Validation of SCALE for 

High Temperature GasCooled Reactor Analysis

Office of Nuclear Regulatory Research

NUREG/CR-7107

ORNL/TM-2011/161
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Validation of SCALE for

High Temperature GasCooled Reactor Analysis

Manuscript Completed: November 2012

Date Published: July 2012

Prepared by: 

Germina Ilas

Dan Ilas

Ryan P. Kelly

Eva E. Sunny

Oak Ridge National Laboratory

Managed by UT-Battele, LLC

Oak Ridge, TN 37831-6170

Don Algama, NRC Project Manager

NRC Job Code N6842

Office of Nuclear Regulatory Research

NUREG/CR-7107

ORNL/TM-2011/161

iii

ABSTRACT

This report documents verification and validation studies carried out to assess the performance of the 

SCALE code system methods and nuclear data for modeling and analysis of High Temperature GasCooled Reactor (HTGR) configurations. Validation data were available from the International Handbook 

of Evaluated Reactor Physics Benchmark Experiments (IRPhE Handbook), prepared by the International 

Reactor Physics Experiment Evaluation Project, for two different HTGR designs: prismatic and pebble 

bed. SCALE models have been developed for HTTR, a prismatic fuel design reactor operated in Japan

and HTR-10, a pebble bed reactor operated in China. The models were based on benchmark 

specifications included in the 2009, 2010, and 2011 releases of the IRPhE Handbook. SCALE models for 

the HTR-PROTEUS pebble bed configuration at the PROTEUS critical facility in Switzerland have also 

been developed, based on benchmark specifications included in a 2009 IRPhE draft benchmark. The 

development of the SCALE models has involved a series of investigations to identify particular issues 

associated with modeling the physics of HTGRs and to understand and quantify the effect of particular 

modeling assumptions on calculation-to-experiment comparisons.

v

FOREWORD

To assess the capability of the SCALE code system to accurately model High Temperature Gas-Cooled 

Reactors (HTGRs), verification and validation studies were performed using validation data from the 

International Handbook of Evaluated Reactor Physics Benchmark Experiments (IRPhE Handbook). 

SCALE models have been developed for HTTR, a prismatic fuel design reactor operated in Japan; HTR10, a pebble bed reactor operated in China; and the HTR-PROTEUS pebble bed configuration at the 

PROTEUS critical facility in Switzerland. The development of the SCALE models has involved a series 

of investigations to identify particular issues associated with modeling the physics of HTGRs and to 

understand and quantify the effect of particular modeling assumptions on calculation-to-experiment 

comparisons.

vii

CONTENTS

Page

ABSTRACT.................................................................................................................................................iii

FOREWORD................................................................................................................................................ v

LIST OF FIGURES ..................................................................................................................................... ix

LIST OF TABLES....................................................................................................................................... xi

ACKNOWLEDGMENTS ......................................................................................................................... xiii

ACRONYMS AND ABBREVIATIONS ................................................................................................... xv

1. INTRODUCTION.................................................................................................................................. 1

2. SCALE VALIDATION FOR HTGRs—PEBBLE BED FUEL DESIGN............................................. 3

2.1 SCALE CROSS SECTIONS FOR PBR ANALYSIS................................................................... 3

2.1.1 Computational Models................................................................................................. 3

2.1.1.1 Configuration typical of HTR-10 first critical core fuel .............................. 3

2.1.1.2 Configuration typical of HTR-10 full power core fuel ................................ 4

2.1.2 Modeling Doubly Heterogeneous Fuel in SCALE....................................................... 5

2.1.3 Results.......................................................................................................................... 6

2.2 ANALYSIS OF THE HTR-10 FIRST CRITICAL CORE ......................................................... 10

2.2.1 HTR-10 Full Core SCALE Model ............................................................................. 10

2.2.1.1 Active core region...................................................................................... 12

2.2.1.2 Dummy pebbles region .............................................................................. 14

2.2.1.3 Reflector region.......................................................................................... 14

2.2.1.4 Cross-section data ...................................................................................... 16

2.2.2 Comparison with MCNP............................................................................................ 16

2.2.3 Results........................................................................................................................ 17

2.3 ANALYSIS OF THE HTR-PROTEUS BENCHMARK EXPERIMENTS ............................... 18

2.3.1 HTR-PROTEUS Experiments Overview................................................................... 18

2.3.2 Computational Models for HTR-PROTEUS Configurations..................................... 21

2.3.2.1 Modeling data ............................................................................................ 21

2.3.2.2 Modeling assumptions ............................................................................... 21

2.3.2.3 Models for Cores 1 to 3.............................................................................. 22

2.3.2.4 Models for Cores 5 to 10............................................................................ 24

2.3.3 Comparison with MCNP............................................................................................ 26

2.3.4 Results........................................................................................................................ 26

3. SCALE VALIDATION FOR HTGRs—PRISMATIC FUEL DESIGN.............................................. 29

3.1 ANALYSIS OF HTTR FUEL BLOCK ...................................................................................... 29

3.1.1 Description of the HTTR Fuel Block ......................................................................... 29

3.1.2 Computational Model for the HTTR Fuel Block ....................................................... 30

3.1.2.1 Fuel pin modeling for continuous-energy calculations.............................. 31

3.1.2.2 Fuel pin modeling for multigroup calculations.......................................... 32

3.1.3 Results for the HTTR Fuel Block............................................................................... 32

3.1.3.1 Multiplication constant .............................................................................. 32

3.1.3.2 Fission density distribution ........................................................................ 33
viii

3.2 ANALYSIS OF CONFIGURATIONS CONTAINING HTTR FUEL BLOCKS...................... 36

3.2.1 Core 1 ......................................................................................................................... 36

3.2.2 Core 2 ......................................................................................................................... 37

3.2.3 Core 3 ......................................................................................................................... 39

3.2.4 Core 4 ......................................................................................................................... 41

3.3 ANALYSIS OF HTTR FULL CORE BENCHMARK EXPERIMENTS .................................. 45

3.3.1 Description of the HTTR Core................................................................................... 45

3.3.2 Experimental Data...................................................................................................... 47

3.3.3 Computational Models for HTTR Core Configurations ............................................ 47

3.3.3.2 Overcoat material simulation ..................................................................... 50

3.3.3.3 Fuel particle modeling in the continuous energy model ............................ 50

3.3.3.4 Fuel mass conservation in the continuous energy model........................... 51

3.3.3.5 Typical runtime .......................................................................................... 52

3.3.4 Results........................................................................................................................ 52

3.3.4.1 Multiplication constant for HTTR critical configurations......................... 52

3.3.4.2 Multiplication constant for HTTR subcritical configurations.................... 55

3.3.4.3 Excess reactivity ........................................................................................ 55

3.3.4.4 Shutdown margin ....................................................................................... 58

3.3.4.5 Control rod worths..................................................................................... 59

3.3.4.6 Isothermal reactivity coefficients............................................................... 61

3.3.4.7 Flux and reaction rates distributions.......................................................... 62

4. SUMMARY ......................................................................................................................................... 69

5. REFERENCES..................................................................................................................................... 71

APPENDIX A. SCALE CONTINUOUS ENERGY MODEL FOR HTTR............................................A-1

APPENDIX B. SCALE MULTIGROUP MODEL FOR HTTR............................................................. B-1

APPENDIX C. SCALE MULTIGROUP MODEL FOR HTR-10 .......................................................... C-1
ix

LIST OF FIGURES

Page

Fig. 2.1. SCALE/KENO-VI model of hexagonal fuel cell...................................................................... 4

Fig. 2.2. MCNP model of hexagonal fuel cell—cross section at half height. ........................................ 4

Fig. 2.3. Pebble unit cell models.............................................................................................................. 5

Fig. 2.4. Double-heterogeneity model for cross-section processing in SCALE...................................... 6

Fig. 2.5. SCALE/KENO-VI model for HTR-10 first core. ................................................................... 12

Fig. 2.6. Modeling of active core region................................................................................................ 13

Fig. 2.7. Modeling of pebbles in active core region and dummy pebbles region.................................. 14

Fig. 2.8. Comparison of Simplified and High-Fidelity models—radial view........................................ 15

Fig. 2.9. High-Fidelity model—channels in reflector region................................................................. 15

Fig. 2.10. HTR-PROTEUS illustration—SCALE/KENO-VI model. ..................................................... 19

Fig. 2.11. Core modeling for HCP pebble arrangements......................................................................... 23

Fig. 2.12. Pebble modeling for Core 3..................................................................................................... 24

Fig. 2.13. Core modeling for CHPOP arrangements. .............................................................................. 25

Fig. 2.14. Pebble modeling for Core 9 state 2. ........................................................................................ 25

Fig. 3.1. (a) Cross-sectional and (b) vertical views of the HTTR fuel block......................................... 31

Fig. 3.2. Three-dimensional pin fission density distribution in the HTTR fuel block with 

SCALE/KENO MG................................................................................................................. 34

Fig. 3.3. Pin fission density distribution in the HTTR fuel block with three models. ........................... 34

Fig. 3.4. Axial fission density distribution in pin 12 of the HTTR fuel block....................................... 35

Fig. 3.5. Horizontal layout of Core 1..................................................................................................... 36

Fig. 3.6. Horizontal layout of Core 2 showing the radial tally regions.................................................. 37

Fig. 3.7. Flux distribution (23-group) in radial regions of Core 2......................................................... 39

Fig. 3.8. Horizontal layout of Core 3 with (a) “rotated” and (b) “not rotated” configurations.............. 40

Fig. 3.9. Detail of Core 3 for (a) “rotated” and (b) “not rotated” setups. .............................................. 41

Fig. 3.10. Horizontal layout of Core 4 (with control rods in).................................................................. 42

Fig. 3.11. Flux distribution (23-group) in radial regions of Core 4 (control rods out). ........................... 43

Fig. 3.12. Flux distribution (23-group) in radial regions of Core 4 (control rods in). ............................. 44

Fig. 3.13. Fully loaded HTTR core configuration. .................................................................................. 46

Fig. 3.14. Partially loaded HTTR core configurations. ........................................................................... 49

Fig. 3.15. Variation of the multiplication constant with the fuel particle lattice positioning. ................. 51

Fig. 3.16. Variation of the multiplication constant with the core fuel mass. ........................................... 52

Fig. 3.17. Variation of keff bias vs. number of fuel columns (critical core)............................................. 54
x

Fig. 3.18. Difference in keff calculated with the SCALE MG and CE models. ....................................... 54

Fig. 3.19. Control rod worth for the FS pattern. ...................................................................................... 60

Fig. 3.20. Control rod worth for the FS pattern at 300 K and 600 K....................................................... 61

Fig. 3.21. Isothermal reactivity coefficients. ........................................................................................... 62

Fig. 3.22. Multigroup and continuous energy flux distributions in the three channels and 

experimental points for 235U(n,f) reaction rate. ....................................................................... 63

Fig. 3.23. Multigroup and continuous energy flux distributions in the three channels and shifted 

experimental points for 235U(n,f) reaction rate. ....................................................................... 64

Fig. 3.24. Multigroup flux and 235U(n,f) reaction rate computed distributions in channel 1 and the 

experimental point for 235U(n,f) reaction rate.......................................................................... 65

Fig. 3.25. Flux and 235U(n,f) reaction rate computed distributions in channel 1 and the 

experimental points for 235U(n,f) reaction rate for critical configuration 3............................. 66

Fig. 3.26. Flux and 235U(n,f) reaction rate computed distributions in channel 1 and the 

experimental points for 235U(n,f) reaction rate for critical configuration 4............................. 67
xi

LIST OF TABLES

Page

Table 2.1. Comparison of kinf values for a hexagonal prism fuel cell ........................................................ 6

Table 2.2. Spectral indices for single fuel pebble cell (at 300 K)............................................................... 7

Table 2.3. 235U cross sections for single fuel pebble cell (at 300 K)........................................................... 7

Table 2.4. 238U cross sections for single fuel pebble cell (at 300 K)........................................................... 7

Table 2.5. Group contributions to reaction rates in U—single fuel pebble cell (at 300 K) ........................ 8

Table 2.6. Spectral indices for single fuel pebble cell (operating temperatures)........................................ 8

Table 2.7. 235U cross sections for single fuel pebble cell (operating temperatures).................................... 9

Table 2.8. 238U cross sections for single fuel pebble cell (operating temperatures).................................... 9

Table 2.9. HTR-10 design features........................................................................................................... 10

Table 2.10. Fuel particle data for HTR-10 fuel........................................................................................... 11

Table 2.11. Material data for pebbles and reflector in HTR-10.................................................................. 11

Table 2.12. Number of fuel and moderator pebbles in the active core region............................................ 13

Table 2.13. Volume verification for the active core region ........................................................................ 13

Table 2.14. Volume verification for the reflector region............................................................................ 16

Table 2.15. Sensitivity of keff to the boron isotopic composition ............................................................... 16

Table 2.16. Sensitivity of keff to the cross-section data .............................................................................. 17

Table 2.17. keff results for simplified benchmark model ............................................................................ 17

Table 2.18. keff results for high-fidelity benchmark model......................................................................... 17

Table 2.19. HTR-PROTEUS configurations .............................................................................................. 20

Table 2.20. Fuel particle data for HTR-PROTEUS fuel............................................................................. 21

Table 2.21. Material data for pebbles and reflector in HTR-PROTEUS .................................................... 21

Table 2.22. keff results for PROTEUS cores with HCP pebble arrangements............................................ 26

Table 2.23. keff results for PROTEUS cores with CHPOP pebble arrangements....................................... 27

Table 2.24. Comparison of SCALE-calculated keff

pebble arrangements................................................................................................................

to benchmark data for PROTEUS cores with HCP 

27

Table 2.25. Comparison of SCALE-calculated Keff

CHPOP pebble arrangements..................................................................................................

to benchmark data for PROTEUS cores with

27

Table 3.1. Fuel block main characteristics.................................................................................................. 29

Table 3.2. Fuel particle data for HTTR....................................................................................................... 30

Table 3.3. Material data for 6.3 wt % enriched HTTR fuel block .............................................................. 30

Table 3.4. Multiplication constants for different models of the HTTR fuel block ..................................... 33

Table 3.5. Multiplication constants for Core 1 ........................................................................................... 37
xii

Table 3.6. Multiplication constants for Core 2 ........................................................................................... 37

Table 3.7. Flux spectrum in 23-group structure for Core 2 ........................................................................ 38

Table 3.8. Multiplication constants for Core 3 ........................................................................................... 40

Table 3.9. Multiplication constants for Core 4 ........................................................................................... 42

Table 3.10. Control rods reactivity for Core 4............................................................................................ 42

Table 3.11. Flux spectrum (23-group) for radial regions of Core 4 (control rods out)............................... 43

Table 3.12. Flux spectrum (23-group) for radial regions of Core 4 (control rods in)................................. 44

Table 3.13. Main characteristics of the HTTR core.................................................................................... 47

Table 3.14. Control rod positions for the six HTTR critical core configurations....................................... 48

Table 3.15. Calculated and experimental keff for HTTR critical core configurations................................. 53

Table 3.16. Multiplication constants for subcritical configurations during the approach to criticality ..... 55

Table 3.17. Multiplication constants for full core subcritical configuration............................................... 55

Table 3.18. Excess reactivity for different fuel loadings............................................................................ 56

Table 3.19. Incremental excess reactivity for different fuel loadings......................................................... 58

Table 3.20. Shutdown reactivities for full core configuration .................................................................... 59

Table 3.21. Isothermal reactivity coefficients............................................................................................. 61
xiii

ACKNOWLEDGMENTS

This work was performed under contract with the U.S. Nuclear Regulatory Commission (NRC) under 

Project N6842, Identification and Evaluation of HTGR Reactor Physics Issues. The authors would like to 

thank Mourad Aissa and Don Algama of the NRC Office of Nuclear Regulatory Research and Steve 

Bowman of Oak Ridge National Laboratory (ORNL) for continued support and guidance. Thanks are 

extended to Brian Ade and Matthew Jessee at ORNL for their review of the manuscript and to Angie 

Alford at ORNL for the formatting of this document.

xv

ACRONYMS AND ABBREVIATIONS

1-D one dimensional

2-D two dimensional

3-D three dimensional

ANL Argonne National Laboratory

BOC beginning of cycle

BP burnable poison

C/E calculated to experimental 

CE continuous energy

DOE U.S. Department of Energy

EBC equivalent boron content

EFPD effective full power days

EOC end of cycle

FS flat standard

HTGR high temperature gas-cooled reactor

HTR high temperature reactor

HTTR High Temperature Engineering Test Reactor

IAEA International Atomic Energy Agency

IRPhE International Reactor Physics Benchmark Experiments

JAERI Japanese Atomic Energy Research Institute

keff

k

effective multiplication factor

inf

LWR light water reactor

infinite medium multiplication factor

MG multigroup

MTU metric ton uranium (106

NRC U.S. Nuclear Regulatory Commission

grams)

ORNL Oak Ridge National Laboratory

PBR pebble bed reactor

ppm parts per million

PSI Paul Scherrer Institute

PWR pressurized water reactor

SCALE Standardized Computer Analyses for Licensing Evaluations

TRISO tristructural isotropic

UO2 uranium dioxide

1

1. INTRODUCTION

The development of advanced methods and computational tools for the analysis of High Temperature 

Gas-Cooled Reactor (HTGR) configurations has been a research area of renewed interest for the 

international community. HTGR configurations are potential candidates for future deployment throughout 

the world—a type of reactor system that would meet the increased requirements of efficiency, safety, and 

proliferation resistance and would support other applications such as process heat applications, hydrogen 

production, or nuclear waste recycling. Only two HTGRs are now operating: the High Temperature 

Engineering Test Reactor (HTTR) in Japan and the High Temperature Reactor–10 (HTR-10) in China. 

HTTR has a prismatic fuel assembly design, whereas HTR-10 is a Pebble Bed Reactor (PBR). In the 

United States, both the prismatic and the pebble bed designs are being considered for future deployment 

by the Next Generation Nuclear Plant (NGNP) Program [1].

The primary challenge in the design and analysis of HTGR configurations is the modeling of the fuel,

which has characteristics very different from those of conventional light water reactor (LWR) fuel. HTGR 

fuel is composed of a large number of tiny tristructural-isotropic (TRISO) fuel particles embedded in a 

graphite matrix and shaped into spherical or cylindrical fuel elements. Each fuel particle has a spherical 

fuel kernel with a radius of approximately 0.025 cm that is covered by carbon-based layers for a total

radius of approximately 0.045 cm. The inherent double heterogeneity of such a fuel makes it more 

difficult to model and requires methods different from those used for a typical LWR fuel. The first level 

of heterogeneity concerns the random distribution of the large number of fuel particles inside the 

cylindrical or spherical fuel element. The second level of heterogeneity refers to the distribution of the 

fuel pebbles inside the reactor core for a PBR or of the fuel elements in fuel assemblies placed in the core 

for a prismatic HTGR. The movement of the fuel pebbles during the reactor operation of a PBR adds 

another level of complexity.

Recent improvements in the SCALE [2] code system, developed and maintained by Oak Ridge National

Laboratory (ORNL), have focused on addressing the particular needs for the design and analysis of

HTGR configurations. As discussed in a later section, improved physics approximations and numerical

techniques for performing resonance self-shielding of the cross sections and for treating doubly 

heterogeneous systems [3] were introduced in the 5.1 release of SCALE. Later, this cross-section 

processing methodology was folded into the 6.0 version of the SCALE/TRITON depletion sequence [4] 

to permit burnup simulation of doubly heterogeneous fuels [5]. In addition to the development work, there 

has been an ongoing effort to qualify and validate the SCALE models, methodologies, and associated 

nuclear data for use with doubly heterogeneous configurations. 

This report documents verification and validation studies carried out to assess the performance of the 

SCALE methods and data for analysis of HTGR configurations. The experimental data used for 

validation was acquired from the International Handbook of Evaluated Reactor Physics Benchmark 

Experiments (IRPhE Handbook) prepared by the International Reactor Physics Experiment Evaluation 

Project for both the prismatic and the pebble bed designs. SCALE models have been developed for HTTR

and the HTR-10 based on benchmark specifications and experimental data included in the 2009, 2010, 

and 2011 editions of the IRPhE Handbook [6,7,8,9,10]. SCALE models for the HTR-PROTEUS pebble 

bed configuration at the PROTEUS critical facility in Switzerland have been developed based on 

benchmark specifications included in a 2009 IRPhE draft benchmark; this draft benchmark has yet to be

included as a final version in the IRPhE Handbook released by the time of the publication of the present 

report. The development of the SCALE models has involved a series of investigations to identify the 

particular issues associated with modeling the physics of the HTGRs and to understand and quantify the 

effect of particular modeling assumptions on calculation-to-experiment comparisons.
2

As described in the HTGR NRC Research Plan (ML110310182) [12], the assessed SCALE code modules 

employ key elements of the SCALE/TRITON lattice physics sequence recently adapted by ORNL to 

enable the PARCS [13], AGREE [14], and MELCOR [15] codes to simulate thermally coupled HTGR 

core physics (i.e., computed core maps of neutron flux, fission power, decay power, fuel burnup, nuclide 

inventories, etc.) during normal power operations, transients, and accidents. The initial benchmark 

validation studies described in this report have been performed against measured data from clean, zeropower, room-temperature critical configurations in HTTR, HTR-10, and HTR-PROTEUS. The report 

thus documents an early step in a code assessment process intended to eventually include benchmarking 

of the NRC's HTGR core simulation code suite (i.e., PARCS-AGREE with SCALE/TRITON lattice 

physics) against startup data, power operating data, and transient test data from existing HTGR tests such 

as for HTTR and HTR-10.
3

2. SCALE VALIDATION FOR HTGRs—PEBBLE BED FUEL DESIGN

This section summarizes the verification and validation studies performed to evaluate the SCALE 

performance for analysis of PBR configurations. Studies to assess the accuracy of SCALE cross sections 

used in the analysis of the PBRs are discussed. Reactor models for validation against experimental data 

for the HTR-10 first critical core are presented in detail. Analysis of PBR configurations from the 

experimental program carried out at the PROTEUS critical facility at the Paul Scherrer Institute (PSI) is 

also included. 

2.1 SCALE CROSS SECTIONS FOR PBR ANALYSIS

As a first step, investigations were carried out on simple models to assess the capabilities of SCALE to 

provide accurate cross sections for analyses of PBR configurations [16]. Establishing the accuracy of the 

cross sections are fundamental for understanding the accuracy of the calculations at the reactor core level. 

Different configurations representative of HTR-10 fuel were analyzed and two operating conditions were

considered—one corresponding to the initial critical core and the other to the full power operating core of 

the HTR-10. 

2.1.1 Computational Models

2.1.1.1 Configuration typical of HTR-10 first critical core fuel

The configuration typical of HTR-10 first critical core fuel was modeled as a hexagonal prism containing 

a mixture of fuel and moderator pebbles in a 53:47 ratio, characteristic of the first critical core, with 

saturated air surrounding the fuel and moderator pebbles. The material composition and geometry data are 

based on the benchmark specifications for the HTR-10 initial core as included in the IRPhE Handbook 

[10]. The fuel pebble has an inner region of 2.5 cm radius and a graphite shell of 0.5 cm thickness. The 

pebble inner region contains 8,335 fuel particles embedded in a graphite matrix. The packing fraction of 

the fuel and moderator pebbles in the reactor core is 61%. Each fuel particle has a 0.025 cm radius kernel 

that contains uranium dioxide (UO2) and is surrounded by four carbon-based layers, for a total outer 

radius of 0.0455 cm.

