 10153 6832 10149 6839 10138 6776 13121 13092 13073 6828 10159 6849 10166 6831 10154 6872 10200 6792 10192 6813 13133 13147 13193 10131 10112 10201 6822 10139 6854 10153 6843 10199 10155 10199 13183 13265 13124 10131 6785 10176 6870 10175

134

2.3952138121 1.6078520154 2.4019455925 1.6088581393 2.3976583319 1.6093430849 2.3953086163 1.6047175285 3.0937290741 3.0997840664 3.1067458186 1.6053115405 2.394516583 1.6125082992 2.3967935872 1.611982141 2.3933662694 1.6153828072 2.4002823862 1.610910169 2.405821938 1.6067524639 3.0970404433 3.0973545148 3.0977846132 2.3893079002 2.4004348889 2.3987565313 1.610128088 2.391798201 1.6157549069 2.3941689147 1.6076513208 2.415674051 2.3919387777 2.3992622721 3.097094609 3.1456533545 3.1056253372 2.4013880691 1.6036360113 2.3992078087 1.6153911269 2.3947769151

N09 N10 N11 N12 N13 N14 P03 P04 P05 P06 P07 P08 P09 P10 P11 P12 P13 R05 R06 R07 R08 R09 R10 R11

425421 424268 424275 424620 422582 425319 424427 425671 422784 423297 425103 423857 420685 424630 423052 423471 422419 423062 422801 426100 424656 425240 422084 421775

6872 10175 6852 10163 13101 13149 13146 13187 13107 6826 13163 6827 13284 6827 13116 13111 13108 13099 13119 13196 13155 13172 13071 13100

135

1.6153410386 2.398248277 1.6149902775 2.3934341293 3.1002267016 3.091561863 3.0973524305 3.0979324408 3.1001646231 1.6125793474 3.0964260426 1.6106847357 3.157707073 1.6077526317 3.1003280921 3.0960797788 3.1030801171 3.0962364854 3.1028781862 3.0969256043 3.0978015146 3.0975449158 3.0967769449 3.1059214036

To determine core-averaged enrichment for each enrichment type (1.6%, 2.4% and 3.1%), the Enrichment column was first separated by enrichment type. Then, all the enrichments for a given type were averaged. In order to compute densities, the total mass of Uranium is needed for each enrichment type. Both of these values are reported in the table below. Enrichment Type

Actual Core-averaged Enrichment

Total Heavy Metal [g]

1.6% 2.4% 3.1%

1.6100562050% 2.3999267408% 3.1022104528%

27570971 27104522 27115256

Core avg. enrichment Total Heavy Metal Mass

2.366789812% 81.79 MT

References [15]

Pages 3, 109, 111, 113

136