The configuration was modeled with both the Monte Carlo transport code MCNP5 [17] using continuous 

energy cross sections and with the SCALE/KENO-VI Monte Carlo transport code using 238-group crosssection libraries. In both cases, the libraries were based on ENDF/B-VII data at 300 K. The 

SCALE/KENO-VI model of the hexagonal fuel cell is illustrated in Fig. 2.1, which shows the whole cell, 

the cell at half height, and the arrangement of the pebbles in three layers inside the hexagonal prism. The

SCALE/KENO-VI model served as a building block to represent the fuel zone in the three-dimensional 

(3-D) model of the HTR-10, as discussed later in this report. The MCNP model of the hexagonal fuel cell 

is similar to the model used by Seker and Colak [18]. A cross-sectional view of the MCNP5 model at half 

height of the cell is illustrated in Fig. 2.2. The MCNP5 model explicitly represents the fuel particles 

inside the fuel pebbles using a lattice representation that ensures the fuel particles do not intersect the 

interface of the graphite matrix with the pebble shell. The fuel particles are not explicitly modeled with 

SCALE/KENO-VI. However, the doubly heterogeneous nature of the fuel is accounted for through the 

method of calculating the cross sections of the fuel zone inside the pebble, as discussed later in this report.
4

 (a) hexagonal fuel cell (b) half of fuel cell (c) pebbles’ arrangement 

Fig. 2.1. SCALE/KENO-VI model of hexagonal fuel cell.

Fig. 2.2. MCNP model of hexagonal fuel cell—cross section at half height.

2.1.1.2 Configuration typical of HTR-10 full power core fuel 

At nominal power operating condition, the fuel core includes only fuel pebbles. A configuration 

consisting of a unit cell with a single fuel pebble surrounded by coolant was considered for this condition. 

This configuration was analyzed with MCNP5 and SCALE for a fresh fuel composition at operating 

temperature. To assess the temperature dependence of the results, the same unit cell was also studied at a 

temperature of 300 K.

The model for the configuration typical of HTR-10 full power core fuel consists of a spherical cell that 

includes a single fuel pebble surrounded by helium coolant. The radius of the spherical cell, 3.53735 cm, 

was calculated to correspond to the 61% packing fraction of the fuel pebbles in the core, knowing that 

there are 27,000 fuel pebbles and no moderator pebbles [19] in the full power core. The geometry and 

material data for the fuel pebble were the same as those used for the HTR-10 first critical core [10]. 

However, in this case the saturated air coolant was replaced by helium at 861.05 K temperature [19]; the 

helium atomic density was calculated based on temperature and pressure (3 MPa) values [20]. 

The single pebble unit cell models are illustrated in Fig. 2.3. In the MCNP5 model, the fuel particles were 

modeled as used in Ref. 18, in a lattice structure that avoids the intersection of the particles with the 

pebble shell inner surface. The SCALE model accounts for double heterogeneity of the fuel through the 

method of processing the cross sections for the fuel zone. The cross sections for fuel pebble materials are 

considered at 1200 K, and the cross sections for the coolant at 900 K, to facilitate a comparison of the 

results obtained with the two codes. These two temperatures were selected to be close to the actual 

operating temperatures reported in literature and to be consistent with the temperatures for which crosssection data are available with MCNP5.
5

 MCNP5 model SCALE model

Fig. 2.3. Pebble unit cell models.

2.1.2 Modeling Doubly Heterogeneous Fuel in SCALE

Double heterogeneity of fuel can be modeled in SCALE using the DOUBLEHET option for cross-section 

processing, which combines the treatment of the first level of heterogeneity (fuel particles in the fuel 

compact—either sphere or cylinder) with the treatment of the second level of heterogeneity (pebbles 

inside the core for a PBR or cylindrical fuel compacts inside a prismatic fuel assembly for a prismatic 

HTGR). Though the fuel particles inside the fuel pebble are not explicitly modeled in the pebble unit cell 

shown in Fig. 2.3, the doubly heterogeneous nature of the fuel is accounted for through the method of 

calculating the cross sections for the fuel zone inside the pebble, which is illustrated in Fig. 2.4.

Problem-dependent multigroup cross sections for transport calculations are determined in SCALE using 

the CENTRM/PMC cross-section processing methodology. For fuels with no double heterogeneity, the 

CENTRM code solves the one-dimensional (1-D) neutron transport equation for a simple building block 

(such as a fuel pin in an LWR assembly) using pointwise cross sections and calculates the flux solution 

on a fine grid (about 50,000 to 70,000 points). This flux is used by the PMC code to weight pointwise 

cross sections for obtaining self-shielded multigroup cross sections for transport calculations with the 

XSDRNPM 1-D, NEWT two-dimensional (2-D), or KENO 3-D transport codes available in SCALE. For 

doubly heterogeneous fuel, the DOUBLEHET option sequentially applies the CENTRM/PMC 

methodology to the two levels of heterogeneity of such a fuel. On the first level of heterogeneity, the fuel 

particles inside the pebble (see Fig. 2.4), pointwise flux disadvantage factors are calculated and used to 

generate zone-weighted pointwise cross sections for the homogenized fuel region inside the pebble 

(radius 2.5 cm). These pointwise cross sections are used on the second level of heterogeneity calculations, 

the pebble in a lattice of pebbles, to determine with CENTRM the flux distribution, which is used then by 

PMC to determine multigroup problem-dependent cross-section data for the fuel element (i.e., pebble or 

cylinder). 

fuel zone

pebble shell

coolant
6

Fig. 2.4. Double-heterogeneity model for cross-section processing in SCALE.

2.1.3 Results

Relevant parameters for the configurations presented in Section 2.1.1 were calculated with SCALE and 

compared to corresponding data calculated with MCNP5. The values of the infinite medium 

multiplication factor (kinf) for the hexagonal prism fuel cell models illustrated in Figs. 2.1 and 2.2, as 

calculated with SCALE/KENO-VI and MCNP5, are presented in Table 2.1. As seen, the SCALE/KENOVI kinf value is within 2 mk (or 0.1%) of the MCNP5 value.

Table 2.1. Comparison of kinf

Code

values for a hexagonal prism fuel cell

Cross-section data kinf σ Difference (mk a b

MCNP5

)

CEc ENDF/B-VII 1.74949 0.00028

SCALE/KENO-VI 238-group ENDF/B-VII 1.75138 0.00017 1.9 ± 0.3 a Standard deviation. b 1 mk = 10-3

. cContinuous energy data.

The following spectral indices were calculated for the pebble unit cells illustrated in Fig. 2.3: fast-tothermal 238U capture ratio (ρ28), fast-to-thermal 235U fission ratio (δ25), ratio of 238U fissions to 235U 

fissions (δ28), and 238U capture to 235

ρ28 = ∫ dV ∫ dEΣa

238

E>0.625eV (E)Φ(E) cell

∫ dV ∫ dEΣa

238

E<0.625eV (E)Φ(E) cell

δ25 = ∫ dV ∫ dEΣf

235

E>0.625eV (E)Φ(E) cell

∫ dV ∫ dEΣf

235

E<0.625eV (E)Φ(E) cell

U fission ratio (C*). The spectral indices were calculated as follows:

δ28 = ∫ dV ∫ dEΣf

238(E)Φ(E) cell

∫ dV ∫ dEΣf

235(E)Φ(E) cell

C∗ = ∫ dV ∫ dEΣa

238(E)Φ(E) cell

∫ dV ∫ dEΣf

235(E)Φ(E) cell

where E is neutron energy, V is volume of the configuration considered, Φ is neutron flux, Σa is 

macroscopic absorption cross section, and Σf is macroscopic fission cross section. The cross sections 

from the unit cell calculation were collapsed to a two-group structure to determine the spectral indices, 

with the group boundary between thermal and fast at 0.625 eV. 

A comparison of the spectral indices and kinf for the pebble cell unit models for the case where all cross 

sections were considered at 300 K is presented in Table 2.2. The SCALE values shown in this table were 

obtained using a 1-D spherical geometry transport calculation for the flux and eigenvalue solution in the 

pebble unit cell; however, the multigroup cross sections in the 1-D transport calculation accounted for the 

fuel particle

pebble core

pebble shell

fuel pebble pebble cell

coolant
7

double heterogeneity of the fuel as the DOUBLEHET option was used for cross-section self-shielding. 

Compared with the 3-D detailed MCNP model, the 1-D SCALE model performs remarkably well and, 

inherent to the approach used for neutron transport, is very fast, requiring about 2 minutes to complete on 

a single processor vs. the 9 hours required to run MCNP in parallel on 10 processors. The differences of 

the spectral indices calculated with SCALE compared to the MCNP values as a reference are less than 2%

in this case. 

Table 2.2. Spectral indices for single fuel pebble cell (at 300 K)

Parameter Significance MCNP5 SCALE a Diff b

ρ

(%)

28 Fast-to-thermal 238U capture ratio 8.028 (0.004) 8.159 1.6

δ25 × 10 Fast-to-thermal 2 235U fission ratio 11.081 (0.004) 11.048 -0.3

δ28 × 104 238U fission to 235U fission ratio 14.117 (0.005) 13.890 -1.6

C* 238U capture to 235U fission ratio 0.196 (0.0001) 0.199 1.5

k Multiplication constant inf 1.6596 (0.0001) 1.6553 -0.3 a Value in parentheses represents the standard deviation. bCalculated as 100*(valueSCALE - valueMCNP)/valueMCNP.

The pebble unit cell total, fission, and absorption microscopic cross sections for 235U and 238U in a fourgroup structure are shown in Tables 2.3 and 2.4. The four-group structure is the same as used in the 

VSOP code [21]. The 235U cross sections are estimated by SCALE within 1% of the corresponding 

MCNP reference values, except for the cross sections in group 3. The fission cross section in group 3 is 

underestimated by about 1.7%; note, however, that this group contributes only 4% to the total number of 

fissions in the system. The largest difference for 238U absorption cross sections is seen for group 2, of 

2.2%; note that the absorption in this group accounts for about 34% of total absorptions in 238U.

Table 2.3. 235

Group

U cross sections for single fuel pebble cell (at 300 K)

Upper

energy

(eV)

Total cross section (b) Fission cross section (b) Absorption cross section (b)

MCN

P

σa

(%)

MCN

P

SCAL

E

Diff

(%)

b MCN

P

σ

(%)

MCNP SCAL

E

Diff

(%)

MCN

P

σ

(%)

MCNP SCAL

E

Diff

(%)

1 2×10 8.86 7 0.01 8.80 -0.7 1.31 0.01 1.30 -1.0 1.49 0.01 1.47 -0.8

2 1×10 29.39 5 0.01 29.36 -0.1 11.81 0.02 11.81 0.0 17.79 0.02 17.78 0.0

3 29.0 73.39 0.02 72.38 -1.4 35.41 0.03 34.81 -1.7 61.91 0.03 60.95 -1.5

4 1.87 342.80 0.03 341.22 -0.5 280.27 0.03 278.98 -0.5 328.62 0.03 327.13 -0.5 a Standard deviation bCalculated as 100*(valueSCALE – valueMCNP)/valueMCNP

Table 2.4. 238

Group

U cross sections for single fuel pebble cell (at 300 K)

Upper

energy

(eV)

Total cross section (b) Fission cross section (b) Absorption cross section (b)

MCN

P

σa

(%)

MCN

P

SCAL

E

Diff

(%)

b MCN

P

σ

(%)

MCNP SCAL

E

Diff

(%)

MCN

P

σ

(%)

MCNP SCAL

E

Diff

(%)

1 2×10 9.04 7 0.01 9.05 0.1 1.5E-1 0.03 1.5E-1 -3.2 0.26 0.02 0.25 -2.2

2 1×10 23.64 5 0.03 23.98 1.4 2.5E-4 0.28 2.5E-4 0.5 3.96 0.06 4.05 2.2

3 29.0 33.78 0.06 33.89 0.3 2.4E-5 0.10 2.4E-5 1.3 21.29 0.08 21.37 0.4

4 1.87 10.46 0.03 10.40 -0.6 8.9E-6 0.03 8.9E-6 -0.5 1.43 0.03 1.43 -0.5 a Standard deviation. bCalculated as 100*(valueSCALE – valueMCNP)/valueMCNP.

For assessing the effect of accuracy in the multigroup cross-section data on the system behavior, the 

contributions of particular groups to the system capture, fission, etc. are listed in Table 2.5. This

information was estimated with the MCNP model illustrated in Fig. 2.2. It facilitates estimating the effect 

of uncertainty in the cross section for a particular energy group and nuclide on the uncertainty in the 

reaction rates for the analyzed system. For example, as the largest contribution to the fission rate in the 

system is due to thermal neutrons (group 4) fission in 235U (as expected, as this is a thermal system), it is 
8

desirable to estimate the fission cross section in this group as accurately as possible. Regarding the 

contribution of 238U to the total capture in the system, it is seen that the largest contribution is due to 

neutrons in the intermediate energy range (groups 2 and 3). 

Table 2.5. Group contributions to reaction rates in U—single fuel pebble cell (at 300 K)

Group Upper

energy (eV)

Total reaction rate in U Fission rate in U Capture rate in U a

235U (%) 238U (%) 235U (%) 235U (%) 238

1

U (%)

2 x 10 1.1 7 1.2 0.3 0.1 0.1

2 1 x 10 6.9 5 5.5 4.1 8.4 5.6

3 29.0 5.0 2.3 3.6 10.9 8.7

4 1.87 75.6 2.3 92.0 64.2 1.9

total 88.7 11.3 100.0 83.7 16.3 a Fission rate in 238U contributes less than 0.1% to the fission rate in U.

A comparison of the results obtained with SCALE and MCNP5 for the single pebble unit cell at operating 

temperatures is shown in Table 2.6 for spectral indices and in Tables 2.7 and 2.8 for the unit cell cross 

sections of 235U and 238U, respectively. The differences observed for kinf and spectral indices in this case 

are consistent with those seen for the same configuration at 300 K. The differences in spectral indices are 

practically the same at the two temperature conditions, with the exception of δ28, for which the difference 

is 1.6% larger at operating temperature compared to 300 K. This latter difference is mainly due to the 

increased underestimation of the 238U fission cross section in the fast energy range at operating 

temperature compared to 300 K; note that this increased underestimation does not significantly impact the 

total fission in the system, as the 238U contribution to the total fission rate in the system is less than 0.1%.

Table 2.6. Spectral indices for single fuel pebble cell (operating temperatures)

Parameter Significance MCNP5 SCALE a Diff b

ρ

(%)

Fast-to-thermal 28 238U capture ratio 10.218 (0.006) 10.414 1.9

δ25 × 10 Fast-to-thermal 2 235U fission ratio 12.319 (0.004) 12.279 -0.3

δ28 × 104 238U fission to 235U fission ratio 14.519 (0.005) 14.058 -3.2

C* 238U capture to 235U fission ratio 0.254 (0.0001) 0.258 1.7

k Multiplication constant inf 1.6081 (0.0002) 1.6034 -0.3 a Value in parentheses represents the standard deviation. bCalculated as 100*(valueSCALE – valueMCNP)/valueMCNP.

With respect to the comparison of cross sections at 300K (Tables 2.3 and 2.4) and at operating 

temperatures (Tables 2.7 and 2.8), the only cases for which the absolute difference between the SCALE 

and the MCNP values changes by more than 0.5% are 235U fission in group 1 and 238U fission in group 1 

and absorption in groups 1 and 3. As the contribution of 235U fission or 238U absorption in group 1 to the

total fission or absorption rate in the system is negligible, a slightly increased underestimation or 

overestimation of the corresponding cross sections would not have significant effect on the system 

properties. In the case of the 238U absorption cross section in group 3, given that the absorption rate in this 

group contributes approximately 9% to the total absorption rate in the system, an increased 

overestimation of this cross section would have some effect on the system behavior. However, the 

magnitude of the overestimation (SCALE vs. MCNP) is not large (1.2%). 
9

Table 2.7. 235

Group

U cross sections for single fuel pebble cell (operating temperatures)

Upper

energy

(eV)

Total cross-section (b) Fission cross-section (b) Absorption cross-section (b)

MCN

P

σa

(%)

MCN

P

SCAL

E

Diff

(%)

b MCN

P

σ

(%)

MCNP SCAL

E

Diff

(%)

MCN

P

σ

(%)

MCNP SCAL

E

Diff

(%)

1 2×10 8.87 7 0.01 8.71 -1.8 1.31 0.01 1.29 -2.1 1.49 0.01 1.46 -1.9

2 1×10 29.39 5 0.01 29.34 -0.2 11.81 0.02 11.79 -0.2 17.79 0.02 17.75 -0.2

3 29.0 73.26 0.02 72.24 -1.4 35.50 0.03 34.86 -1.8 61.81 0.03 60.79 -1.6

4 1.87 242.09 0.04 244.08 -0.8 192.47 0.04 194.20 0.9 228.00 0.04 229.97 0.9 a Standard deviation. bCalculated as 100*(valueSCALE – valueMCNP)/valueMCNP.

Table 2.8. 238

Group

U cross sections for single fuel pebble cell (operating temperatures)

Upper

energy

(eV)

Total cross-section (b) Fission cross-section (b) Absorption cross-section (b)

MCN

P

σa

(%)

MCN

P

SCAL

E

Diff

(%)

b MCN

P

σ

(%)

MCNP SCAL

E

Diff

(%)

MCN

P

σ

(%)

MCNP SCAL

E

Diff

(%)

1 2×10 9.04 7 0.01 8.95 -1.0 1.5E-1 0.03 1.4E-1 -5.2 0.26 0.02 0.25 -3.8

2 1×10 26.46 5 0.03 26.78 1.2 2.6E-4 0.20 2.6E-4 -0.3 4.95 0.06 5.03 1.8

3 29.0 42.26 0.06 42.69 1.0 3.2E-5 0.08 3.3E-5 1.8 28.27 0.07 28.61 1.2

4 1.87 10.13 0.03 10.16 0.3 6.4E-6 0.04 6.5E-6 0.8 1.04 0.03 1.06 0.8 a Standard deviation. bCalculated as 100*(valueSCALE - valueMCNP)/valueMCNP.
10

2.2 ANALYSIS OF THE HTR-10 FIRST CRITICAL CORE

The HTR-10 reactor is a test reactor intended to serve in the development of the technology for 

construction of PBRs in China. It is a small reactor, with a diameter and height of the cylindrical core of 

180 and 197 cm, respectively. HTR-10 is helium cooled, graphite moderated, and operated at 10 MW 

thermal power. The reactor main design features [10] are listed in Table 2.9. 

Table 2.9. HTR-10 design features

Parameter Value

Thermal power (MW) 10

Core diameter (cm) 180

Core height (cm) 197

Primary coolant pressure (MPa) 3

Coolant inlet temperature (°C) 250

Coolant outlet temperature (°C) 700

Fuel type UO

Number of fuel elements in equilibrium core

2

27,000

Heavy metal loading per fuel element (g) 5

Initial fuel enrichment (wt % 235U) 17

Number of control rods in side reflector 10

Number of absorber ball units in side reflector 7

Fuel loading mode multipass

The first core of HTR-10 reached criticality in 2000. A set of benchmark specifications for the HTR-10 

initial critical core experiment was released before the actual experiment took place, for a benchmark 

exercise coordinated by the International Atomic Energy Agency (IAEA). The actual configuration for 

the first criticality was different than the pre-experiment specifications, leading to a new set of benchmark

specifications that was provided later. Both the initial and an updated set of benchmark specifications,

along with results obtained with different codes by the participants to the IAEA benchmark exercise, were

presented in IAEA TECDOC-1382 [22]. The post-experiment benchmark specifications were included 

and presented in detail in the 2009 release of the IRPhE Handbook [10].

2.2.1 HTR-10 Full Core SCALE Model

A full 3-D model for the HTR-10 reactor has been developed using the SCALE/KENO-VI Monte Carlo 

transport code [23]. The core configuration is based on the IRPhE benchmark description [10] used for 

the evaluation of the initial critical configuration of the HTR-10. A vertical cutaway view of the

SCALE/KENO-VI model for HTR-10 is illustrated in Fig. 2.5. The reactor has a cylindrical active core 

region located above a conical pebble discharge tube and a cylindrical discharge tube. For the initial 

critical configuration, there were a total of 16,890 fuel and moderator pebbles in the active core region

(9,627 fuel pebbles and 7,263 moderator pebbles), for a 57:43 fuel-to-moderator pebble ratio. The conical 

and cylindrical discharge tubes beneath the active core region were filled with moderator pebbles only, 

with a packing fraction of 61%. The reflector region surrounding the active core region and the discharge 

tubes are zones with varying material densities of carbon, natural boron, and coolant components. 

The uranium load in each fuel pebble is 5 g, and the fuel enrichment is 17 wt% 235U. Each fuel pebble 

contains 8,335 fuel particles. Each fuel particle includes a spherical UO2 kernel surrounded by four 

carbon-based layers. The IRPhE benchmark specifications [10] for the fuel particle data and material data 

for pebbles and moderator that were used to develop the HTR-10 core model are summarized in 

Tables 2.10 and 2.11.
11

Table 2.10. Fuel particle data for HTR-10 fuel

Zone description Material Density

(g/cm3

Outer radius

) (mm)

Fuel kernel UO2 10.4 0.250

Buffer layer Graphite 1.1 0.350

Inner pyrolitic carbon layer Graphite 1.9 0.390

SiC layer Silicon carbide 3.18 0.425

Outer pyrolitic carbon layer Graphite 1.9 0.465

Matrix Graphite 1.73 N/A

Table 2.11. Material data for pebbles and reflector in HTR-10

Parameter Value

Uranium mass per pebble (g) 5

Uranium enrichment (wt % 235U) 17

Equivalent boron in uranium (ppm) 4

Density of graphite in fuel pebble shell (g/cm3) 1.73

Density of graphite in moderator pebble (g/cm3) 1.84

Density of graphite reflector (g/cm3) 1.76

Equivalent boron in graphite moderator pebble (ppm) 0.125

Equivalent boron in graphite of fuel particle coatings (ppm) 1.3

Equivalent boron in graphite reflector (ppm) 4.8366

The pre-experiment set of benchmark (IAEA) specifications [22] considered that both the graphite in the 

dummy pebbles and the graphite in the fuel pebble outer shell had the same density, 1.73 g/cm3

. Later, in 

the IRPhE benchmark, the graphite density in the moderator (dummy) pebble was modified to 1.84 g/cm3

.

In addition, the equivalent boron specified in the IRPhE for the moderator pebbles was much lower than 

in the pre-experiment specifications: 0.125 ppm vs. 1.3 ppm. The actual experiment was conducted under 

atmospheric air at 15 °C [10] instead of helium as stated in the pre-experiment benchmark

specifications [22]. For the work documented in this report, only the IRPhE benchmark specifications 

were used for developing the core models.

Two sets of benchmark specifications are included in the IRPhE Handbook for HTR-10, called Simplified 

Model and High-Fidelity Model, respectively. The difference between these two models is the level of 

detail for the structures in the reflector region. The specifications for all the other regions in the reactor 

are the same in both models. In the High-Fidelity Model, 20 coolant flow channels, 13 control 

rod/irradiations channels, 7 small absorber ball channels, and one hot gas duct are explicitly modeled in 

the reflector region. In the Simplified Model, the ducts and borings in the reflector region are 

homogenized with the reflector material. The dimensions and locations for these regions were used as

provided in Table 3.2 of Ref. [10].
12

Dummy pebbles’ region

Fig. 2.5. SCALE/KENO-VI model for HTR-10 first core.

2.2.1.1 Active core region

The active core region contains fuel and moderator pebbles, with a 57:43 ratio of the fuel-to-moderator 

pebble numbers. The fuel and moderator pebbles are explicitly represented in the SCALE model using a 

hexagonal prism unit cell as a building block. Albeit the fuel particles inside each of the fuel pebbles are 

not explicitly modeled with SCALE, the double-heterogeneous structure is taken into account through the 

way the cross sections for the fuel zone inside the fuel pebble are calculated, as described in Section 2.1.2. 

The geometry of the hexagonal unit cell is illustrated in Fig. 2.6 (a). The different colors used in this 

figure signify the presence of different materials. The dimensions of this unit cell are calculated to ensure 

that both the packing fraction of the pebbles in the active core region and the fuel-to-moderator pebble 

ratio are conserved as specified in the benchmark, to 61% and 57:43, respectively. The hexagonal unit 

cells are packed into layers, as illustrated in Fig. 2.6 (b), and these layers are stacked vertically to form the

detailed active core region. The height for the active core is 123.574 cm.

To preserve the total number of fuel and moderator pebbles in the active core region, addition of the

pebbles and the stacks of pebble layers when building the active core model needs be done in a manner

that would ensure a minimal clipping of fuel and moderator pebbles by the cylindrical boundary of the 

core. The building of the core model as described above resulted (see Table 2.12) in a number of 

Active core region
13

16,885 fuel and moderator pebbles in the active core region, similar to the number reported in Ref. 18. 

The difference of five fuel pebbles, compared to the benchmark specifications [10], would correspond to 

a reduction of 0.05% in the total mass of uranium in the core. 

 (a) hexagonal prism unit cell (b) pebble layer in active core region

Fig. 2.6. Modeling of active core region.

Table 2.12. Number of fuel and moderator pebbles in the active core region

Total number of 

pebbles

Number of 

fuel pebbles

Number of 

moderator pebbles

Fuel-to-moderator 

pebble ratio

SCALE/KENO-VI model 16,885 9,622 7,263 56.99 : 43.01

Benchmark specifications [7] 16,890 9,627 7,263 57.00 : 43.00

Difference 5 5 0 –

The number of fuel and moderator pebbles in the SCALE/KENO-VI model for the active core region was 

verified by comparing the calculated volumes of the unique material regions in the active core region to 

the volumes corresponding to the expected number of pebbles modeled in this region. The volume 

calculation was performed using two different methods: (1) stochastic calculation within SCALE/KENOVI using the random sampling option for volume calculation and (2) analytical calculation with Keno3D, 

the 3-D visualization software designed for interactively viewing SCALE/KENO-VI geometry models on 

Windows computers. The results of the comparison are shown in Table 2.13. The comparison shows that 

the underestimation of the total volume of graphite material in the active core region is less than 0.2%, 

whereas the total volume of the fuel mixture in the fuel pebbles is exactly conserved (corresponds to 

9,622 fuel pebbles). The modeling of the pebbles in the active core region is illustrated in Fig 2.7, which 

also shows the pebbles in the dummy pebbles regions.

Table 2.13. Volume verification for the active core region

Material in active core

Expected volume

(105 cm3

Keno3D

) calculated volume

(105 cm3

Calculated-toexpected volume ratio

)

Fuel mixture in fuel pebble 6.2976 6.2976 1.0000

Graphite shell of fuel pebble 4.5856 4.5736 0.9974

Graphite in moderator pebbles 8.2139 8.2056 0.9990
14

2.2.1.2 Dummy pebbles region

The dummy pebbles region located underneath the active core region, which contains only graphite 

pebbles, was also modeled in detail in the SCALE/KENO-VI model, as illustrated in Fig. 2.7. The volume 

occupied by the graphite material in this region was calculated with Keno3D to verify that the packing of 

the graphite pebbles in this region is consistent with the expected value of 61%. The calculated packing 

fraction was 60.5%, in good agreement with the expected value. The very small difference of 0.5% in the 

total graphite volume is due to the inherent clipping of the graphite pebbles at the outer surfaces of the 

cylindrical and conical portions of the discharge tube.

Fig. 2.7. Modeling of pebbles in active core region and dummy pebbles region.

2.2.1.3 Reflector region

The IRPhE benchmark description [10] for the High-Fidelity Model includes explicit representation of the 

ducts and borings in the reflector: small absorber ball channels, coolant channels, control rod and 

irradiation channels, and the hot gas duct. The benchmark description for the Simplified Model [10] 

represents the radial zones containing borings as azimuthally homogenized. The difference between the 

High-Fidelity and Simplified models is illustrated in Fig. 2.8, which shows a radial view of the core, as 

modeled with SCALE/KENO-VI. Details of the channels in the reflector in the SCALE/KENO-VI model 

are presented in Fig. 2.9. 

The volumes of the ducts and borings in the reflector region were analytically calculated based on the 

provided geometry specifications and also calculated within SCALE/KENO-VI to ensure that the 

modeled geometry is consistent with the actual specifications. The volume comparison in Table 2.14 

shows a very good agreement. The very small differences can be explained by uncertainty in the 

stochastic volume calculation with KENO-VI.
15

 

 Simplified model High-Fidelity model

Fig. 2.8. Comparison of Simplified and High-Fidelity models—radial view.

Fig. 2.9. High-Fidelity model—channels in reflector region.
16

Table 2.14. Volume verification for the reflector region

Region in reflector

Expected volume

(105 cm3

Keno-VI 

) calculated volume

(105 cm3

Calculated-to-expected

)

volume ratio

Coolant channels 5.0768 5.0772 1.0001

Control rod/irradiation channels 7.7648 7.7646 1.0000

KLAK channels 2.2941 2.2929 0.9995

Hot gas duct 0.7069 0.7066 0.9996

2.2.1.4 Cross-section data

Calculations for the HTR-10 full core SCALE/KENO-VI model were carried out using the SCALE 238-

group ENDF/B-VII cross sections. 

2.2.2 Comparison with MCNP

The IRPhE Handbook [10] provides calculation results for the HTR-10 first core benchmark as obtained 

with an MCNP model. Though no information is provided on the nuclear cross-section libraries used for 

calculating the reported keff value, it was noted that the MCNP input file included in an appendix of the 

IRPhE Handbook shows ENDF/B-V (release unknown) data as being used in the model. This MCNP 

input file, corresponding to the high-fidelity benchmark, was used by ORNL to repeat calculations with 

different sets of continuous energy cross-section libraries. Both ENDF/B-V.0-based libraries and 

ENDF/B-VII.0-based libraries were employed to try reproducing the IRPhE-reported results and to ensure 

a consistent comparison with the SCALE results that were obtained with ENDF/B-VII libraries. 

A few modifications were made to the provided MCNP input for complete consistency with the 

benchmark data, as it was observed that some values for material densities in the input were slightly 

different from the provided benchmark specifications. The thermal scattering data S(α,β) for graphite that 

were used in the MCNP calculations were taken from dataset endf70sab for ENDF/B-VII.0 and from 

dataset tmccs for ENDF/B.V.0. [17]

The MCNP model was used to study the sensitivity of the effective multiplication factor (keff) results to 

the cross-section library data and to the boron isotopic composition data. Two sets of data were used for 

the boron isotopic composition: (1) 19.9% 10B and 80.1% 11B, as specified in the IRPhE benchmark [10]; 

and (2) 19.8% 10B and 80.2% 11B, as specified in the Nuclear Wallet Card 2005 [24]. The sensitivity of 

keff results to the boron isotopic composition are presented in Table 2.15, which shows practically no 

impact, irrespective of the cross-section dataset used. On the other hand, the effect of the ENDF/B library 

on keff is significant, of the order of 300 pcm, as shown in Table 2.16.

Table 2.15. Sensitivity of keff

Cross section data

to the boron isotopic composition

Boron isotopic composition keff σ(keff) keff

ENDF/B-V.0

difference (pcm)

19.8% 10B 80.2% 11B 1.01187 0.00022 21 ± 30 19.9% 10B 80.1% 11B 1.01166 0.00021

ENDF/B-VII.0 19.8% 10B 80.2% 11B 1.01472 0.00021 1 ± 30 19.9% 10B 80.1% 11B 1.01473 0.00021
17

Table 2.16. Sensitivity of keff

Boron isotopic composition

to the cross-section data

Cross section data keff σ(keff) keff

19.8% 

difference (pcm)

10B 80.2% 11 ENDF/B-V.0 B 1.01187 0.00022 285 ± 30 ENDF/B-VII.0 1.01472 0.00021

19.9% 10B 80.1% 11 ENDF/B-V.0 B 1.01166 0.00021 307 ± 30 ENDF/B-VII.0 1.01473 0.00021

2.2.3 Results

The keff value calculated with the SCALE/KENO-VI model for the simplified benchmark model is

compared in Table 2.17 to the corresponding MCNP-calculated value and the expected benchmark value 

as reported in Ref. 10. The difference between the two calculated keff values is approximately 300 pcm. 

Both MCNP and SCALE overestimate the expected benchmark value by 1.2% and 1.5%, respectively. 

Table 2.17. keff results for simplified benchmark model

Cross-section data keff σ(keff) keff difference (pcm)

Expected benchmark value (Ref. 9)

a

1.0131 0.0037

SCALE/KENO-VI ENDF/B-VII.0 1.02804 0.00027

MCNP5 (Ref. 9) N/A 1.02500 b 0.00021 304 ± 34 a Calculated as 105 × (kSCALE – kMCNP). b Not available.

The keff value calculated with SCALE/KENO-VI for the High-Fidelity Model is compared to the 

corresponding MCNP-calculated value reported in Ref. 10 and to the experimental result in Table 2.18.

The SCALE-calculated value was obtained using 238-group ENDF/B-VII cross sections, whereas the 

MCNP-calculated value was obtained using continuous energy (CE) ENDF/B-VII cross sections. As 

observed, there is a relatively good agreement between SCALE and MCNP, with a difference in the 

calculated keff of 162 ± 33 pcm. However, both MCNP and SCALE overestimate the experimental values,

by 1.5% and 1.3%, respectively.

Table 2.18. keff results for high-fidelity benchmark model

Cross-section data keff σ(keff) keff difference (pcm)

Expected benchmark value (experiment)

a

1.0000 0.0037

SCALE/KENO-VI ENDF/B-VII.0 1.01311 0.00025

MCNP5 (calculated by ORNL) ENDF/B-VII.0 1.01473 0.00021 -162 ± 33 a Calculated as 105 × (kSCALE – kMCNP).

One possible source of the difference between the calculated and experimental keff values may be due to 

possible uncertainties in the benchmark specifications that were not included in the IRPhE description

[10]. As specified in Ref. 10, the sources of information used to develop the benchmark specifications do 

not contain a complete set of data on the uncertainties or tolerances of all relevant parameters. Sensitivity 

studies on various parameters such as variations in boron concentration in the fuel element, density of 

graphite matrix in the fuel pebble, or dimensions of the core and fuel that were presented in Ref. 10

showed that part of the difference may be related to uncertainties in these parameters. A large contributor 

in the observed code bias might be uncertainty in the carbon capture cross section for graphite-rich reactor 

systems. A Japanese study [25] showed that a new evaluation of the carbon capture cross section that was 

used in the recent release of the Japanese JENDL 4.0 data led to significantly better agreement between 

calculated and experimental reactivity for HTTR annular cores compared to other evaluations. The 

reactivity for three HTTR annular cores calculated using ENDF/B-VII data for the carbon capture cross 

section overestimated the experimental values by 0.8 to 1.7%; whereas when JENDL 4.0 data were used 

the calculated reactivity agreed within 0.3% with the experiment [25].
18

2.3 ANALYSIS OF THE HTR-PROTEUS BENCHMARK EXPERIMENTS

PROTEUS is a zero-power research reactor facility located at the Paul Scherrer Institut in Switzerland. 

This facility has been used over the years to carry out experiments relevant to different types of reactor 

configurations. PROTEUS has a cylindrical graphite annulus with a central cavity for which the content 

can be changed according to the type of reactor being investigated. Though it has been used mostly to 

study light water reactors, the facility was configured as a pebble bed reactor critical facility from 1992 to 

1996 and designated as HTR-PROTEUS. During this period, 13 critical configurations were assembled 

and various reactor physics experiments were conducted [11]. This section includes a summary of the

experiments as described in Ref. 11, along with the description of the SCALE models developed for the 

corresponding configurations and the results obtained with these models.

2.3.1 HTR-PROTEUS Experiments Overview

PROTEUS consists of a graphite cylinder of 3.26 m diameter and 3.30 m height and has a central 

polygonal cavity that can be approximated as a cylinder with a 1.25 m effective radius [11]. Thirteen 

critical PBR configurations were studied with HTR-PROTEUS. In ten of these configurations, the 

pebbles were manually arranged in the core in a fixed lattice arrangement, whereas in the other three 

configurations the pebbles were randomly arranged. Only the cores with a deterministic lattice 

arrangement are addressed in this report. The HTR-PROTEUS configuration is illustrated in Fig. 2.10, 

which shows one of the models developed with SCALE/KENO-VI.

The main characteristics of the configurations with deterministic pebble arrangements are summarized in 

Table 2.19, which is a simplified version of Table 1.2 in the IRPhE draft benchmark [11]. The identifiers 

are as used in the original PSI documentation [26,27]. These configurations can be placed in two main 

groups depending on the pebble arrangement in the configuration: (1) cores 1 to 3 have a hexagonalclosed-packed (HCP) pebble arrangement and (2) cores 5 to 10 have a columnar hexagonal point-on-point

(CHPOP) packing arrangement. The number 4 core that is missing from the table (in the sequence from 1 

to 10) corresponds to a random arrangement of the pebbles in the core (not modeled here). For cores 1a, 

5, and 9, more than one state was considered, and named as such in the original documents. The original 

naming may not be necessarily associated with large changes in configurations. 

Differences among core configurations can relate to

• Total number of layers of pebbles in the configuration.

• Fuel-to-moderator pebble ratio in all or most of the layers in a configuration. In some 

configurations, the end layer is much different than the other layers, e.g., the 23rd layer in cores 5 

and 8 or the 28th

• Type and number of control rods.

layer in core 9 state 2.

• Presence of polyethylene rods in the core and/or the cross-sectional shape of these rods—

cylindrical vs. triangular.

The differences between these configurations will be discussed in detail further in this section.

The HTR-PROTEUS experiments included, in addition to criticality experiments, measurements of 

differential and integral control rod and safety rod worths and reaction rates ratios. These later 

measurements were not evaluated in the IRPhE draft benchmark [11], but compiled data were included.

Only the criticality experiments are addressed in the current report. 
19

Fig. 2.10. HTR-PROTEUS illustration—SCALE/KENO-VI model.

Pebbles in central cavity

1250 cm

3262 cm

Outer radial reflector

Inner radial reflector

3304 cm
20

Table 2.19. HTR-PROTEUS configurations

Core

Identifier

Date Packing Pebble Configuration Detail a Fuel-to-Moderator

Pebble Ratio

1 

State 1 July 1992 HCP 22 layers 2.00425

1A

State 1

State 2

June 1993

Feb. 1994

HCP 21 layers

As State 1, but slightly different locations 

for control rods

2.00445

2

State 1 Aug 1993 HCP 16 layers

17th layer

2.00425

Moderator pebbles only

3

State 1 Oct 1993 HCP 17 layers

18th

327 cylindrical polyethylene rods

layer is partially filled

2.0045

5

State 1

State 2

State 3

July 1994

July 1994

Nov 1995

CHPOP 22 layers

23rd

Same pebble arrangement in all three 

states, but small differences in bottom 

reflector or/and small changes in control 

rod positioning 

layer

2.000378

0.6188 

6

State 1 April 1995 CHPOP 21 layers

22nd

654 triangular polyethylene rods 

layer

2.0000

0.5628 

7

State 1 May 1995 CHPOP 17 layers

18th

654 triangular polyethylene rods

layer

1.99951

0.5628 

8

State 1 Jan 1996 CHPOP 22 layers

23rd

654 triangular polyethylene rods 

layer 

2.00378

0.6188

9

State 1

State 2

Feb 1996

Feb 1996

CHPOP 27 layers

State 2 has 28th layer pure moderator

0.998565

0.929744 in State 2

10

State 1 May 1996 CHPOP 27 layers

654 cylindrical polyethylene rods 

0.998565

a HCP = hexagonal closed packing; CHPOP = columnar hexagonal point-on-point.
21

2.3.2 Computational Models for HTR-PROTEUS Configurations

2.3.2.1 Modeling data

Data used to develop the computational models for the HTR-PROTEUS configurations were taken to 

large extent from the IRPhE draft benchmark. [11] Other references were used or assumptions were made 

in the cases where the information in Ref. 11 was inconsistent or incomplete. Data of most relevance will 

be discussed in this report. For more details the reader is encouraged to consult the references provided.

All HTR-PROTEUS configurations included both fuel and moderator pebbles, arranged in different 

lattices, as summarized in Table 2.19. The uranium load in each fuel pebble is ~ 6 g and the fuel 

enrichment is 16.7 wt % 235U. Each fuel pebble contains a 2.35-cm-radius spherical fuel region with 9,394

fuel particles and a graphite shell with a total radius of 3.0 cm. Each fuel particle includes a spherical 

UO2 kernel surrounded by four carbon-based layers. The IRPhE draft benchmark specifications [11] for 

the fuel particle data and material data for pebbles and moderator that were used to develop the HTRPROTEUS core models are summarized in Tables 2.20 and 2.21.

Table 2.20. Fuel particle data for HTR-PROTEUS fuel

Zone description Material Density

(g/cm3

Outer radius

) (mm)

Fuel kernel UO2 10.88 0.2510

Buffer layer Graphite 1.10 0.3425

Inner pyrolitic carbon layer Graphite 1.90 0.3824

SiC layer Silicon carbide 3.18 0.4177

Outer pyrolitic carbon layer Graphite 1.89 0.4577

Matrix Graphite 1.73 N/A

Table 2.21. Material data for pebbles and reflector in HTR-PROTEUS

Parameter Value

Uranium mass per pebble (g) 5.97

Uranium enrichment (wt % 235U) 16.7

Density of graphite in fuel pebble shell (g/cm3) 1.73

Density of graphite in moderator pebble (g/cm3) 1.68

Density of graphite reflector (g/cm3) 1.76

Equivalent boron in graphite of moderator pebble (ppm) 1.7149

Equivalent boron in graphite of fuel pebble (ppm) 0.3883

There are a large number of borings in the reflector near the core, as seen in Fig. 2.10, which are arranged 

in rings, some containing control elements. A variety of control rods were used in the studied 

configurations: Cd/Al ZEBRA-type rods, an automatic control rod, withdrawable stainless steel control 

rods, safety/shutdown rods, and static measurement rods [11]. The ZEBRA-type rods were used only in 

Core 1.

2.3.2.2 Modeling assumptions

The specifications in the HTR-PROTEUS IRPhE draft benchmark [11] are not a complete set—there are 

cases with missing information or cases containing conflicting information. Assumptions were necessary 

in order to generate the data needed in computational models in these cases, such as assumptions about 

reflector structure and graphite composition, details of the polyethylene rods, or details on control rods. 
22

The modeling assumptions used for creating the reflector model are as follows:

1. Type of graphite used in different zones of the graphite reflector. Based on data provided in 

Table 1.7 and Figure 4.2 of Ref. 11, it was assumed that the graphite spacers used in the cores, the 

graphite rods filling the borings in the radial reflector, the filled pieces for the ZEBRA rod 

borings in Core 1, the graphite plug for the axial neutron source, and the central section of the 

axial reflectors utilized the so-called “axial graphite” composition, while all other parts of the 

reflector, including the top 12 cm, and the other filler rods utilized the so-named “radial” 

graphite.

2. Effect of external structures. The effect of external structure on the core reactivity was assumed

of minimal importance. This is supported by results in Ref. 28, which indicate that this effect 

amounts to less than a 100 pcm change in the multiplication factor. 

3. Elevation of the central graphite plug in the upper reflector. It was assumed 14.9 cm, though no 

consistency exist for this data in figures of Ref. 11.

4. Status of holes in the upper axial reflector. The assumption in Ref. 11 that the 34 holes in the 

upper axial reflector plug were kept opened was used, though it is different than that used in other 

sources [29].

5. Height of graphite spacers used to transform the central cavity into a 12-sided polygonal prism. 

This was inferred from figures provided in Ref. 11 as 174.4 cm, reaching the bottom of the upper 

reflector.

Polyethylene rods were used in some of the cores to increase moderation. The following modeling 

assumptions were used for these rods:

1. Data on the type of rods used in Core 7 were inconsistent between Table 1.2 and Table 1.29 of 

Ref. 11. Since the information in Table 1.2 was moderately vague, the rod information in 

Table 1.29 was used.

2. The precise locations of polyethylene rods in Core 8 were not available. The rods were specified 

as only 12 cm long for this case, but their precise position was not mentioned. As Table 1.30 in 

Ref. 11 indicated that the goal for this core was to simulate high water loading at the bottom of 

the core, it was assumed that the rods were placed at the bottom of the core cavity.

Assumptions made about the control rods included:

1. Level of full insertion. It was assumed that the full insertion level for cores 2 to 9 was when the 

entirety of the withdrawable control rod or the copper wedge for the autorod was contained 

within the upper graphite reflector. This assumption was based on Fig. 3.14 in Ref. 11, which 

shows the withdrawn shutdown rod. More detailed information was available for control rods in 

Core 1, so in this later case a more accurate model was possible. 

2. Radial location of withdrawable control rods. Since Table 1.21 in Ref. 11 indicated that the 

withdrawable control rods were inserted in the 5th boring ring and no other indication of radial 

location was ever given, all withdrawable control rods were assumed to be located in the 5th

3. Status of unused withdrawable control rod channels and ZEBRA rod channels. Based on Fig. 4.3 

of Ref. 11, it was assumed that the unused withdrawable control rod channels and ZEBRA rod 

channels were filled with graphite, although the safety/shutdown rod channels were left empty.

ring. 

2.3.2.3 Models for Cores 1 to 3

Four of the HTR-PROTEUS configurations used an HCP arrangement of the pebbles in the core. These 

configurations, as specified in Table 2.19, were identified as 1, 1a, 2, and 3. The theoretical packing 

fraction of the pebbles is 0.7045 for this arrangement, though it cannot be achieved in the actual core 

volume because of the unoccupied spaces in the proximity of the inner cavity outer boundary. The 

building block used to model the HCP core configurations consisted of a hexagonal prism designed to 
23

preserve the geometry and moderator-to-fuel pebble ratio of a given core arrangement, as illustrated in 

Fig. 2.11. Though the TRISO particles in each fuel pebble were not explicitly modeled, the double 

heterogeneity of the fuel was accounted for by using the DOUBLEHET option for cross-section 

processing within SCALE, as described in Section 2.1.2.

 

Fig. 2.11. Core modeling for HCP pebble arrangements.

Cores 1 and 1a had 22 and 21 pebble layers, respectively, each of the layers with a pebble ratio (fuel-tomoderator) of 2.0. Cores 2 and 3 had 17 and 18 layers of pebbles; the most top layer consisted of only 

moderator pebbles for Core 2, whereas for Core 3 the topmost layer was partially filled, as illustrated in 

Fig. 2.12. Another difference between Core 3 and the other three HCP cores is the presence of 

polyethylene rods inserted vertically in the interstices between pebbles, as shown in Fig 2.12. The purpose 

in this experiment was to study the effect of water ingress by means of the hydrogen in the polyethylene.

HCP unit cell

core pebbles
24

Fig. 2.12. Pebble modeling for Core 3.

2.3.2.4 Models for Cores 5 to 10

Cores 5 to 10 used a CHPOP arrangement of the pebbles in the core. The theoretical packing fraction of 

the pebbles is 0.6046 for this arrangement, though it cannot be achieved in the actual core volume 

because of the unoccupied spaces in the proximity of the inner cavity outer boundary. The building block 

used to model the CHPOP core configurations consisted of a hexagonal prism designed to preserve the 

geometry and moderator-to-fuel pebble ratio of a given core arrangement, as illustrated in Fig. 2.13. The 

modeling of the top and bottom of the core, as well as of pebbles in proximity to the core boundary, was 

handled separately. Cores 5 to 8 had more moderator pebbles than fuel pebbles in the topmost pebble 

layer, as shown in Fig. 2.13 for Core 5. Cores 6, 7, 8, and 10 included polyethylene rods inserted axially 

between the pebbles. There were differences in dimensions and shapes for the polyethylene rods in these 

cores. Core 9 in particular was more challenging to model than the others, as it contained seven different 

types of layer arrangements, as illustrated in Fig. 2.14.
25

 

 

Fig. 2.13. Core modeling for CHPOP arrangements.

Fig. 2.14. Pebble modeling for Core 9 state 2.

CHPOP unit cell

Core 5
26

2.3.3 Comparison with MCNP

The IRPhE draft benchmark provides calculation results for the critical configurations as obtained with 

MCNP models. [11] Though the MCNP models are not included in the draft benchmark, it is mentioned 

that the cross sections used with these models were continuous-energy cross sections from ENDF-B/V 

and ENDF/B-VI. The provided MCNP results for keff are used for comparison with the corresponding 

results obtained for the current report with SCALE models. 

2.3.4 Results

The SCALE/KENO-VI models for the HTR-PROTEUS configurations were used to calculate the keff

values. The results are compared to the MCNP results [11] in Tables 2.22 and 2.23 for the configurations 

with HCP and CHPOP pebble arrangements, respectively. The SCALE results shown in these tables were 

obtained using 238-group ENDF/B-VI cross sections, for better consistency with the data that were used 

with MCNP. The average difference between SCALE and MCNP results for configurations with HCP 

packing of the pebbles is 252 ± 93 pcm. The average difference between SCALE and MCNP results for 

configurations with CHPOP packing of the pebbles is 422 ± 93 pcm.

The comparison of SCALE-calculated keff values to the experimental data provided in Ref. 11 is 

presented in Tables 2.24 and 2.25. The SCALE results were obtained in these cases using the most recent 

238-group ENDF/B-VII cross sections available in SCALE. The average difference between the 

calculated and benchmark keff data shown in Tables 2.24 and 2.25 is 797 pcm.

Table 2.22. keff results for PROTEUS cores with HCP pebble arrangements

Core ID 1 1A (1) 1A (2) 2 e 3

SCALE/KENO-VI keff 1.00900 1.01078 1.00969 1.01078 1.01145

(ORNL) σ(k a eff)

c 0.00120 0.00081 0.00080 0.00099 0.00075

MCNP5 keff 1.00767 1.00725 1.00753 1.00845 1.00818

(IRPhE) σ(k b

eff) 0.00022 0.00021 0.00017 0.00023 0.00022

∆keff [pcm] 133 d 353 216 233 327

keff difference σ(∆keff) [pcm] 122 84 82 102 78

∆keff [%] 0.1 0.3 0.2 0.2 0.3 a Used 238-group ENDF/B-VI cross sections. b Used continuous-energy ENDF/B-V or ENDF/B-VI cross sections. c Standard deviation of calculated keff value. d ∆(keff) = (kSCALE – kMCNP) ; 1 pcm = 10-5

. e

Core identified 1A (see Table 2.19) had two states.
27

Table 2.23. keff results for PROTEUS cores with CHPOP pebble arrangements

Core ID 5 (1) e 5 (2) 5 (3) 6 7 8 9 (1) 9 (2) 10

SCALE keff 1.00932 1.00750 1.00715 1.01343 1.00880 1.00841 1.00460 1.00910 1.00697

(ORNL) σ(k a eff) 0.00091 c 0.00083 0.00079 0.00080 0.00071 0.00088 0.00100 0.00140 0.00088

MCNP5 keff 1.00338 1.00286 1.00333 1.00676 1.00678 1.00370 1.00299 1.00325 1.00426

(IRPhE) σ(k b

eff) 0.00018 0.00019 0.00021 0.00017 0.00017 0.00019 0.00019 0.00019 0.00018

keff ∆keff [pcm] 594 d 464 382 667 202 471 161 585 271

difference σ(∆keff) [pcm] 93 85 82 82 73 90 102 141 90

∆keff [%] 0.6 0.5 0.6 0.7 0.2 0.5 0.2 0.6 0.3 a Used 238-group ENDF/B-VI cross sections. b Used continuous-energy ENDF/B-V or ENDF/B-VI cross sections. c Standard deviation of calculated keff value. d ∆(keff) = (kSCALE – kMCNP) ; 1 pcm = 10-5

. e Core 5 had three states and core 9 had two states (see Table 2.19).

Table 2.24. Comparison of SCALE-calculated keff to benchmark data

for PROTEUS cores with HCP pebble arrangements

Core ID 1 1A (1) 1A (2) 2 e 3

SCALE/KENO-VI keff 1.01117 1.01060 1.01165 1.00998 1.00847

(ORNL) σ(k a eff)

c 0.00082 0.00099 0.00081 0.00094 0.00079

Benchmark keff 1.00316 1.00291 1.00371 1.00243 1.00054

(IRPhE) σ(k b

eff) 0.00022 0.00024 0.00072 0.00022 0.00018

∆keff [pcm] 801 d 769 794 755 793

keff difference σ(∆keff) [pcm] 85 102 108 97 81

∆keff [%] 0.8 0.8 0.8 0.8 0.8 a Used 238-group ENDF/B-VII cross sections. b As reported in Ref. 17. c Standard deviation of calculated keff value. d ∆(keff) = (kSCALE – kMCNP) ; 1 pcm = 10-5

. e Core identified 1A (see Table 2.19) had two states.

Table 2.25. Comparison of SCALE-calculated Keff to benchmark data

for PROTEUS cores with CHPOP pebble arrangements

Core 

ID 5 (1) e 5 (2) 5 (3) 6 7 8 9 (1) 9 (2) 10

SCALE keff 1.00816 1.00748 1.00798 1.01355 1.00945 1.00964 1.00530 1.00868 1.00894

(ORNL) σ(k a eff) 0.00079 c 0.00083 0.00085 0.00077 0.00088 0.00085 0.00100 0.00079 0.00089

Benchmark keff 1.00071 1.00071 1.00071 1.00053 1.00053 1.00071 1.00108 1.00108 1.00073

(IRPhE) σ(k b

eff) 0.00014 0.00014 0.00014 0.00024 0.00024 0.00014 0.00024 0.00024 0.00014

k

∆k

eff

eff

[pcm] 745 d 677 727 1302 892 893 422 760 821

difference σ(∆keff

80

) 

[pcm] 84 86 81 91 86 103 83 90

∆keff

[%] 0.7 0.7 0.7 1.3 0.9 0.9 0.4 0.8 0.8 a Used 238-group ENDF/B-VII cross sections. b As reported in Ref. 17. c Standard deviation of calculated keff value. d ∆(keff) = (kSCALE – kMCNP) ; 1 pcm = 10-5

. e Core 5 had three states and core 9 had two states (see Table 2.19).

29

3. SCALE VALIDATION FOR HTGRs—PRISMATIC FUEL DESIGN

Verification and validation studies performed to evaluate the SCALE analysis of HTGRs with prismatic 

fuel design was carried out to large extent using experimental data available for the HTTR. The 

documentation describing the measurements performed at HTTR is available from reactor physics 

benchmarks that were published in the IRPhE in 2009, 2010, and 2011 [6, 7, 8, 9].

The HTTR is a 30 MWth, prismatic core, graphite-moderated, helium-cooled reactor that was built by the 

Japan Atomic Energy Agency (JAEA). The first criticality of the HTTR was achieved with an annular 

core on November 10, 1998, while full core criticality was attained on December 16, 1998. At full power, 

the reactor can supply 950 °C helium that can be further used for high temperature applications. The 

950 °C coolant temperature was first achieved on April 19, 2004, for a short time. At the beginning of 

2010, the reactor was operated at 950 °C for a period of 50 days. Each of these maximum designed high 

temperature operations were preceded by 850 °C full power tests (achieved for a short time on 

December 7, 2001, and then for a period of 30 days in 2007). The core of this reactor consists of prismatic 

fuel blocks that use TRISO fuel with 12 different fuel enrichments, between 3.4 and 9.9 wt % 235U.

The analyses performed for an HTTR prismatic fuel block are first discussed in this section, including a 

few modeling considerations for the annular fuel pin that is characteristic of the HTTR design. Then the 

analyses and results obtained for the HTTR critical and subcritical configurations are presented in detail. 

3.1 ANALYSIS OF HTTR FUEL BLOCK

3.1.1 Description of the HTTR Fuel Block

The HTTR fuel blocks are hexagonal prisms that can contain either 31 or 33 pins. The fuel block 

analyzed in this section was a 33-pin block with TRISO fuel at 6.3 wt % 235U enrichment and containing

burnable poison (BP) rods with 2.5% 10B content. Only the main characteristics of the fuel block 

considered for analysis are summarized in Table 3.1. Detailed specifications for the HTTR fuel blocks 

can be found in Ref. 6.

Table 3.1. Fuel block main characteristics 

Parameter Value

Shape Hexagonal prism

Height (cm) 58

Side to side distance (cm) 36

Number of fuel pins 31 or 33

Fuel pin inner radius (cm) 0.5

Fuel pin outer radius (cm) 1.3

Fuel pin pitch—triangular (cm) 5.15

Fuel pin height (cm) 54.6

Number of burnable poison pins 2

Burnable poison pin radius (cm) 0.7

Mass of uranium per fuel pin (g) 188.58

Each of the 33 fuel pins is annular and contains 12,987 TRISO fuel particles embedded in a graphite 

matrix, for a total mass of 188.58 ± 5.66 g of uranium per pin. Each fuel pin is enclosed in a graphite 

sleeve, with helium circulated outside this sleeve. There are 14 annular TRISO fuel compacts, each 

3.9 cm high, stacked on top of each other in a fuel pin, for a total fuel pin height of 54.6 cm. The TRISO 

fuel particle is made of a relatively large, spherical fuel kernel with 0.03 cm radius that is surrounded by 

four layers of carbon or silicon carbide. The dimensions of the different layers of the TRISO fuel grains 
30

are listed in Table 3.2. The isotopic material composition for all the materials used in the fuel block 

model, as obtained from Ref. 6, are summarized in Table 3.3.

Table 3.2. Fuel particle data for HTTR

Zone Description Material Outer Radius

(μm)

Fuel kernel UO2 300

Buffer layer Graphite 360

Inner pyrolitic carbon layer Graphite 390

SiC layer Silicon carbide 415

Outer pyrolitic carbon layer Graphite 460

Matrix Graphite N/A

Table 3.3. Material data for 6.3 wt % 235

Component

U enriched HTTR fuel block

Material Composition Number density

(atoms cm-1 b-1

Density 

) (g/cm3

Fuel kernel (6.3 wt %

)

235U) UO2

234U 235U 236

O

U

10

1.1293 x 10

B

1.4783 x 10

-5

2.1699 x 10

-3

4.6343 x 10

-2

1.7276 x 10

-2

10.39

-7

Buffer layer graphite C

10

5.5153 x 10

B 1.8290 x 10

-2

-8 1.1

IPyC layer graphite C

10

9.2758 x 10

B 3.0761 x 10

-2

-8 1.85

SiC layer SiC

C

Si

10

4.8061 x 10

B

4.8061 x 10

-2

5.3208 x 10

-2 3.2 -8

OPyC layer graphite C

10

9.2758 x 10

B 3.0761 x 10

-2

-8 1.85

Graphite compact graphite a C

10

8.5237 x 10

B 1.5452 x 10

-2

-8 1.7

Graphite (IG-110) in fuel block graphite C

10

8.8243 x 10

B 7.8036 x 10

-2

-9 1.74

Burnable poison pin (2.5 wt %) B4

C

C in graphite 10B

11

8.7995 x 10

B

4.9882 x 10

-2

2.0078 x 10

-4 1.247 -5

Helium coolant He He 2.4616 x 10 0.000164 -5

a

accounts for them using a 0.5% reduction in the nominal graphite density.

Values included in Ref. 6 are 0.5% smaller; the model used in Ref. 6 does not include the fuel handling positions, but it

3.1.2 Computational Model for the HTTR Fuel Block

A 3-D model of the HTTR fuel block described previously was developed with SCALE/KENO-VI. Cross 

sectional and axial views of this model are illustrated in Fig. 3.1. In this report, the locations of the fuel 

and burnable absorber pins in the cross-sectional view of the fuel block are identified using the format 

mn, with m identifying the row from the bottom to the top in Fig. 3.1(a) and n identifying the position on 

the row from left to right (e.g., “11” identifies the BP pin in the lower left corner; “12” is the fuel pin to 

its right; “44” is the handling hole; and “47” is the empty BP location).
31

Fig. 3.1. (a) Cross-sectional and (b) vertical views of the HTTR fuel block.

One important feature of the HTTR fuel block design is the spatial double heterogeneity. The first level of 

heterogeneity consists of the distribution of the TRISO particles inside the fuel compact, while the second 

level is represented by the lattice of fuel pins in the fuel block. In modeling the first level of 

heterogeneity, the parameter that primarily needs to be conserved is the amount of fuel per fuel pin, which 

is 188.58 ± 5.66 g uranium for fresh HTTR fuel [6].

3.1.2.1 Fuel pin modeling for continuous-energy calculations

A fuel block model was developed to represent fuel particles in detail and treat the neutron transport using 

continuous-energy (CE) cross-section data with SCALE/KENO-VI. The distribution of the fuel particles 

was modeled using a regular lattice representation. One method to conserve the fuel mass in a lattice 

representation of the fuel particles would be to fully include the lattice of fuel grains within the fuel pin. 

In using this approach, however, the lattice model must have a smaller pitch than the actual value to avoid 

the clipping of the TRISO particles at the boundaries of the fuel pin. This will create a different spatial 

distribution (and different local packing fraction) of the TRISO particles, with the regions near the 

boundaries of the pin containing no TRISO particles. A rigorous random placement (not based on a 

lattice) of the individual TRISO particles within the fuel pin that also preserves the mass of fuel can be 

used and has been previously demonstrated [30]. However, because the number of TRISO particles is 

very large (~5 million per fuel block in this case), this latter modeling approach is computationally 

feasible only for small configurations (e.g., single fuel compact). 

An alternative approach was proposed by Ilas and Gehin to mitigate the above-mentioned modeling 

concerns [31], which conjectured to conserve the mass in a fuel pin in a statistical sense, while also 

preserving the uniform spatial distribution by shifting the lattice using a random vector with components 

smaller than half the size of the lattice pitch. This is the approach used for the CE model in this report. 
32

This approach alleviates the error due to the shift of the lattice of grains within the fuel pin boundaries, an 

error that was pointed out by Žáková and Talamo [32]. 

3.1.2.2 Fuel pin modeling for multigroup calculations

A fuel block SCALE/KENO-VI model was developed for use in calculations with a multigroup crosssection library. The double heterogeneity of the fuel was accounted for in this model through the use of 

the DOUBLEHET option in SCALE for cross-section processing. Details about this cross-section 

processing approximation are included in Section 2.1.2 of this report. In this approximation, both the 

mass of fuel and its uniform spatial distribution are rigorously preserved. Availability of a multigroup 

model is very important for depletion simulations, sensitivity/uncertainty problems, or simply as a 

replacement for the more rigorous but longer-running continuous energy models. The multigroup option 

is at this time the only available option in SCALE for sensitivity/uncertainty analysis and for depletion 

calculations.

The DOUBLEHET treatment in SCALE, however, is presently available only for solid cylindrical pins. 

Therefore, for annular cylindrical pins as characteristic to the HTTR core, additional geometry 

approximations [31] need to be made before a double-heterogeneous treatment can be applied to the 

generation of the multigroup cross-section libraries for use with SCALE/KENO-VI. The approximation 

used in this report consisted of transforming the annular pin into a solid cylindrical pin by homogenizing

the graphite matrix in the fuel regions with the inside and the outside helium regions. This approximation 

is used both for applying the double-heterogeneous treatment to the cross-section processing and in the 

transport geometry model of the problem input.

3.1.3 Results for the HTTR Fuel Block

The results obtained with SCALE/KENO-VI for both continuous energy and multigroup models are 

compared to corresponding results obtained with MCNP5 for eigenvalue and fission source distribution.

The fuel block configuration illustrated in Fig. 3.1 was modeled with both SCALE/KENO-VI and 

MCNP5. Because the double-heterogeneity procedure for cross-section processing does not support

annular pins as noted above, the annular fuel was homogenized with the central hole to form a solid 

cylindrical pin for the multigroup option in SCALE/KENO-VI. To assess the possible uncertainty

introduced by this homogenization, the same configurations with homogenized pins were modeled with 

continuous energy SCALE/KENO-VI.

3.1.3.1 Multiplication constant

The values obtained for the multiplication constant keff are presented in Table 3.4. As seen, there is an 

excellent agreement between the SCALE/KENO-VI CE and MCNP5 models, with a difference in keff of 

85 ± 35 pcm. The keff difference between the MG and CE SCALE/KENO-VI models is 336 ± 37 pcm. 

The homogenization of the fuel pins with their central holes (see cases 1 and 4 in Table 3.4) leads to a 

small overestimation of the keff result, of 68 ± 37 pcm. The axial homogenization of the central handling 

hole has virtually no effect on the multiplication constant (see cases 1 and 5 in Table 3.4), the difference 

being 22 ± 35 pcm.

The last column of Table 3.4 compares the CPU time for each calculation. The MCNP5 code used the 

OpenMPI-compiled parallel version. Both the SCALE/KENO-VI and the MCNP5 simulations used

11 million particles, with 110 generations (cycles), first 10 generations skipped, and 100,000 particles per 

generation. As seen, the multigroup version of SCALE/KENO-VI is more than three times faster than the 

continuous energy version for the same number of particles simulated.
33

Table 3.4. Multiplication constants for different models of the HTTR fuel block

Case # Description k a eff σk

b CPU time

(hours)

c

1 SCALE/KENO-VI CE 1.33186 0.00027 14.0

2 SCALE/KENO-VI MG 1.32850 0.00025 4.3

3 MCNP5 CE 1.33101 0.00024 142.5

4

*

SCALE/KENO-VI CE 

with homogenized pins 1.33254 0.00026 13.8

5 SCALE/KENO-VI CE 

with homogenized handling hole 1.33164 0.00022 14.0

6 SCALE/KENO-VI CE 

with periodic boundary conditions 1.32325 0.00033 14.0

a CE = continuous energy cross sections; MG = 238-group cross sections. b Standard deviation in keff. c SCALE cases were run on single processor (CPU) using the prelease version of SCALE 6.1. MCNP5 

version 1.51 was run on a parallel cluster and included fuel pin mesh tally computations.

Calculations for cases 1 through 5 in Table 3.4 were performed using reflective boundary conditions on 

the outer boundary, in accordance with the current lattice level methodology for light water reactors. The 

application of a white boundary condition (results not shown) has virtually no effect on the multiplication 

constant, as expected. The use of a periodic boundary condition (case 6 in Table 3.4), however, seems to 

have a relatively large effect; the multiplication constant in this case is with 861 ± 43 pcm lower than that 

for the case when a reflective boundary condition was used (case 2 in Table 3.4). This difference is due to 

the different virtual positions of the BP pins around the fuel block when the periodic boundary condition 

is used as opposed to the reflective boundary condition.

3.1.3.2 Fission density distribution

Pin fission density distributions were calculated using three models: (1) MCNP5 CE, (2) SCALE/KENOVI CE, and (3) SCALE/KENO-VI MG. In all three cases, a reflective boundary condition was used on the 

outer boundary.

The 3-D distribution of the fission density in all 33 fuel pins, as calculated with the SCALE/KENO-VI

MG model and illustrated using the Keno3D plotting software, is shown in Fig. 3.2. Each axial zone 

corresponds to a fuel compact, in which the fission density was averaged. The color-coded values for 

fission density clearly suggest that the distribution peaks at the top and bottom of the pins furthest from 

the BP pins.

The radial-azimuthal distribution of the calculated fission density in each pin for each of the three models 

is illustrated in Fig. 3.3. The symmetry of the fuel block was taken into account to reduce the number of 

distinct pins from 33 to 19. In accord with the pin numbering convention introduced in Section 3.1.2, each 

decade on the abscissa axis in Fig. 3.3 corresponds to a row of pins in Fig. 3.1, from row 1 to row 4. 
34

Fig. 3.2. Three-dimensional pin fission density distribution in the HTTR fuel block 

with SCALE/KENO MG.

10 20 30 40 50

0.90

0.95

1.00

1.05

1.10

1.15

KENO-CE

KENO-MG

MCNP5

Fission Density

Pin #

Fig. 3.3. Pin fission density distribution in the HTTR fuel block with three models.

BP Pins

Pin 12 with a

W-shaped fission 

density distribution

Pin 36 with highest average 

fission density. The fission 

density peaks at the top and 

bottom

Symmetry plane
35

As seen in Fig. 3.3, the three models listed above show an excellent agreement in calculated pin fission 

density. The differences in data obtained with these models are small, below 1% between their predictions 

for all the pins, and are hardly visible on the plot. The statistical errors are negligibly small (~0.1%) and 

are not shown. The fission density peaks in pin 36, which is the furthest from the BP pins. It is interesting 

to notice the parabolic shape of the fission density distribution in each row of pins; a parabolic fit of the 

data points resulted in a goodness-of-fit coefficient (R2 value) better than 0.99. The parabolic shape 

distribution of the fission source density is important, as it provides grounds for the use of a (secondorder) polynomial function in x and y to describe the neutron flux in a nodal code. Fig. 3.3 shows the 

fitting parabolas for the SCALE/KENO-VI CE values only; the shapes for the other two models are 

similar.

The axial fission density distribution takes a cosine shape with a minimum at the middle of the pin (as 

opposed to an LWR fission density distribution, which usually peaks at the middle) when the fuel pin is 

far from the BP pins. However, the fission density is “W” shaped for fuel pins near the BP pin as a result 

of the graphite region in the middle of the BP pins, as illustrated in Fig. 3.4 for pin 12 (symmetric with 

pin 72), which is located near the BP pin. The same good agreement (differences no larger than 1%) 

between SCALE/KENO-VI values and MCNP values as seen axially was also observed radially.

Fig. 3.4. Axial fission density distribution in pin 12 of the HTTR fuel block.

As seen for the multiplication constant, the use of a periodic boundary condition instead of a reflective 

one leads to large changes in fission density distribution, by as much as 7% for pin 36, which is near the 

empty BP location. For a periodic boundary condition, the fission density has almost equal values in 

pins 13, 36, and 41. Also, this boundary condition leads to a flatter pin fission density distribution 

throughout the fuel block. The large differences in fission density distribution, together with the large 

difference in the multiplication eigenvalue predicted with the periodic boundary condition, demonstrate 

the importance of using the correct boundary conditions for the fuel block calculations.

-3.9 0.0 3.9 7.8 11.7 15.6 19.5 23.4 27.3 31.2 35.1 39.0 42.9 46.8 50.7 54.6 58.5

0.94

0.96

0.98

1.00

1.02

1.04

1.06

1.08

1.10

1.12

Fission Density

z (cm)

KENO-CE

KENO-MG

MCNP5
36

3.2 ANALYSIS OF CONFIGURATIONS CONTAINING HTTR FUEL BLOCKS

A number of core configurations built with HTTR-like fuel blocks were analyzed with SCALE/KENO-VI 

to assess the effect on keff of gradual changes in these configurations, from simpler to more complex 

cores. It also served in assessing the effect on keff results of SCALE/KENO-VI modeling assumptions as 

a function of core complexity. The considered cores consisted of four quasi–2-D problems (labeled 

“Core 1” through “Core 4” and described below) that resemble one-block layers of the HTTR core.

3.2.1 Core 1

This problem consisted of 6.3% enriched identical HTTR fuel blocks arranged in five rings (counting also 

the central block as a ring), surrounded by one ring of radial reflector blocks as shown in Fig. 3.5. All the 

fuel blocks had the same rotational orientation. Vacuum boundary conditions were assumed for the lateral 

surfaces, and reflective boundary conditions were used for the top and bottom surfaces. This 

configuration would be a difficult problem for a diffusion code because of the large lateral leakage.

Fig. 3.5. Horizontal layout of Core 1.

The multiplication constants obtained for this configuration with the multigroup and continuous energy 

SCALE/KENO-VI models are shown in Table 3.5. As seen, the difference between the multigroup and 

the continuous energy models is

Δk = kMG – kCE = -219 ± 38 pcm .
37

Table 3.5. Multiplication constants for Core 1

Model k a eff σ

SCALE/KENO-VI MG

b

1.21715 0.00023

SCALE/KENO-VI CE 1.21934 0.00030 a MG = multigroup; CE = continuous energy. b Standard deviation of keff.

3.2.2 Core 2

The Core 2 problem is similar to the Core 1 problem, but contains four rings of fuel blocks and two rings 

of radial graphite blocks, as illustrated in Fig. 3.6. This configuration, therefore, diminishes the lateral 

neutron leakage by increasing the amount of reflector graphite, compared to Core 1. Vacuum boundary 

conditions are used on the outer lateral surfaces, and reflective boundary conditions are applied at the top 

and bottom of the configuration. The multiplication constants obtained for this configuration, for which 

both continuous energy and multigroup models were created, are shown in Table 3.6. The difference 

between the multigroup and the continuous energy models is

Δk = kMG – kCE = -294 ± 36 pcm .

Fig. 3.6. Horizontal layout of Core 2 showing the radial tally regions.

Table 3.6. Multiplication constants for Core 2

Model k a eff σ

SCALE/KENO-VI MG

b

1.20879 0.00024

SCALE/KENO-VI CE 1.21173 0.00027 a MG = multigroup; CE = continuous energy. b Standard deviation of keff.
38

In addition to the multiplication constants, the radial distribution of the neutron scalar flux in 23 groups

was calculated for this configuration. The flux results are presented in Table 3.7 and illustrated in Fig. 3.7.

For the purpose of this calculation, the test problem was divided into seven concentric rings (see 

Fig. 3.6)—a central fuel block, three fuel rings numbered 1 to 3, two reflector rings, and the outer void.

Each column of Table 3.7 and each curve on the plot in Fig. 3.7 correspond to one of these regions. The 

SCALE/KENO-VI transport calculation was performed using a 238-group cross-section library, and the 

obtained 238-group fluxes were later collapsed to 23 groups.

The neutron spectrum in the central fuel block is almost identical with that in the first ring blocks and 

therefore is barely distinguishable on Fig. 3.7. As observed, the 23-group spectrum in the four radial 

regions that contain fuel is fairly constant. The highest thermal spectrum is obtained in the first ring of 

radial reflector. The flux decreases rapidly, by about one order of magnitude, outside the core (the void 

region, made up of the triangular regions just outside of the radial reflector).

Table 3.7. Flux spectrum in 23-group structure for Core 2

Group

#

Upper Energy

(eV)

Center

Fuel Block

Ring 1

Fuel

Ring 2

Fuel

Ring 3

Fuel

Reflector

Ring 1

Reflector

Ring 2

Outer

Void

1 2.00E+07 1.48E-13 1.40E-13 1.20E-13 9.36E-14 1.06E-14 5.37E-16 1.01E-16

2 3.00E+06 5.08E-12 4.79E-12 4.12E-12 3.16E-12 3.78E-13 1.30E-14 1.54E-15

3 1.36E+06 1.48E-11 1.40E-11 1.20E-11 9.00E-12 1.28E-12 4.46E-14 3.47E-15

4 5.00E+05 4.29E-11 4.05E-11 3.48E-11 2.54E-11 4.19E-12 1.56E-13 9.10E-15

5 1.00E+05 1.24E-10 1.17E-10 1.00E-10 7.19E-11 1.33E-11 5.32E-13 2.98E-14

6 6.00E+04 3.38E-10 3.19E-10 2.74E-10 1.93E-10 4.00E-11 1.75E-12 8.90E-14

7 9.50E+03 3.31E-09 3.12E-09 2.68E-09 1.83E-09 4.56E-10 2.55E-11 1.30E-12

8 3.05E+02 1.11E-07 1.05E-07 8.98E-08 6.01E-08 1.93E-08 1.53E-09 8.79E-11

9 4.00E+00 2.72E-06 2.56E-06 2.18E-06 1.46E-06 5.69E-07 5.64E-08 3.31E-09

10 1.50E+00 5.45E-06 5.16E-06 4.39E-06 2.95E-06 1.16E-06 1.22E-07 8.11E-09

11 1.10E+00 6.61E-06 6.24E-06 5.31E-06 3.57E-06 1.42E-06 1.52E-07 9.35E-09

12 1.05E+00 7.11E-06 6.70E-06 5.70E-06 3.83E-06 1.53E-06 1.65E-07 9.63E-09

13 9.75E-01 7.93E-06 7.47E-06 6.36E-06 4.28E-06 1.72E-06 1.86E-07 1.16E-08

14 8.50E-01 1.15E-05 1.09E-05 9.23E-06 6.22E-06 2.52E-06 2.84E-07 1.77E-08

15 5.00E-01 1.82E-05 1.71E-05 1.46E-05 9.80E-06 4.08E-06 4.77E-07 3.24E-08

16 4.00E-01 2.28E-05 2.16E-05 1.83E-05 1.24E-05 5.25E-06 6.34E-07 4.32E-08

17 3.50E-01 2.77E-05 2.62E-05 2.22E-05 1.51E-05 6.57E-06 8.30E-07 6.01E-08

18 3.00E-01 3.55E-05 3.35E-05 2.84E-05 1.93E-05 9.01E-06 1.27E-06 9.38E-08

19 2.50E-01 5.76E-05 5.43E-05 4.60E-05 3.24E-05 1.86E-05 3.79E-06 3.45E-07

20 1.75E-01 9.52E-05 8.92E-05 7.57E-05 5.60E-05 4.12E-05 1.10E-05 1.09E-06

21 1.50E-01 1.58E-04 1.49E-04 1.27E-04 1.01E-04 9.80E-05 3.14E-05 3.33E-06

22 1.00E-01 3.04E-04 2.86E-04 2.44E-04 2.19E-04 3.06E-04 1.14E-04 1.22E-05

23 5.00E-02 2.71E-04 2.55E-04 2.19E-04 2.29E-04 4.72E-04 1.95E-04 2.09E-05
39

Fig. 3.7. Flux distribution (23-group) in radial regions of Core 2.

3.2.3 Core 3

The Core 3 problem represents the same fuel block distribution as in the midplane of the actual HTTR 

core, but has two rings of radial graphite. The control rod blocks in the real HTTR midplane were 

replaced with graphite blocks. This configuration, therefore, adds an additional level of heterogeneity 

over the previous Core 2. As for the previous cases, vacuum boundary conditions were iused on the 

lateral surface and reflective boundary conditions at the top and bottom of the configuration. 

This configuration was used to assess the importance of a correct modeling of the fuel block orientation 

on the keff results for the core. As illustrated in Fig 3.8, two cases were studied: (1) a case labeled

“rotated” that corresponds to the actual arrangement of the fuel blocks at the middle of the HTTR core

and (2) a case labeled “not rotated” that corresponds to a hypothetical arrangement of the fuel blocks, in 

which these have a fixed orientation.

The results for the multiplication constants for the two cases, each case assessed with both the multigroup 

and the continuous energy models, are presented in Table 3.8. As observed, the “not rotated” setup leads 

to a significant increase, of approximately 1% (or 1000 pcm), in the multiplication constant. The

difference between the multigroup and the continuous energy models for the correct configuration 

(“rotated”) is

Δk = kMG – kCE = -351 ± 39 pcm .

The difference between the “rotated” and the “not rotated” cases is significant. The large difference 

between these two cases can be explained by carefully inspecting the corresponding input files and 

configurations details. As seen in the detailed configuration in Fig. 3.9, there are four instances in the 

“not rotated” case in which the boron pin (BP) positions (marked with a red circle, as opposed to the 

empty position, which is yellow) are close to each other. This creates a “shadowing” effect between the 

two BP pins, which reduces their effectiveness as a neutron absorber. In other words, the two neighbors 

1.E-16

1.E-15

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08

Energy (eV)

Flux Spectrum (n/cmsq/s/eV)

center

ring 1

ring 2

ring 3

reflector 1

reflector 2

void
40

compete for the same thermal neutrons. This leads to a decrease in the absorption rate and, consequently,

to an increase in keff for the “not rotated” case.

Fig. 3.8. Horizontal layout of Core 3 with (a) “rotated” and (b) “not rotated” configurations.

Table 3.8. Multiplication constants for Core 3

Model a Rotated blocks Not rotated blocks

keff σ k b eff σ

SCALE/KENO-VI MG

b

1.17700 0.00024 1.18843 0.00027

SCALE/KENO-VI CE 1.18051 0.00031 1.19117 0.00031 a MG = multigroup; CE = continuous energy. b Standard deviation of keff.

a b
41

Fig. 3.9. Detail of Core 3 for (a) “rotated” and (b) “not rotated” setups.

3.2.4 Core 4

The Core 4 problem, illustrated in Fig. 3.10, represents the same fuel block distribution as in the midplane 

of the real HTTR core, with two rings of radial graphite. Compared to Core 3, the control rod blocks as in 

the real HTTR midplane were explicitly modeled. This configuration, therefore, further adds a level of 

heterogeneity over the previous Core 3. As for the previous cases, vacuum boundary conditions were 

applied on the lateral surface and reflective boundary conditions at the top and bottom of the 

configuration.

The multiplication constants obtained for Core 4 for two cases—with control rods in and control rods out,

for which both continuous energy and multigroup models were created—are presented in Table 3.9. The 

difference between the multigroup and the continuous energy models is

Δk = kMG – kCE

Δk = k

= -307 ± 35 pcm (control rods out) ,

MG – kCE = -268 ± 38 pcm (control rods in) .

The data for control rods reactivity insertions, ρ, are presented in Table 3.10. The value for ρ was 

calculated as

ρ = keff

CRin − keffCRout

keff

CRinkeffCRout

The difference in reactivity calculated with multigroup and continuous energy models is Δρ = 0.00158 or 

0.5%.

a b
42

Fig. 3.10. Horizontal layout of Core 4 (with control rods in).

Table 3.9. Multiplication constants for Core 4

Model a Control Rods Out Control Rods In

keff σ k b eff σ

SCALE/KENO-VI MG 1.16964 0.00023 0.83638 0.00021

SCALE/KENO-VI CE 1.17271 0.00027 0.83906 0.00032 a MG = multigroup; CE = continuous energy. b Standard deviation of keff.

Table 3.10. Control rods reactivity for Core 4

Model Reactivity a

SCALE/KENO-VI MG -0.34066

SCALE/KENO-VI CE -0.33908 a MG = multigroup; CE = continuous energy. b Standard deviation of reactivity.

For the two Core 4 configurations, with control rods out and control rods in, the flux spectrum was 

evaluated on a radial meshing similar with the one used for Core 2—that is, concentric rings. The 

calculated 238-group flux was collapsed to a 23-group structure and volume-averaged over the concentric 

rings. The flux results are shown in Table 3.11 and illustrated in Fig. 3.11 for the case with control rods 

out. The data for the case with the control rods fully inserted are shown in Table 3.12 and illustrated in 

Fig. 3.12.
43

Table 3.11. Flux spectrum (23-group) for radial regions of Core 4 (control rods out)

Group

#

Upper Energy

(eV)

Center

Fuel Block

Ring 1

Fuel

Ring 2

Fuel

Ring 3

Fuel

Reflector

Ring 1

Reflector

Ring 2

Outer

Void

1 2.00E+07 6.59E-14 1.41E-13 1.01E-13 1.15E-13 1.26E-14 6.25E-16 1.14E-16

2 3.00E+06 2.39E-12 4.75E-12 3.50E-12 3.87E-12 4.54E-13 1.54E-14 1.62E-15

3 1.36E+06 7.82E-12 1.36E-11 1.04E-11 1.08E-11 1.52E-12 5.39E-14 4.34E-15

4 5.00E+05 2.54E-11 3.88E-11 3.11E-11 3.01E-11 5.02E-12 1.86E-13 1.22E-14

5 1.00E+05 7.98E-11 1.10E-10 9.16E-11 8.40E-11 1.60E-11 6.34E-13 3.68E-14

6 6.00E+04 2.36E-10 2.98E-10 2.56E-10 2.22E-10 4.80E-11 2.10E-12 1.09E-13

7 9.50E+03 2.58E-09 2.88E-09 2.58E-09 2.07E-09 5.47E-10 3.04E-11 1.54E-12

8 3.05E+02 1.02E-07 9.80E-08 9.25E-08 6.75E-08 2.31E-08 1.83E-09 1.04E-10

9 4.00E+00 2.80E-06 2.45E-06 2.40E-06 1.66E-06 6.82E-07 6.77E-08 4.06E-09

10 1.50E+00 5.64E-06 4.98E-06 4.84E-06 3.36E-06 1.40E-06 1.47E-07 9.10E-09

11 1.10E+00 6.84E-06 6.06E-06 5.85E-06 4.05E-06 1.70E-06 1.81E-07 1.07E-08

12 1.05E+00 7.35E-06 6.50E-06 6.31E-06 4.38E-06 1.83E-06 1.99E-07 1.27E-08

13 9.75E-01 8.20E-06 7.28E-06 7.04E-06 4.89E-06 2.05E-06 2.23E-07 1.36E-08

14 8.50E-01 1.20E-05 1.06E-05 1.02E-05 7.09E-06 3.02E-06 3.40E-07 2.15E-08

15 5.00E-01 1.91E-05 1.69E-05 1.63E-05 1.13E-05 4.89E-06 5.74E-07 3.62E-08

16 4.00E-01 2.43E-05 2.14E-05 2.06E-05 1.42E-05 6.28E-06 7.58E-07 5.19E-08

17 3.50E-01 3.02E-05 2.62E-05 2.53E-05 1.73E-05 7.89E-06 1.00E-06 6.50E-08

18 3.00E-01 3.95E-05 3.40E-05 3.30E-05 2.24E-05 1.08E-05 1.55E-06 1.15E-07

19 2.50E-01 6.98E-05 5.80E-05 5.66E-05 3.85E-05 2.28E-05 4.69E-06 4.31E-07

20 1.75E-01 1.29E-04 1.02E-04 1.01E-04 6.93E-05 5.14E-05 1.37E-05 1.43E-06

21 1.50E-01 2.52E-04 1.89E-04 1.89E-04 1.31E-04 1.24E-04 3.96E-05 4.16E-06

22 1.00E-01 6.27E-04 4.27E-04 4.43E-04 3.11E-04 3.95E-04 1.44E-04 1.53E-05

23 5.00E-02 7.90E-04 4.62E-04 5.15E-04 3.53E-04 6.17E-04 2.46E-04 2.63E-05

Fig. 3.11. Flux distribution (23-group) in radial regions of Core 4 (control rods out).

1.E-16

1.E-15

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08

Energy (eV)

Flux Spectrum (n/cm2/s/eV)

center

ring 1

ring 2

ring 3

reflector 1

reflector 2

void
44

Table 3.12. Flux spectrum (23-group) for radial regions of Core 4 (control rods in)

Group

#

Upper Energy

(eV)

Center

Fuel Block

Ring 1

Fuel

Ring 2

Fuel

Ring 3

Fuel

Reflector

Ring 1

Reflector

Ring 2

Outer

Void

1 2.00E+07 3.82E-14 1.05E-13 8.15E-14 1.30E-13 1.61E-14 7.81E-16 1.47E-16

2 3.00E+06 1.41E-12 3.54E-12 2.81E-12 4.37E-12 5.84E-13 1.96E-14 2.03E-15

3 1.36E+06 4.94E-12 1.01E-11 8.58E-12 1.22E-11 1.96E-12 6.90E-14 5.86E-15

4 5.00E+05 1.62E-11 2.90E-11 2.57E-11 3.37E-11 6.40E-12 2.40E-13 1.47E-14

5 1.00E+05 5.12E-11 8.26E-11 7.58E-11 9.34E-11 2.03E-11 8.18E-13 4.49E-14

6 6.00E+04 1.47E-10 2.23E-10 2.09E-10 2.45E-10 6.05E-11 2.69E-12 1.42E-13

7 9.50E+03 1.46E-09 2.15E-09 2.01E-09 2.23E-09 6.79E-10 3.91E-11 1.99E-12

8 3.05E+02 4.31E-08 7.13E-08 6.19E-08 6.90E-08 2.80E-08 2.32E-09 1.27E-10

9 4.00E+00 9.86E-07 1.72E-06 1.43E-06 1.61E-06 8.16E-07 8.59E-08 5.20E-09

10 1.50E+00 1.90E-06 3.44E-06 2.82E-06 3.21E-06 1.66E-06 1.86E-07 1.14E-08

11 1.10E+00 2.26E-06 4.16E-06 3.41E-06 3.85E-06 2.03E-06 2.30E-07 1.18E-08

12 1.05E+00 2.44E-06 4.48E-06 3.64E-06 4.15E-06 2.17E-06 2.50E-07 1.58E-08

13 9.75E-01 2.73E-06 4.98E-06 4.05E-06 4.62E-06 2.45E-06 2.82E-07 1.68E-08

14 8.50E-01 3.87E-06 7.20E-06 5.82E-06 6.66E-06 3.59E-06 4.29E-07 2.88E-08

15 5.00E-01 6.03E-06 1.13E-05 9.11E-06 1.04E-05 5.79E-06 7.19E-07 4.66E-08

16 4.00E-01 7.65E-06 1.43E-05 1.14E-05 1.31E-05 7.43E-06 9.52E-07 6.15E-08

17 3.50E-01 9.40E-06 1.74E-05 1.39E-05 1.59E-05 9.31E-06 1.25E-06 9.31E-08

18 3.00E-01 1.20E-05 2.23E-05 1.77E-05 2.04E-05 1.28E-05 1.92E-06 1.45E-07

19 2.50E-01 1.98E-05 3.65E-05 2.88E-05 3.41E-05 2.64E-05 5.63E-06 5.17E-07

20 1.75E-01 3.36E-05 6.11E-05 4.80E-05 5.95E-05 5.88E-05 1.61E-05 1.59E-06

21 1.50E-01 5.94E-05 1.06E-04 8.27E-05 1.10E-04 1.40E-04 4.61E-05 4.88E-06

22 1.00E-01 1.29E-04 2.18E-04 1.70E-04 2.53E-04 4.42E-04 1.67E-04 1.79E-05

23 5.00E-02 1.42E-04 2.15E-04 1.72E-04 2.85E-04 6.87E-04 2.84E-04 3.05E-05

Fig. 3.12. Flux distribution (23-group) in radial regions of Core 4 (control rods in).

1.E-16

1.E-15

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08

Energy (eV)

Flux Spectrum (n/cm2/s/eV)

center

ring 1

ring 2

ring 3

reflector 1

reflector 2

void
45

3.3 ANALYSIS OF HTTR FULL CORE BENCHMARK EXPERIMENTS

3.3.1 Description of the HTTR Core

The HTTR core consists of fuel blocks that use TRISO fuel with 12 different fuel enrichments, between 

3.4 and 9.9 wt % 235U, grouped into four fuel zones. These fuel blocks are arranged axially in five-block 

columns for a total active height of 290 cm. The four fuel zones are intermixed with control rod columns 

and are surrounded by reflector blocks, as illustrated in Fig. 3.13 that shows a cross-sectional view of the 

HTTR fully loaded core (30 fuel columns).

The control rods, made of B4C, are operated in pairs. Each pair of control rods occupies two of the three 

available channels in each control rod guide column. There are a total of 16 pairs of control rods in the 

HTTR core. The third hollow position in each of the control rod guide columns can be used as a reserved 

shutdown pellet insertion hole. These pellets, also made of B4C, can be released into the holes under 

gravity as a backup mechanism for emergency shutdown.

In addition to the fuel and control blocks, the active core also contains three columns reserved for 

irradiation tests and 12 replaceable reflector columns.

The IG-110 graphite used in the fabrication of the fuel blocks, control rod blocks, irradiation blocks, and 

replaceable reflector blocks is a high purity graphite with an equivalent boron content (EBC) less than 

1 ppm. The EBC of the PGX graphite that is used for the permanent reflector is under 5 ppm. During the 

approach to criticality, dummy graphite blocks are also used to replace the fuel blocks. These blocks are 

fabricated from IG-11 graphite, which also has an EBC under 5 ppm.

The main characteristics of the HTTR core are summarized in Table 3.13. Details about the fuel type and 

fuel assembly have been included in Tables 3.1 and 3.2 of this report.
46

Fuel zones: 1, 2, 3, 4

Control rods: C central

 R1 ring 1

 R2 ring 2

 R3 ring 3

I Instrumentation column

RR Replaceable reflector column

Fig. 3.13. Fully loaded HTTR core configuration.

Permanent reflector graphite

C

R1

R1

R1

R1

R1

R1

R2

R2

R2 R2

R2

R2

R3

R3 R3

I I

I

RR RR

RR

RR

RR

RR

RR

RR RR

RR

RR

RR

1

1 1

1 1

1

2 2

2 2

2 2

3

3

3

3

3

3

3 3

3 3

3 3

4

4

4

4

4

4
47

Table 3.13. Main characteristics of the HTTR core

Parameter Value

Thermal power (MW) 30

Inlet temperature (°C) 395

Maximum outlet temperature (°C) 950

Fuel type TRISO in prismatic blocks

Number of fuel columns 30

Number of fuel blocks per column 5

Fuel enrichment (wt % 235U) 3.4 to 9.9

Moderator Graphite

Coolant Helium

3.3.2 Experimental Data

The experimental data used for validation in this report were taken from the HHTR benchmarks included 

in the IRPhE Handbook [6,7,8,9]. The following data were analyzed in this report:

• Criticality measurements for fully loaded (30 fuel columns) or partially loaded (19–27 fuel 

columns) critical core configurations

• Criticality measurements for full core subcritical configuration (30 fuel columns, all control rods 

fully inserted)

• Shutdown margin

• Excess reactivity

• Control rod worths

• Isothermal reactivity coefficients

Details about the measured data are provided in the section discussing the calculation-to-experiment 

comparison. 

3.3.3 Computational Models for HTTR Core Configurations

For the HTTR core simulations, detailed full core models were developed, based on IRPhE benchmark 

[6,7,8,9] descriptions, for both the continuous energy case and the multigroup case. Material composition 

data used for all HTTR simulations in this report are as provided in Ref. 6.The main difference between 

the multigroup and continuous energy models consists in the way that materials assigned to different 

regions are defined. In particular, for the multigroup model a homogeneous mixture is assigned as fuel, 

the cross sections for this homogeneous mixture being computed using the DOUBLEHET processing 

capability in SCALE (see Section 2.1.2). In the continuous energy model the fuel particles are represented 

in detail using a lattice representation for their distributions inside the fuel pins. Both multigroup and 

continuous energy cross-section sets that were used with SCALE for HTTR simulations are based on 

ENDF/B-VII data.

The SCALE/KENO-VI input files for the continuous energy model and the multigroup model of the full 

core HTTR (30 fuel columns) are included in Appendices A and B. The continuous energy model has 

about 1,600 lines of input, while the multigroup model contains approximately 1,700 lines. These include 

several lines of descriptive comments for better readability of the input.

The fresh core HTTR critical configurations differ by the number of fuel columns or the positions of the 

four banks of control rods. The positions of the tips of the control rod banks in the six critical core 

configurations considered, as measured from the bottom of the fuel, are listed in Table 3.14. 

Configuration 1 (19 fuel columns) uses mainly the central pair of control rods, whereas configuration 4 
48

(24 fuel columns) uses the control rods in rings 2 and 3 (F23 pattern). The other four configurations use 

an FS (flat standard) pattern, in which the control rods in ring 3 are fully withdrawn. 

The SCALE/KENO-VI model for the fully loaded (30 column) HTTR core is illustrated in Fig 3.13. The 

models for partially loaded cores are presented in Fig. 3.14. 

Table 3.14. Control rod positions for the six HTTR critical core configurations

Configurationa Control Rod Bankb

C

Position, Measured from the Bottom of the Fuel (mm)

R1 A.1 R2 A.2 R3

1 (19 columns) 1739 4050 3325 4050

2 (21 columns, FS) 2646 2646 2646 4049

3 (24 columns, FS) 2215 2215 2215 4049

4 (24 columns, F23) 4050 4050 1592 1592

5 (27 columns, FS) 1900 1900 1900 4050

6 (30 columns, FS) 1775 1775 1775 4049 a FS = Flat standard—control rods in ring 2 are fully withdrawn; F23 = pattern identification—uses control rods in rings 2 and 3. b C = Central control rod bank; R1, R2, and R3 are control rod banks in rings 1, 2, and 3 respectively.

Development of the HTTR core models included a series of investigations to assess the effect of various 

modeling assumptions on the results of the simulations. Some of these investigations are summarized 

further.
49

From left to right and top to bottom: 19 fuel columns, 21 fuel columns, 24 fuel columns (F23 pattern shown; 

the FS pattern differs through the control rod positions), and 27 fuel columns. The dummy graphite blocks 

(light green) are visible.

Fig. 3.14. Partially loaded HTTR core configurations.
50

3.3.3.2 Overcoat material simulation

The overcoat is the outermost layer of a TRISO particle. It is made of graphite with the same number 

density as the compact graphite matrix but with a 1.5 wt ppm of boron impurity, thus making it more 

absorbing than the compact graphite matrix, which has an EBC of 0.82 ppm. In a CE model, the fuel 

particles are modeled by means of a particle lattice in which the particles are represented using various 

arrangements. Given that the outer radius of a fuel particle including the overcoat material is 0.066 cm, 

issues arise when trying to fit the particles into the fuel compact using a simple cubic (SC) cell lattice 

arrangement. In the MCNP model of Ref. 6, the overcoat was simulated as an incomplete sphere of radius 

equal to the real radius (0.066 cm) but cut by the cube’s surfaces. This approach does not conserve the 

mass of overcoat material—it underestimates it, while overestimating the amount of compact matrix 

material.

A sensitivity analysis was conducted to assess the effect of different modeling approximations for the 

overcoat material in a detailed continuous energy model. The simple cubic lattice used in the simulations 

has a packing fraction of ~0.52. Four different approximations have been considered, as follows:

a) Using overcoat material everywhere outside the outer pyrolitic carbon layer (no compact matrix 

material)

b) Using compact matrix material everywhere outside the outer pyrolitic carbon layer (no overcoat 

material)

c) Using volume-homogenized overcoat and matrix material everywhere outside the outer pyrolitic 

carbon layer

d) Using a segregated representation of the overcoat and the compact, with the overcoat modeled as 

a cubical region (to fit within the cubical lattice cell)

The results of these simulations, all performed with the continuous energy HTTR core model, show a 

minimal impact on the eigenvalue result for the core, within 1σ from the MCNP reference value for cases 

a, c, and d, and within 2σ for case b. For all results reported in Section 3.3.4 of this report, assumption c 

as listed above was used in the models.

3.3.3.3 Fuel particle modeling in the continuous energy model

For a continuous energy model, the fuel particles are explicitly modeled by using a cubical lattice 

arrangement. When this lattice is positioned in a cylindrical or annular fuel pin, clipping might occur at 

the intersection of the fuel particle outer surface with the pin surfaces that might lead to fuel mass 

nonconservation.

To assess the maximum expected error resulting from this clipping in the lateral direction, calculations 

were performed to evaluate the variation of the multiplication constant with different modes of 

positioning the fuel particle lattice within the fuel pin. Because of the symmetry of the problem with 

respect to the x and y axes in a rectangular geometry, it is sufficient to assess the effect of the lattice 

shifting along one axis (say, x) that is perpendicular on the axial symmetry axis (z) of the cylindrical fuel 

pin. The reference case is considered the case when one grain of the lattice is centered at the geometrical 

center of the fuel pin. If this lattice is shifted with δx with respect to the reference, the multiplication 

constant will differ slightly from the corresponding reference value. All the calculations were performed 

using the full core CE model, and the shift of the particles was applied uniformly in all the pins of all the 

fuel blocks in the core model. The variation of the multiplication constant with respect to its reference 

value as a function of the shift (δx) is presented in Fig. 3.15. As noted from this figure, the maximum 

expected error caused by the positioning of the fuel particle lattice within the annular cylindrical fuel pin 

is ~150 pcm. The fitting curve in the figure shows a sinusoid-like shape. The period of this sinusoid 

(theoretically equal to the particle lattice pitch, ~0.11 cm) is confirmed through the fitting in Fig. 3.15.
51

Fig. 3.15. Variation of the multiplication constant with the fuel particle lattice positioning.

An alternative that avoids clipping would be to move those particles that intersect the pins’ surfaces inside 

the fuel volume, therefore carefully conserving the mass of the fuel. This procedure would require making 

the lattice pitch smaller, therefore having more cells within the same volume, to fit those particles that 

would have been clipped inside the pin’s volume. It would require additional work for the manual 

placement of the particles within the lattice or to automate this placement. However, as it was determined, 

the effect of using this approach is the same magnitude (~150 pcm) as the use of a regular cubical lattice 

arrangement discussed above. 

3.3.3.4 Fuel mass conservation in the continuous energy model

The sensitivity of the multiplication constant to fuel mass nonconservation is estimated by using the 

multigroup model of the HTTR core. The results of this estimation will indicate the effect of fuel mass 

nonconservation in a CE model, in which mass nonconservation may occur from the geometry 

representation of the fuel particle lattices. It can also indicate the effect on keff due to uncertainty in fuel 

mass specification in both CE and MG core models. For example, the precision (uncertainty) in the 

experimental determination of the mass of fuel per fuel pin is approximately ±3%. If a normal distribution 

is assumed for the distribution of mass of fuel in all fuel pins in the core, the resulting uncertainty in the 

mass of fuel in the core will be ~0.04%.

Because of the specifics of the multigroup model representation of fuel, the mass is always conserved 

exactly in this case compared to a CE model. Therefore, any applied change to this mass is exactly 

characterized. The fuel mass in the reference MG core model was perturbed slightly with respect to the 

reference mass value, and criticality calculations were carried out to determine the corresponding keff

values. The results are illustrated in Fig. 3.16, which presents the difference in keff

-100

-50

0

50

100

150

200

250

-0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08

δx (cm)

Δkeff (pcm)

as a function of percent 

fuel mass change. The fit of the calculated points in Fig. 3.16 to a straight line indicates that a 1% change 

in the mass of core fuel leads to a change of ~150 pcm in the core multiplication constant. 
52

Fig. 3.16. Variation of the multiplication constant with the core fuel mass.

3.3.3.5 Typical runtime 

All SCALE calculations summarized in Section 3.3.3 were performed on a 2.26 GHz Linux workstation 

with no code parallelization used. The typical runtime for different sensitivity studies for the full core 

continuous energy model was slightly under 19 hours when 11 million particles were simulated (for 

10 million active histories) to achieve typical statistical standard deviations in keff of ~30 pcm. 

Approximately 16 of these 19 hours were spent in particle tracking itself, while the rest of the time was 

the overhead needed for different tasks performed by the code. For the multigroup model with the same 

number of histories as for the continuous energy case, the runtime is ~4 times smaller, with ~4 hours 

needed for particle tracking.

For the other studies summarized in Section 3.3.4 of this report, however, the number of histories was 

increased tenfold to achieve better accuracy, below 10 pcm in the eigenvalue. There was a corresponding 

increase in the runtime (~5 days for continuous energy models).

3.3.4 Results

3.3.4.1 Multiplication constant for HTTR critical configurations

A comparison of the experimental and calculated keff values for the HTTR critical core benchmarks is 

presented in Table 3.15. As discussed in Section 3.3.3 of this report, there were six fresh core critical 

configurations (see Figs. 3.13 and 3.14). These configurations differ through the number of fuel columns 

or the positions of the four banks of control rods (see Table 3.14). 

Table 3.15 includes data calculated with MCNP, as reported in Ref. 7, and data calculated with SCALE in 

this report with both CE and MG models. As seen, both MCNP and SCALE results show a positive bias

compared to the experiment. Part of this bias may be due to uncertainty in material data used in the 

computational models. As evaluated in the IRPhE, the uncertainties in keff

-250

-200

-150

-100

-50

0

50

100

150

-0.6% -0.4% -0.2% 0.0% 0.2% 0.4% 0.6%

Δm/m0

Δkeff (pcm)

for the fully loaded core [7]

and for the annular cores [8] are in the range ~±1000 pcm. The most significant contributors to the 
53

evaluated uncertainties for the full-core keff are [7]: the IG-110 (core) graphite impurity, the PGX 

(reflector) graphite impurity, the 10B concentration (abundance) in BP rods, and the uncertainty in the fuel 

enrichment. Each of these have contributions to the uncertainty in keff in the range 145-442 pcm. 

Table 3.15. Calculated and experimental keff

Critical Configuration

for HTTR critical core configurations

Experimental MCNP a a SCALE6.1 (benchmark) CE

SCALE6.1

MG

1. 19 columns 1.0048 1.0276 (1) 1.01931 (10) 1.01753 (8)

2. 21 columns 1.0040 1.0297 (1) 1.02539 (9) 1.02323 (9)

3. 24 columns, FS 1.0035 1.0249 (1) 1.02120 (9) 1.01868 (8)

4. 24 columns, F23 1.0032 1.0287 (1) 1.02066 (9) 1.01827 (9)

5. 27 columns 1.0029 1.0218 (1) 1.01711 (10) 1.01445 (9)

6. 30 columns (fully loaded) 1.0025 1.0229 (1) 1.01847 (9) 1.01510 (8) a As provided in Refs. 7 and 8 for calculations performed with ENDF/B-VII cross sections. b The numbers in parentheses are statistical standard deviations affecting the last digit(s) of the result. For example, 1.01931 (10) should be 

read as 1.01931 ± 0.00010. 

The relative differences in keff for the six critical configurations are illustrated in Fig. 3.17, which shows 

these differences as a function of the number of fuel columns in the critical core. The average biases for 

the three simulations are 1473, 1735, and 2238 pcm for SCALE MG, SCALE CE, and MCNP, 

respectively. The standard deviation of these biases is approximately 300 pcm in each of these three

cases. The causes of these biases can range from insufficiently detailed benchmark specifications

(geometry, materials, etc.) of the critical states to the quality of the nuclear data used in simulations. The 

similarity of the curves in Fig. 3.17 indicates a possible cause of the deviation due to systematic issues. 

The difference between the SCALE continuous energy and multigroup models is synthesized in Fig. 3.18

for the six critical configurations. The plot shows the difference (in pcm) between the eigenvalue 

predicted by the continuous energy model and the eigenvalue predicted by the multigroup model and 

includes the statistical standard deviation for this difference. It is observed that this difference increases 

with the number of fuel columns used for the critical configuration. The maximum difference, for the full 

core (30 fuel columns), is slightly below 350 pcm.
54

Fig. 3.17. Variation of keff bias vs. number of fuel columns (critical core).

Fig. 3.18. Difference in keff calculated with the SCALE MG and CE models.

30, -337

19, -178

21, -216

27, -266 24, -252

24, -240

-400

-350

-300

-250

-200

-150

18 19 20 21 22 23 24 25 26 27 28 29 30 31

# fuel columns

Δk (pcm)
55

3.3.4.2 Multiplication constant for HTTR subcritical configurations

Subcritical configurations were obtained while approaching criticality during the initial fuel loading. 

Measurements are reported [7] for these configurations, as listed in Table 3.16, but the description of 

these configurations lacks the position of the control rods. As mentioned in Ref. 7, the control rods were 

most likely fully withdrawn for all these measurements. These configurations were not simulated with 

SCALE.

Table 3.16. Multiplication constants for subcritical 

configurations during the approach to criticality

# Subcritical Configuration Experimental k

1

eff

9 columns 0.9282

2 12 columns 0.9481

3 15 columns 0.9652

4 16 columns 0.9701

5 17 columns 0.9785

6 18 columns 0.9913

For the full core (30 fuel columns) subcritical configuration, the information in the HTTR benchmark 

report [7] is somehow contradictory: in the description of experiments (Chapter 1), the control rods are 

inserted to the bottom of the fuel; in later chapters (Chapters 3, 4), this subcritical configuration is said to 

have been obtained with the control rods fully inserted (55 mm below the bottom of the fuel). The value 

for the multiplication constant is given as 0.685 ± 0.010, and 0.6876 ± 0.0104 to account for bias in 

control instrumentation. The full core subcritical configuration simulated with SCALE for the current

study is the same as the full core critical configuration, but with the control rods fully inserted (55 mm 

below the bottom of the fuel). This configuration was modeled with both continuous energy and 

multigroup models. The results obtained are showed in Table 3.17.

Table 3.17. Multiplication constants for full core subcritical configuration

Subcritical Configuration Experimental keff MCNP a SCALE CE b SCALE MG c

30 columns, all CR fully inserted

d

0.6876 (1004) 0.6999 (1) 0.69760 (9) 0.69541 (8) a For the experimental result, the number in parenthesis represents the uncertainty as evaluated in Ref.7. All other numbers in 

parentheses are statistical standard deviations.

b As provided in Ref. 7, from calculations performed with ENDF/B-VII.0 cross sections.

As shown in Table 3.17, the SCALE results are marginally within the evaluated experimental uncertainty. 

As noted also for the critical configurations, both MCNP and SCALE calculations (CE and MG models) 

show a positive bias when compared with the experimental result, but SCALE results are slightly closer 

to the experiment than MCNP.

3.3.4.3 Excess reactivity

The excess reactivity of a reactor core is defined as the amount of reactivity of the reactor with no control 

devices inserted. It is a quantity that cannot be measured directly when defined as such, because the 

reactor cannot be brought to such a state (which typically would be prompt critical). Computationally, 

however, such a reactor state can be simulated. The excess reactivity ρ can be calculated as















 = × −

crit CRup k k

1 1

ρ 100

where kcrit is the multiplication constant corresponding to the critical configuration and kCRup is the 

multiplication constant corresponding to the reactor state with all the control rods fully withdrawn. The 
56

excess reactivity was calculated for each HTTR critical configuration by considering reactor states with 

the control rods fully withdrawn and with the control rods inserted so that a critical configuration is 

achieved. The “critical configuration” of the core was considered the core configuration with the control 

rods inserted as in the corresponding experimental critical configuration, although the multiplication 

constant produced by the calculation for such a configuration is not exactly unity. The results of these 

simulations are listed in Table 3.18. The statistical uncertainties for these calculations were negligible and 

were not included in the table. For the SCALE calculations, they were typically below 0.01% Δk/k, while 

for MCNP they were below 0.02% Δk/k. The experimental uncertainties, as provided in Ref. 7, are much 

larger, typically 25–30%. Details on the methods used to infer the so-called experimental excess reactivity 

shown in Table 3.18 are provided later in this section.

Table 3.18. Excess reactivity for different fuel loadings

Core loading Experimentala SCALE MG

(%Δk/k)

SCALE CE MCNP

(%Δk/k) C/Eb

(%)

-1 (%Δk/k) C/E-1

(%) (%Δk/k) C/E-1(%)

18 columns -0.9 ± 0.6 0.40 - 0.39 - - -

19 columns 1.5 ± 0.24 2.16 43.74 2.14 42.74 1.98 32.00

21 columns 4.0 ± 1.1 4.36 9.03 4.32 8.04 4.28 7.05

24 columns 7.7 ± 2.1 8.11 5.30 8.04 4.46 8.29 7.63

27 columns 10.7 ± 3.0 10.90 1.91 10.86 1.48 11.52 7.67

30 columns 12.0 ± 3.3 11.54 -3.87 11.44 -4.67 11.38 -11.79 a As provided in Ref. 7, from calculations performed with ENDF/B-VII.0 cross sections. b C = calculated value; E = experimental value.

From a literature search, there seems to be some ambiguity about the excess reactivity corresponding to 

the “19 columns” configuration. This excess reactivity is listed as 1.5% Δk/k in [33], but as 2.4% Δk/k in

[7]. The reason given in [7] for this value is that this reactivity represents “the cumulative worth of fuel 

addition from the subcritical 18-fuel-column core and the 19-fuel-column core.” This definition, however, 

would contradict the definition of excess reactivity given above. Therefore, the value 1.5% Δk/k as 

defined in [33] was included in Table 3.18. As observed in this table, the corresponding uncertainty of 

0.24% Δk/k for the 19 column core, as taken from [7], is significantly different (~16%) than the other 

uncertainty values in the table, and is possibly underestimated.

Further ambiguities exist for the value listed for the (subcritical) 18 column configuration excess 

reactivity. Reference [33] gives a value of -0.3% Δk/k, whereas reference [7] gives a value of -0.9% Δk/k, 

which is listed in Table 3.18. This later value is believed to be closer to the true value, given its agreement 

with the multiplication constant listed in Table 3.16. 

Because the “excess reactivity” for the 18-column core is, in fact, a “reactivity deficit,” the configuration 

being subcritical, a particular approach was assumed to calculate the reactivity with SCALE in this case, 

as further described. First, the multiplication constant for the configuration with all the control rods fully 

withdrawn was calculated, as one would calculate for the excess reactivity. Then, this multiplication 

constant was corrected with the bias inferred from the 19 column critical core result in Table 3.15 (the 

multiplication constants listed in Table 3.15 correspond to critical configurations, hence the true k should 

be exactly 1). Therefore, the reactivity was calculated as

















− − = × − 













 = × − ( 1)

1 100 1 1 100 1 18, 18 19

CRup crit

corrected

CRup k k k ρ

where 18

CRup k is the uncorrected value for the multiplication constant for the 18 column core configuration 

(all control rods fully withdrawn), and 19

crit k is the multiplication constant for the 19 column critical core 
57

as listed in Table 3.15. The quantity 1 19 kcrit − represents the code bias for the 19 column configuration,

whose applicability was extended for correcting the 18 column core multiplication constant.

The positive value (~0.4% Δk/k) predicted for the 18 column core reactivity using the procedure 

summarized above would lead to the conclusion that the core can reach criticality with only 18 fuel 

columns, which does not correspond to the reality. Note, in this context, that the correction underlined 

above is an a posteriori correction (it makes use of the knowledge of the criticality achieved with 19 fuel 

columns) and therefore has no merit in predicting the first criticality of the HTTR core.

As inferred from Table 3.18, the departure from the experiment of the calculated values (C/E-1) shows a 

decreasing trend with the increase in the number of fuel columns and becomes negative (the computation 

underestimates the experiment) for the full core. As also observed in this table, there is excellent 

agreement between the MG and the CE predicted values for this later case.

The experimental procedure for measuring the excess reactivity assumed that a summation method from 

one critical state to the next was holding [7,33]. Experimentally, after each fuel addition (e.g., from 

21 fuel columns to 24 fuel columns), the control rods were inserted deeper into the core to maintain

criticality. The additional depth to which the control rods were inserted gave the additional reactivity 

excess that was added by the increase in the amount of fuel. According to Refs. 7 and 33, the reactivity 

was measured after each fuel addition using the inverse kinetics method. Neither of the above references 

describes this method. According to Ref. 33, the excess reactivity ρex was calculated as

= ∑∆

i

i

m ρ ex ρi R

where m ∆ρi is the increment in reactivity measured with the inverse kinetics method and Ri is a 

correction factor inferred through calculations using the following:

a

i

v

i Ri

ρ

ρ

∆

∆ =

In the above expression for Ri

v ∆ρi , is the increment in reactivity calculated with all the control rods 

fully withdrawn, and a ∆ρ i is the increment in reactivity for the actual control rod pattern for 

configuration i.

The evaluation procedure for the excess reactivity presented above indicates that the numbers presented

as “experimental” are not based purely on experimental measurements but also use corrections based on 

calculations. These corrections are necessary to account for the shadowing effect of the control rods.

Based on the described procedure, the incremental change in reactivity was evaluated in this report (i.e., 

the quantity i

m ∆ρi R for i = 24, 27, and 30) by considering the reactivity added through fuel addition (i.e., 

fuel addition to cores identified by i = 21, 24, and 27). The results are presented in Table 3.19.
58

Table 3.19. Incremental excess reactivity for different fuel loadings

Core fuel 

loading

Experimentala SCALE MG

(% Δk/k)

SCALE CE MCNP

(% Δk/k) C/Eb

(%)

-1 (% Δk/k) C/Ea

(%)

-1 (% Δk/k) C/Ea

(%)

-1

24 columns (FS) 3.7 ± 1.0 3.67 -0.0 3.67 -0.0 4.01 8.3

27 columns 3.0 ± 0.9 3.00 0.0 3.01 0.0 3.23 7.7

30 columns 1.3 ± 0.3 1.48 13.8 1.53 17.7 1.30 0.1 a As provided in Ref. 7, from calculations performed with ENDF/B-VII.0 cross sections. b C = calculated value; E = experimental value.

As observed in Table 3.19, the agreement between SCALE calculations and experiment is excellent for 

24 and 27 fuel columns configurations, but the difference is larger for the fully loaded (30 fuel columns) 

core. The opposite is true for the MCNP estimations [7]. All the SCALE calculations, however, are within 

the reported experimental uncertainties.

3.3.4.4 Shutdown margin

For the purpose of this analysis, the “shutdown margin” does not coincide with NRC’s definition of the 

shutdown margin. In NRC’s glossary of terms at http://www.nrc.gov, the shutdown margin is defined as 

“The instantaneous amount of reactivity by which the reactor is subcritical or would be subcritical from 

its present condition assuming all full-length rod cluster assemblies (shutdown and control) are fully 

inserted except for the single rod cluster assembly of highest reactivity worth that is assumed to be fully 

withdrawn.”

The shutdown margin, as used in this section and as measured experimentally, was evaluated for two 

shutdown cases on the fully loaded core configuration:

1. Reflector CR in. It is assumed that the central and first ring of control rods (C and R1 rods in 

Fig 3.13) maintain their position at a critical configuration, that is, 1775 mm above the bottom of 

the fuel blocks (Table 3.14), while the reflector rods (R2 and R3 in Fig 3.13) are fully inserted at

55 mm below the bottom of the fuel blocks.

2. All control rods fully inserted. At 55 mm below the bottom of the fuel blocks.

The reactivity insertion was calculated using the following relationship:















 = × −

CRin crit k k

1 1

ρ 100

where kcrit is the multiplication constant corresponding to the critical configuration and kCRin is the 

multiplication constant corresponding to any of the two shutdown configurations with the control rods 

inserted as mentioned above. Note that for a critical system, kcrit should be unity. However, because of 

code biases and approximations in the computational models, the computed value of this quantity can be 

different from unity. 

The results of the simulations are listed in Table 3.20 for both the CE and MG SCALE models, along 

with the experimental results and the MCNP simulation results as provided in Ref. 7. As seen, the 

agreement calculation–experiment is within the estimated experimental uncertainty for the case with all 

the control rods inserted. A larger difference in calculation–experiment is observed for the case where 

only the radial reflector control rods are inserted for all computational models. In both cases, the SCALE 

calculated data are in very good agreement with MCNP. Also, there is excellent agreement between the 

predictions of the MG and CE SCALE models.
59

Because the computational results for both SCALE models as well as for the MCNP model are in very 

good agreement, and because all three are quite far from the published experimental value for case 1 

(Reflector CR in), it is believed that the large difference calculation–experiment in this case is due to an 

inconsistency in the specification for control rod positions.

Table 3.20. Shutdown reactivities for full core configuration

# Configuration Experimental

(% Δk/k)

SCALE MG

(% Δk/k)

SCALE CE

(% Δk/k)

MCNP CE

(% Δk/k)

1 Reflector CR in -12.1 ± 0.6 -9.13 -9.06 -9.27

2 All CR in -46.3 ± 1.2 -45.29 -45.16 -46.59

The above discrepancy for the shutdown margin with reflector CR inserted is even larger for calculations 

performed by the Japanese [33] using a diffusion code: -8.6% Δk/k. The same code predicts a -

42.9% Δk/k shutdown margin for the case with all CR fully inserted, also significantly different from the 

reported experimental value.

3.3.4.5 Control rod worths

The worth of each control rod is an important parameter in reactor operation. Knowing the differential 

worth (calibration curve) of each control rod and/or bank of control rods allows for correct gauging of 

different reactivity effects. During normal operation, the core is assumed to be critical at all times. The 

reactivity inserted by different mechanisms such as fuel addition, temperature increase, xenon buildup, 

fuel depletion, etc. is compensated for by the movement of the control rods in such a way that the reactor 

is maintained critical. Therefore, measuring the insertion depth of the control rods allows for the 

estimation of the reactivity effects produced by different events, if the worth of the control rods is known 

as a function of their axial location.

The recent literature on HTTR experiments [7,8,33] mentions two types of control rod worth 

measurements. The first measurement is for the worth of a control rod at the center of the core. The 

description of this measurement, however, lacks important elements, and an attempt [6] to reproduce the 

experimental data was not successful. The set of data for the second experiment is described in [7] in the 

context of its use for the estimation of the reactivity coefficients and is presented as a calibration curve 

(reactivity as a function of the control rod position) for an FS pattern in the fully loaded core. The 

specification of the FS pattern is sufficient to fully characterize the core configuration.

Given the above considerations, it was only the second measurement that was modeled using the SCALE 

code system. The reference results were obtained by digitizing the experimental calibration curve in 

Figure 2.7 of [7]. The total reactivity worth of the control rods was evaluated by varying the position of 

the control rods in the fully loaded core. All control rods, except for those in ring R3 (Fig. 3.13) that were 

fully withdrawn, were moved synchronously, in an FS pattern. For each height of the control rods, the 

multiplication constant was calculated with SCALE. As used in Figure 2.7 of [7], the reference position

was considered for a control rod insertion height of ~186 cm. The quantity calculated was















 ≡ × − ∆

ref h k k k

k 1 1 % 100

where kref is the multiplication constant corresponding to the reference insertion (~186 cm) of the control 

rods and kh is the multiplication constant corresponding to the insertion height h.

The digitized experimental curve [7] and the corresponding data calculated with both MG and CE 

SCALE models are presented in Figure 3.19. The agreement between experiment and calculation is very 

good over the whole range of the measurements. A slight overprediction of the control rod worth can be 
60

seen in the mid range of the curve (corresponding to the control rod tip near the top of the fuel) and an 

underprediction in the high range (corresponding to the control rod tip in the top axial graphite, i.e., the 

control rod fully extracted). The agreement between the MG and CE models is very good.

Fig. 3.19. Control rod worth for the FS pattern.

The calculations illustrated in Fig. 3.19 were extended for the whole height of the reactor core, starting at 

-5.5 cm below the fuel bottom, although no experimental data were available for the full range. The 

results are illustrated in Fig. 3.20 for the CE models. The results for the MG models are similar to those 

for the corresponding CE models. The curves shown in Fig. 3.20 for 300 K can be used to assess the 

sensitivity of the CR reactivity insertion, �

∂ρ

dz�, as a function of the CR position. As observed from the 

slope of the curve, this sensitivity reaches a maximum at ~65 cm and decreases towards zero as the 

control rods are either extracted or inserted. It was calculated that for an insertion depth of ~65 cm, the 

sensitivity is very high, ~500 pcm/cm.

The calculated reactivity curves corresponding to an isothermal core temperature of 600 K is also 

represented in Fig. 3.20. Comparison of the 300 K and 600 K curves shows that the sensitivity of the CR 

reactivity insertion increases with the core temperature—that is, the CR becomes more effective at higher 

temperatures. No experimental data with which to validate the calculated results were available for the 

600 K temperature.

0

1

2

3

4

5

6

7

8

9

10

11

150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420

z (cm, CR tip position from bottom of fuel)

%Δk/k

%Δk/k experimental

%Δk/k CE, ENDF/B-VII

%Δk/k MG, ENDF/B-VII
61

Fig. 3.20. Control rod worth for the FS pattern at 300 K and 600 K.

3.3.4.6 Isothermal reactivity coefficients

The isothermal temperature coefficient of reactivity was calculated using the reference SCALE full core 

MG model, for a temperature range from 0 to 500 °C. The results are presented in Table 3.21 and 

illustrated in Fig. 3.21. These SCALE results are compared to the experimental data and to the MCNPcalculated data as reported in Ref. 9. The SCALE results illustrated in Fig. 3.21 were obtained for a fixed 

insertion depth of the control rods; the corresponding points in the plot were fitted with a linear function.

The SCALE results agree reasonably well with the experimental values and the MCNP-calculated values, 

even though the computational model did not account for the thermal dilation. As noted in Fig. 3.21, the 

computed values are generally within 1σ experimental uncertainty.

Table 3.21. Isothermal reactivity coefficients

T(°C) ∂ρ/∂T (pcm/°C) 

Experimental

∂ρ/∂T (pcm/°C) 

MCNP

∂ρ/∂T 

(pcm/°C)

SCALE MG

72.85 -12.3 (3.2) -11.6 (0.2) a -15.0 b

133.85 -13.2 (3.3) -12.8 (0.2) -14.7

147.85 -21.7 (13) -12.8 (0.2) -14.7

259.85 -16.5 (2.9) -12.9 (0.2) -14.1

368.85 -10.3 (2.8) -12.6 (0.2) -13.5

462.85 -8.6 (2.7) -12.1 (0.2) -13.1 a Data in parentheses correspond to 1σ experimental uncertainty. b Data in parentheses correspond to 1σ statistical uncertainty.

-50 0 50 100 150 200 250 300 350 400 450

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

% 

∆k/k

z (cm, CR tip position from bottom of fuel)

experimental

% dk/k, CE, 300K

% dk/k, CE, 600K
62

Fig. 3.21. Isothermal reactivity coefficients.

3.3.4.7 Flux and reaction rates distributions

Fully Loaded Core

Experimental fission rates for 235U were reported for the HTTR full core from measurements performed

using a fission chamber located at selected heights along the irradiation column [7]. However, no 

information was provided on the configuration of the fission chamber to facilitate an accurate 

representation of this chamber in the computational model. 

To facilitate a comparison of calculation and experiment to some extent, two types of data were extracted 

using the computational model: scalar flux distribution and reaction rate distribution, using some 

assumptions. Both the computational results and the measurement data were normalized to their largest 

value. In a first approximation, the relative scalar flux distribution (normalized to its maximum value) is 

similar to the relative reaction rate distribution, calculated as

( ) ( )

( ) ( ) ∫

∫

∞

∞

Σ Φ

Σ Φ

=

0

0 0

0

, ,

, ,

r E r E dE

r E r E dE

Rnorm

 

 

where Σ and Φ identify the macroscopic cross section and scalar flux, and r

 and E stand for neutron 

spatial location and energy. The quantity in the denominator represents the maximum reaction rate used 

for normalization. In the assumption that the macroscopic cross section is independent of position, the 

above ratio is identically equal with the normalized flux (expression shown below) if the flux is a 

separable function of position and energy. 

-35

-30

-25

-20

-15

-10

-5

0

0 50 100 150 200 250 300 350 400 450 500

T(°C)

∂ρ/∂T (pcm/°C)

SCALE6.1 MG Experimental MCNP
63

( )

( ) ∫

∫

∞

∞

Φ

Φ

Φ =

0

0

0

,

,

r E dE

r E dE

norm





The above assumption is equivalent to assuming that the spectrum of the neutrons reaching the fission 

chamber is virtually independent of the position of the chamber in the irradiation column.

Calculations were performed for all three positions reported [7] for the fission chamber location along the 

irradiation column, with both the continuous energy and the multigroup SCALE models. The comparison 

between the SCALE computed normalized scalar fluxes and the normalized experimental fission rates are

shown in Fig. 3.22. Three series of values for the flux are shown in the figure, corresponding to the three 

measurement locations. The agreement of calculation–experiment is consistent with the agreement 

observed between MCNP computations and experiment [7]. A possible cause of the observed difference 

between calculation and experiment may be that the experimental values were reported at shifted height 

values. This hypothesis is sustained by the fact that a shift of 10 cm in the location would bring the 

computed values in very good agreement with the experimental values, as illustrated in Fig. 3.23. The 

agreement between the flux distributions computed with the MG model and the CE model is excellent, as 

seen in Figs. 3.22 and 3.23.

Fig. 3.22. Multigroup and continuous energy flux distributions in the three channels and 

experimental points for 235

0.000

0.200

0.400

0.600

0.800

1.000

1.200

0 50 100 150 200 250 300 350 400

z (cm)

normalized Φ

normalized MG Φ1

normalized MG Φ2

normalized MG Φ3

normalized CE Φ1

normalized CE Φ2

normalized CE Φ3

Benchmark Reaction Rate

U(n,f) reaction rate.
64

Fig. 3.23. Multigroup and continuous energy flux distributions in the three channels and shifted 

experimental points for 235U(n,f) reaction rate.

0.000

0.200

0.400

0.600

0.800

1.000

1.200

0 50 100 150 200 250 300 350 400

z (cm)

normalized Φ

normalized MG Φ1

normalized MG Φ2

normalized MG Φ3

normalized CE Φ1

normalized CE Φ2

normalized CE Φ3

Benchmark Reaction Rate
65

In a second approximation, fission rates for 235U were estimated based on the computed values for the 

scalar fluxes and the 235U(n,f) infinite dilution (without resonance self-shielding) reaction cross-section 

data from the ENDF/B-VII.0 library. The normalized fission reaction rate thus computed is compared to 

the corresponding normalized scalar flux and the measurement data for one of the experiment locations, 

as illustrated in Fig. 3.24. This computed fission rate is labeled “normalized MG RR1” in the figure. 

Although the reaction rate seems to be closer to the experimental points, the difference is still large and 

cannot be explained by the use of a reaction rate in lieu of the flux.

Fig. 3.24. Multigroup flux and 235U(n,f) reaction rate computed distributions in channel 1 and the 

experimental point for 235U(n,f) reaction rate.

0.000

0.200

0.400

0.600

0.800

1.000

1.200

0 50 100 150 200 250 300 350 400

z (cm)

normalized Φ

normalized MG Φ1

Benchmark Reaction Rate

normalized MG RR1
66

Critical Configuration 3

The flux and reaction rate computations were also obtained for annular critical core 3 (24 fuel columns, 

with control rods in FS pattern). The agreement of calculation–experiment in this case, illustrated in 

Fig. 3.25, is similar to that seen for the full core. Again, the calculated reaction rates agree well with the 

experiment, and the agreement improves when a 10 cm shift is applied to the experiment location. As 

with the full core, there is practically no difference in results from SCALE MG and the CE simulations.

Fig. 3.25. Flux and 235U(n,f) reaction rate computed distributions in channel 1 and the experimental 

points for 235U(n,f) reaction rate for critical configuration 3.

0.000

0.200

0.400

0.600

0.800

1.000

1.200

0 50 100 150 200 250 300 350 400

z (cm)

normalized Φ

normalized MG Φ1

normalized CE Φ1

Benchmark Reaction Rate

normalized MG RR1
67

Critical Configuration 4

Flux and reaction rates were calculated for the annular critical core 4 (24 fuel columns, with control rods

in F23 pattern) and are compared to experimental data in Fig. 3.26. The agreement is excellent between 

the SCALE MG and the CE calculations. The calculated reaction rate, however, departs more from the 

flux distribution, meaning that the spectrum changes with the height on the irradiation column. The 

calculated reaction rate agrees better with the experiment than the scalar flux, as seen in Fig. 3.26. 

Fig. 3.26. Flux and 235U(n,f) reaction rate computed distributions in channel 1 and the experimental 

points for 235U(n,f) reaction rate for critical configuration 4.

0.000

0.200

0.400

0.600

0.800

1.000

1.200

0 50 100 150 200 250 300 350 400

z (cm)

normalized Φ

normalized MG Φ1

normalized CE Φ1

Benchmark Reaction Rate

normalized MG RR1

69

4. SUMMARY

This report documents verification and validation studies to assess the performance of the SCALE code 

system for analysis of HTGR configurations. The experimental data used for validation were available 

from the International Handbook of Evaluated Reactor Physics Benchmark Experiments for two different 

HTGR designs: prismatic and pebble bed. SCALE 3-D models have been developed for HTTR, a

prismatic fuel design reactor operated in Japan; HTR-10, a pebble bed reactor operated in China; and 

HTR-PROTEUS, a pebble bed configuration at the PROTEUS critical facility in Switzerland. The 

development of these models has involved a series of investigations to identify the particular issues 

associated with modeling the physics of the HTGRs and to understand and quantify the effect of 

particular modeling assumptions on calculation-to-experiment comparisons.

The 3-D simulations performed at the core level for the HTR-10 and HTTR cores were supplemented 

with investigations at the fuel pebble and fuel block level for better understanding of the underlying 

physics and for estimating the effects of the modeling assumptions and the cross-section data employed. 

In addition, four quasi 2-D configurations containing HTTR fuel blocks were studied to assess the effect 

on keff of gradual changes in the arrangement and orientation of fuel and moderator blocks, from simple 

to more complex cores. 

The SCALE calculations were performed using both continuous energy and multigroup (238-group) 

models, both based on ENDF/B-VII.0 nuclear data. The continuous energy model used an explicit 

representation of the fuel particles inside the fuel compacts. The multigroup model used the doubleheterogeneity feature incorporated in SCALE.

Comparisons of experiment data with calculations were performed for criticality measurements available 

for all three reactor configurations considered. In addition, subcritical HTTR experiments were analyzed 

with SCALE, as well as HTTR experiments for determining important safety parameters such as control 

rod worth, excess reactivity, shutdown margin, isothermal reactivity coefficients, and reaction rates. The 

SCALE results were also compared with the corresponding MCNP-calculated results reported in the 

literature. The results of the simulations showed a relatively good agreement between SCALE and MCNP

calculations. Both MCNP and SCALE consistently overestimated the experimental values of keff for all 

three cores and all criticality measurements considered. The calculation–experiment agreement is 

generally good for differential quantities such as control rod worth, shutdown margin, and excess 

reactivity. 

All experimental data used for validation in this report were obtained for cold cores at zero power and 

with fresh fuel. Conclusions on SCALE performance for these types of cores cannot be extended to 

analyses of higher temperature full-power cores without further confirmatory simulations. However, the 

models already developed and the lessons learned from the investigations performed would greatly 

facilitate such an additional benchmark effort when new measurement data become available.

71

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17. X-5 Monte Carlo Team, MCNP—A General N-Particle Transport Code, Version 5, Volume I: 

Overview and Theory, LA-UR-03-1987, Los Alamos National Laboratory, 2003.

18. V. Seker and U. Colak, “HTR-10 Full Core First Criticality Analysis with MCNP,” Nuclear 

Engineering and Design 222, 263 (2003).
72

19. Z. Wu, D. Lin, and D. Zhong, “The Design Features of the HTR-10,” Nuclear Engineering and 

Design 218, 22 (2002).

20. L. Yuanzhong and C. Jianzhu, “Fission Product Release and Its Environment Impact for Normal 

Reactor Operations and for Relevant Accidents,” Nuclear Engineering and Design 218, 81 (2002).

21. E. Teuchert, K. A. Haas, H. J. Rütten, H. Brockmann, H. Gerwin, U. Ohlig, and W. Scherer, 

V.S.O.P. Computer Code System for Reactor Physics and Fuel Cycle Simulation, JUL-2897, 

Forschungszentrum Jülich, 1994.

22. Evaluation of High Temperature Gas Cooled Reactor Performance: Benchmark Analysis Related to 

Initial Testing of HTTR and HTR-10, IAEA TECDOC 1382, International Atomic Energy Agency,

2003. Available on http://www.iaea.org/inisnkm/nkm/aws/htgr/fulltext/te_1382_web.pdf.

23. E. E. Sunny and G. Ilas, “SCALE 6 Analysis of HTR-10 Pebble-Bed Reactor for Initial Critical 

Configuration,” CD Proceedings, PHYSOR 2010, Pittsburgh, PA, 2010.

24. K. Tuli, Nuclear Wallet Card 2005, National Nuclear Data Center, Brookhaven National Laboratory, 

www.nndc.bnl.gov.

25. S. Shimakawa, M. Goto, S. Nakagawa, and Y. Tachibana, “Impact of Capture Cross-Section of 

Carbon on Nuclear Design for HTGRs,” CD Proceedings, HTR 2010, Prague, Czech Republic, 2010.

26. T. Williams, LEU-HTR-PROTEUS: Configuration Descriptions and Critical Balances for the Cores 

of the HTR-PROTEUS Experimental Programme, TM-41-95-18 (version 1), Paul Scherrer Institut, 

1996. 

27. D. Mathews and T. Williams, LEU-HTR-PROTEUS System Component Description, TM-41-93-43 

(version 2), Paul Scherrer Institut, 1996.

28. F. C. Difilippo, “Monte Carlo Calculations of Pebble Bed Benchmark Configurations of the 

PROTEUS Facility,” Nuclear Science and Engineering 143, 240 (2003).

29. Critical Experiments and Reactor Physics Calculations for Low Enriched High Temperature Gas 

Cooled Reactors, IAEA-TECDOC-1249, 2001.

30. E. Bomboni, N. Cerullo, and G. Lomonaco, “Analysis of Pebble-Fueled Zone Modeling Influence on 

High-Temperature Reactor Core Calculations,” Nuclear Science and Engineering 162, 282–298 

(2009).

31. D. Ilas and J. C. Gehin, “HTTR Fuel Block Simulations With SCALE,” CD Proceedings of PHYSOR 

2010 – Advances in Reactor Physics to Power the Nuclear Renaissance, Pittsburgh, PA, 2010.

32. J. Žáková and A. Talamo, “Criticallity assessment for prismatic high temperature reactors by fuel 

stochastic Monte Carlo modeling,” Annals of Nuclear Energy 35, 856–860 (2007).

33. N. Nojiri, S. Shimakawa, N. Fujimoto, and M. Goto, “Characteristic Test of Initial HTTR Core,” 

Nuclear Engineering and Design 233, 283–290 (2004).
73

APPENDIX A. 

SCALE CONTINUOUS ENERGY MODEL FOR HTTR
74
A-1

APPENDIX A. SCALE CONTINUOUS ENERGY MODEL FOR HTTR

=csas26 

Dan Ilas, 2009, 2010: HTTR core based on HTTR-GCR-RESR-001

ce_v7

' ---------------------------------------------------------------------------

' --- References:

' [1] John D. Bess, Nozomu Fujimoto: Evaluation of the Start-up Core Physics 

' Tests at Japan's High Temperature Engineering Test Reactor

' (Fully-Loaded Core), Revision 0, March, 2009

' ---------------------------------------------------------------------------

' --- Materials -------------------------------------------------------------

read comp 

' Material References:

' --------------------

' m=1 to 12 CFP fuel atom densities from Table 3.1, pag. 195 of [1]

' m=13 Buffer atom densities from Table 3.2, pag. 196 of [1]

' m=14 IPyC atom densities from Table 3.2, pag. 196 of [1]

' m=15 SiC atom densities from Table 3.2, pag. 196 of [1]

' m=16 OPyC atom densities from Table 3.2, pag. 196 of [1]

' m=17 Overcoat atom densities from Table 3.2, pag. 196 of [1]

' m=18 Compact atom densities from Table 3.3, pag. 196 of [1]

' m=19 Sleeve atom densities from Table 3.4, pag. 196 of [1]

' m=20 IG-110 atom densities from Table 3.6, pag. 197 of [1]

' by multiplying with 1.005

' m=21 Helium coolant from 3.1.3.10, page 199 of [1]

' m=22 Disks atom densities in BP pins from Table 3.5, pag. 197 of [1]

' m=23 BP atom densities (2.0%) from Table 3.5, pag. 197 of [1]

' m=24 BP atom densities (2.5%) from Table 3.5, pag. 197 of [1]

' m=25 PGX Graphite from Table 3.9, pag. 199 of [1]

' m=26 Absorber Compacts in CR from Table 3.7, pag. 198 of [1]

' m=27 Alloy 800H Clad in CR from Table 3.8, pag. 198 of [1]

'

' 

=============================================================================

' --- Fuel Kernel, 3.4% enrichment: 

 U-234 1 0 6.0946E-06 293.65 end

 U-235 1 0 7.9784E-04 293.65 end

 U-238 1 0 2.2376E-02 293.65 end

 O-16 1 0 4.6343E-02 293.65 end

 B-10 1 0 1.7276E-07 293.65 end

' --- Fuel Kernel, 3.9% enrichment: 

 U-234 2 0 6.9909E-06 293.65 end

 U-235 2 0 9.1517E-04 293.65 end

 U-238 2 0 2.2259E-02 293.65 end

 O-16 2 0 4.6343E-02 293.65 end

 B-10 2 0 1.7276E-07 293.65 end

' --- Fuel Kernel, 4.3% enrichment: 

 U-234 3 0 7.7079E-06 293.65 end

 U-235 3 0 1.0090E-03 293.65 end

 U-238 3 0 2.2166E-02 293.65 end

 O-16 3 0 4.6343E-02 293.65 end

 B-10 3 0 1.7276E-07 293.65 end

' --- Fuel Kernel, 4.8% enrichment: 
A-2

 U-234 4 0 8.6041E-06 293.65 end

 U-235 4 0 1.1264E-03 293.65 end

 U-238 4 0 2.2049E-02 293.65 end

 O-16 4 0 4.6343E-02 293.65 end

 B-10 4 0 1.7276E-07 293.65 end

' --- Fuel Kernel, 5.2% enrichment: 

 U-234 5 0 9.3211E-06 293.65 end

 U-235 5 0 1.2202E-03 293.65 end

 U-238 5 0 2.1955E-02 293.65 end

 O-16 5 0 4.6343E-02 293.65 end

 B-10 5 0 1.7276E-07 293.65 end

' --- Fuel Kernel, 5.9% enrichment: 

 U-234 6 0 1.0576E-05 293.65 end

 U-235 6 0 1.3845E-03 293.65 end

 U-238 6 0 2.1792E-02 293.65 end

 O-16 6 0 4.6343E-02 293.65 end

 B-10 6 0 1.7276E-07 293.65 end

' --- Fuel Kernel, 6.3% enrichment: 

 U-234 7 0 1.1293E-05 293.65 end

 U-235 7 0 1.4783E-03 293.65 end

 U-238 7 0 2.1699E-02 293.65 end

 O-16 7 0 4.6343E-02 293.65 end

 B-10 7 0 1.7276E-07 293.65 end

' --- Fuel Kernel, 6.7% enrichment: 

 U-234 8 0 1.2010E-05 293.65 end

 U-235 8 0 1.5722E-03 293.65 end

 U-238 8 0 2.1605E-02 293.65 end

 O-16 8 0 4.6343E-02 293.65 end

 B-10 8 0 1.7276E-07 293.65 end

' --- Fuel Kernel, 7.2% enrichment: 

 U-234 9 0 1.2906E-05 293.65 end

 U-235 9 0 1.6895E-03 293.65 end

 U-238 9 0 2.1489E-02 293.65 end

 O-16 9 0 4.6343E-02 293.65 end

 B-10 9 0 1.7276E-07 293.65 end

' --- Fuel Kernel, 7.9% enrichment: 

 U-234 10 0 1.4161E-05 293.65 end

 U-235 10 0 1.8538E-03 293.65 end

 U-238 10 0 2.1325E-02 293.65 end

 O-16 10 0 4.6343E-02 293.65 end

 B-10 10 0 1.7276E-07 293.65 end

' --- Fuel Kernel, 9.4% enrichment: 

 U-234 11 0 1.6850E-05 293.65 end

 U-235 11 0 2.2058E-03 293.65 end

 U-238 11 0 2.0975E-02 293.65 end

 O-16 11 0 4.6343E-02 293.65 end

 B-10 11 0 1.7276E-07 293.65 end

' --- Fuel Kernel, 9.9% enrichment: 

 U-234 12 0 1.7746E-05 293.65 end

 U-235 12 0 2.3231E-03 293.65 end

 U-238 12 0 2.0858E-02 293.65 end

 O-16 12 0 4.6343E-02 293.65 end

 B-10 12 0 1.7276E-07 293.65 end

' --- Buffer:

 C-graphite 13 0 5.5153E-02 293.65 end

 B-10 13 0 1.8290E-08 293.65 end

' --- IPyC:

 C-graphite 14 0 9.2758E-02 293.65 end
A-3

 B-10 14 0 3.0761E-08 293.65 end

' --- SiC:

 C-graphite 15 0 4.8061E-02 293.65 end

 Si 15 0 4.8061E-02 293.65 end

 B-10 15 0 5.3208E-08 293.65 end

' --- OPyC:

 C-graphite 16 0 9.2758E-02 293.65 end

B-10 16 0 3.0761E-08 293.65 end

' --- Graphite overcoat:

 C-graphite 17 0 8.5237E-02 293.65 end

 B-10 17 0 2.8267E-08 293.65 end

' --- Graphite compact:

 C-graphite 18 0 8.5237E-02 293.65 end

 B-10 18 0 1.5452E-08 293.65 end

' --- Graphite sleeve:

 C-graphite 19 0 8.8747E-02 293.65 end

 B-10 19 0 7.2596E-09 293.65 end

' --- IG-110 Graphite:

 C-graphite 20 0 8.8243E-02 293.65 end

 B-10 20 0 7.8036E-09 293.65 end

' --- Helium coolant:

 He 21 0 2.4616E-05 293.65 end

' --- Graphite disks:

 C-graphite 22 0 8.8747E-02 293.65 end

 B-10 22 0 7.2596E-09 293.65 end

' --- Burnable poison (2.0wt%):

 C-graphite 23 0 8.8446E-02 293.65 end

 B-10 23 0 3.9906E-04 293.65 end

 B-11 23 0 1.6063E-03 293.65 end

' --- Burnable poison (2.5wt%):

 C-graphite 24 0 8.7995E-02 293.65 end

 B-10 24 0 4.9882E-04 293.65 end

 B-11 24 0 2.0078E-03 293.65 end

' --- PGX Graphite:

 C-graphite 25 0 8.6134E-02 293.65 end

 B-10 25 0 3.6372E-08 293.65 end

' --- Absorber Compacts in CR:

 C-graphite 26 0 6.6685E-02 293.65 end

 B-10 26 0 6.8220E-03 293.65 end

 B-11 26 0 2.4974E-02 293.65 end

' --- Alloy 800H Clad in CR:

 C-graphite 27 0 3.2210E-04 293.65 end

 Al 27 0 6.7209E-04 293.65 end

 Si 27 0 6.0263E-04 293.65 end

 P 27 0 3.1225E-05 293.65 end

 S 27 0 1.5081E-05 293.65 end

 Ti 27 0 3.7884E-04 293.65 end

 Cr 27 0 1.9530E-02 293.65 end

 Mn 27 0 8.8022E-04 293.65 end

 Fe 27 0 3.8092E-02 293.65 end

 Ni 27 0 2.6777E-02 293.65 end

 Cu 27 0 2.2830E-04 293.65 end

' --- Helium coolant used in CR to mark the CR placement:

 He 28 0 2.4616E-05 293.65 end

end comp

' ---------------------------------------------------------------------------

' --- Parameters ------------------------------------------------------------
A-4

read parm 

 gen=1100

 npg=100000

 nsk=100

 tba=100

 htm=no

 flx=yes

 fdn=yes

end parm

' ---------------------------------------------------------------------------

' --- Geometry --------------------------------------------------------------

read geom

' Dimensions for block and pin details based on Figure 1.52 page 68 of [1]

' Counting of pins starts at the lower left corner, going horizontally and

' then vertically

' Dimensions for grain cells based on Figure 3.1 page 176 of [1]

'

' Numbering scheme for cells that make up fuel block units:

' zlb1 fuel grain

' zlb2 BP pin

' zlb3 fuel pin

' zlb4 central hole

' zlb5 empty pin

' zlb6 graphite

' zlb block

'

' Block numbering (Fig. 3.15, page 190 of [1]):

' Each block is numbered according to the scheme 100*z+10*l+b, where:

' z=1,...,8 zone number

' **Fuel: z=1,2 for zones 1 and 2, respectively

' z=3,5 alternatively as one goes 

counterclockwise

' for zone 3, z=4 for zone 4

' **Replaceable Reflectors in fuel columns follow the 

same

' pattern as fuel blocks, but with different l: 

l=1,2,8,9

' **CR: z=6 for "C" (b=1) and "R1" (b=2,...,7)

' z=7 for "R2" and "R3" (b=1,...,9, going 

' counterclockwise)

' **Instrumentation Blocks have z=8 (b=1,2,3)

' l=1,...,9 layer number from top to bottom

' (fuel blocks in layers 3 to 7 from top)

' b=1,...,bmax(z) block number (starting from positive x, counterclockwise)

' bmax(1)=...=bmax(5)=6

' bmax(6)=7, bmax(7)=9

' bmax(8)=3

' Replaceable Reflector (RR) blocks that are not in fuel columns are assigned

' block# 900

' Graphite blocks to make up the Permanent Reflector are assigned block# 100

'

'================ Graphite Block =================

unit 100

 rhexprism 1 18. 29. -29.

 media 25 1 1

 boundary 1

unit 10
A-5

 rhexprism 1 18. 261. -261.

 array 10 1 place 1 1 5 0.0 0.0 0.0

 boundary 1

'================ Fuel Column: Zone 1 Block 1 =================

'================ Block 111 =================

unit 1113

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 5

 media 20 1 6 -5

 boundary 6

unit 1114

 cone 1 2.5 29. 1.5 20.

 cylinder 2 1.5 20. 14.

 cylinder 3 2.25 14. 4.

 cylinder 4 2.505 29. -29.

 hexprism 5 2.575 29. -29.

 media 21 1 1

 media 21 1 2

 media 21 1 3

 media 20 1 4 -1 -2 -3

 media 20 1 5 -4

 boundary 5

unit 1116

 hexprism 1 2.575 29. -29.

 media 20 1 1

 boundary 1

unit 111

 rhexprism 1 18. 29. -29.

 array 111 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 131 =================

unit 1311

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 8 1 1

 media 13 1 2 -1

 media 14 1 3 -2

 media 15 1 4 -3

 media 16 1 5 -4

 media 17 1 6 -5

 boundary 6

unit 1312

 cylinder 1 0.7 5.2 -4.8

 cylinder 2 0.7 25.2 -24.8

 cylinder 3 0.75 25.2 -24.8

 cylinder 4 0.75 29. -29. 

 hexprism 5 2.575 29. -29.

 media 22 1 1

 media 23 1 2 -1

 media 21 1 3 -2

 media 20 1 4 -3

 media 20 1 5 -4

 boundary 5
A-6

unit 1313

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 1311 2 -1 place 13 13 248 0.0 0.0 0.0

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 1315

 cylinder 1 0.75 25.2 -24.8

 cylinder 2 0.75 29. -29. 

 hexprism 3 2.575 29. -29.

 media 21 1 1

 media 20 1 2 -1

 media 20 1 3 -2

 boundary 3

unit 131

 rhexprism 1 18. 29. -29.

 array 131 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 141 =================

unit 1411

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 5 1 1

 media 13 1 2 -1

 media 14 1 3 -2

 media 15 1 4 -3

 media 16 1 5 -4

media 17 1 6 -5

 boundary 6

unit 1412

 cylinder 1 0.7 5.2 -4.8

 cylinder 2 0.7 25.2 -24.8

 cylinder 3 0.75 25.2 -24.8

 cylinder 4 0.75 29. -29. 

 hexprism 5 2.575 29. -29.

 media 22 1 1

 media 24 1 2 -1

 media 21 1 3 -2

 media 20 1 4 -3

 media 20 1 5 -4

 boundary 5

unit 1413

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 1411 2 -1 place 13 13 248 0.0 0.0 0.0

 cylinder 3 1.325 27.45 -27.45
A-7

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 141

 rhexprism 1 18. 29. -29.

 array 141 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 151 =================

unit 1511

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 3 1 1

 media 13 1 2 -1

 media 14 1 3 -2

 media 15 1 4 -3

 media 16 1 5 -4

 media 17 1 6 -5

 boundary 6

unit 1513

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 1511 2 -1 place 13 13 248 0.0 0.0 0.0

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 151

 rhexprism 1 18. 29. -29.

 array 151 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 161 =================

unit 1611

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 1 1 1

 media 13 1 2 -1

 media 14 1 3 -2

 media 15 1 4 -3
A-8

 media 16 1 5 -4

 media 17 1 6 -5

 boundary 6

unit 1613

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 1611 2 -1 place 13 13 248 0.0 0.0 0.0

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 161

 rhexprism 1 18. 29. -29.

 array 161 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Generic fuel column for ring 1 =================

unit 110

 rhexprism 1 17. 261. -261.

 array 11 1 place 1 1 5 0.0 0.0 0.0

 boundary 1

'================ Ring 1: place the above-defined fuel column in six places 

====

unit 11

 rhexprism 1 18. 261. -261.

 hole 110 rotate a1=0

 media 20 1 1

 boundary 1

unit 12

 rhexprism 1 18. 261. -261.

 hole 110 rotate a1=60

 media 20 1 1

boundary 1

unit 13

 rhexprism 1 18. 261. -261.

 hole 110 rotate a1=120

 media 20 1 1

 boundary 1

unit 14

 rhexprism 1 18. 261. -261.

 hole 110 rotate a1=180

 media 20 1 1

 boundary 1

unit 15

 rhexprism 1 18. 261. -261.

 hole 110 rotate a1=240

 media 20 1 1

 boundary 1

unit 16

 rhexprism 1 18. 261. -261.

 hole 110 rotate a1=300

 media 20 1 1

 boundary 1
A-9

'================ Fuel Column: Zone 2 Block 1 =================

'================ Block 211 =================

unit 211

 rhexprism 1 18. 29. -29.

 array 211 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 231 =================

unit 2311

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 10 1 1

 media 13 1 2 -1

 media 14 1 3 -2

 media 15 1 4 -3

 media 16 1 5 -4

 media 17 1 6 -5

 boundary 6

unit 2313

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 2311 2 -1 place 13 13 248 0.0 0.0 0.0

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 231

 rhexprism 1 18. 29. -29.

 array 231 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 241 =================

unit 2411

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 7 1 1

 media 13 1 2 -1

 media 14 1 3 -2

 media 15 1 4 -3

 media 16 1 5 -4

 media 17 1 6 -5

 boundary 6

unit 2413

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 2411 2 -1 place 13 13 248 0.0 0.0 0.0
A-10

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 241

 rhexprism 1 18. 29. -29.

 array 241 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 251 =================

unit 2511

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 5 1 1

 media 13 1 2 -1

 media 14 1 3 -2

 media 15 1 4 -3

 media 16 1 5 -4

 media 17 1 6 -5

 boundary 6

unit 2513

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 2511 2 -1 place 13 13 248 0.0 0.0 0.0

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 251

 rhexprism 1 18. 29. -29.

 array 251 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 261 =================

unit 2611

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 2 1 1

 media 13 1 2 -1

 media 14 1 3 -2
A-11

 media 15 1 4 -3

 media 16 1 5 -4

 media 17 1 6 -5

 boundary 6

unit 2613

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 2611 2 -1 place 13 13 248 0.0 0.0 0.0

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 261

 rhexprism 1 18. 29. -29.

 array 261 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Generic fuel column for ring 2 =================

unit 210

 rhexprism 1 17. 261. -261.

 array 21 1 place 1 1 5 0.0 0.0 0.0

 boundary 1

'============= Ring 2: place the above-defined fuel column in six places ====

unit 21

 rhexprism 1 18. 261. -261.

 hole 210 rotate a1=0

 media 20 1 1

 boundary 1

unit 22

 rhexprism 1 18. 261. -261.

 hole 210 rotate a1=60

 media 20 1 1

 boundary 1

unit 23

 rhexprism 1 18. 261. -261.

 hole 210 rotate a1=120

 media 20 1 1

 boundary 1

unit 24

 rhexprism 1 18. 261. -261.

 hole 210 rotate a1=180

 media 20 1 1

 boundary 1

unit 25

 rhexprism 1 18. 261. -261.

 hole 210 rotate a1=240

 media 20 1 1

 boundary 1

unit 26

 rhexprism 1 18. 261. -261.

 hole 210 rotate a1=300

 media 20 1 1

 boundary 1
A-12

'================ Fuel Column: Zone 3 Block 1.1 =================

'================ Block 311 =================

unit 311

 rhexprism 1 18. 29. -29.

 array 311 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 331 =================

unit 3311

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 11 1 1

 media 13 1 2 -1

 media 14 1 3 -2

 media 15 1 4 -3

 media 16 1 5 -4

 media 17 1 6 -5

 boundary 6

unit 3313

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 3311 2 -1 place 13 13 248 0.0 0.0 0.0

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 331

 rhexprism 1 18. 29. -29.

 array 331 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 341 =================

unit 3411

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 9 1 1

 media 13 1 2 -1

 media 14 1 3 -2

 media 15 1 4 -3

 media 16 1 5 -4

 media 17 1 6 -5

 boundary 6

unit 3413

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 3411 2 -1 place 13 13 248 0.0 0.0 0.0
A-13

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 341

 rhexprism 1 18. 29. -29.

 array 341 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 351 =================

unit 3511

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 6 1 1

 media 13 1 2 -1

 media 14 1 3 -2

 media 15 1 4 -3

 media 16 1 5 -4

 media 17 1 6 -5

 boundary 6

unit 3513

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 3511 2 -1 place 13 13 248 0.0 0.0 0.0

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 351

 rhexprism 1 18. 29. -29.

 array 351 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 361 =================

unit 3611

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 3 1 1

 media 13 1 2 -1

 media 14 1 3 -2
A-14

 media 15 1 4 -3

 media 16 1 5 -4

 media 17 1 6 -5

 boundary 6

unit 3613

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 3611 2 -1 place 13 13 248 0.0 0.0 0.0

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 361

 rhexprism 1 18. 29. -29.

 array 361 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Generic fuel column for ring 3 =================

unit 310

 rhexprism 1 17. 261. -261.

 array 31 1 place 1 1 5 0.0 0.0 0.0

 boundary 1

'============= Ring 3: place the above-defined fuel column in twelve places =

unit 31

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=0

 media 20 1 1

 boundary 1

unit 51

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=120

 media 20 1 1

 boundary 1

unit 32

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=60

 media 20 1 1

 boundary 1

unit 52

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=180

 media 20 1 1

 boundary 1

unit 33

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=120

 media 20 1 1

 boundary 1

unit 53

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=240

 media 20 1 1

 boundary 1
A-15

unit 34

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=180

 media 20 1 1

 boundary 1

unit 54

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=300

 media 20 1 1

 boundary 1

unit 35

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=240

 media 20 1 1

 boundary 1

unit 55

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=0

 media 20 1 1

 boundary 1

unit 36

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=300

 media 20 1 1

 boundary 1

unit 56

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=60

 media 20 1 1

 boundary 1

'================ Fuel Column: Zone 4 Block 1 =================

'================ Block 411 =================

unit 411

 rhexprism 1 18. 29. -29.

 array 411 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 431 =================

unit 4311

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 12 1 1

 media 13 1 2 -1

 media 14 1 3 -2

 media 15 1 4 -3

 media 16 1 5 -4

 media 17 1 6 -5

 boundary 6

unit 4313

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 4311 2 -1 place 13 13 248 0.0 0.0 0.0

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

cylinder 5 2.05 29. -29. 
A-16

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 431

 rhexprism 1 18. 29. -29.

 array 431 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 441 =================

unit 4411

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 10 1 1

 media 13 1 2 -1

 media 14 1 3 -2

 media 15 1 4 -3

 media 16 1 5 -4

 media 17 1 6 -5

 boundary 6

unit 4413

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 4411 2 -1 place 13 13 248 0.0 0.0 0.0

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 441

 rhexprism 1 18. 29. -29.

 array 441 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 451 =================

unit 4511

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 7 1 1

 media 13 1 2 -1

media 14 1 3 -2

 media 15 1 4 -3

 media 16 1 5 -4

 media 17 1 6 -5
A-17

 boundary 6

unit 4513

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 4511 2 -1 place 13 13 248 0.0 0.0 0.0

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 451

 rhexprism 1 18. 29. -29.

 array 451 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 461 =================

unit 4611

 sphere 1 0.03

 sphere 2 0.036

 sphere 3 0.039

 sphere 4 0.0415

 sphere 5 0.046

 cuboid 6 6p0.055377

 media 4 1 1

 media 13 1 2 -1

 media 14 1 3 -2

 media 15 1 4 -3

 media 16 1 5 -4

 media 17 1 6 -5

 boundary 6

unit 4613

 cylinder 1 0.5 27.3 -27.3

 cylinder 2 1.3 27.3 -27.3

 array 4611 2 -1 place 13 13 248 0.0 0.0 0.0

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 21 1 1

 media 21 1 3 -2

 media 19 1 4 -3

 media 21 1 5 -4

 media 20 1 6 -5

 boundary 6

unit 461

 rhexprism 1 18. 29. -29.

 array 461 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Generic fuel column for ring 4 =================

unit 410

 rhexprism 1 17. 261. -261.

 array 41 1 place 1 1 5 0.0 0.0 0.0

 boundary 1

'============= Ring 4: place the above-defined fuel column in six places ====
A-18

unit 41

 rhexprism 1 18. 261. -261.

 hole 410 rotate a1=0

 media 20 1 1

 boundary 1

unit 42

 rhexprism 1 18. 261. -261.

 hole 410 rotate a1=60

 media 20 1 1

 boundary 1

unit 43

 rhexprism 1 18. 261. -261.

 hole 410 rotate a1=120

 media 20 1 1

 boundary 1

unit 44

 rhexprism 1 18. 261. -261.

 hole 410 rotate a1=180

 media 20 1 1

 boundary 1

unit 45

 rhexprism 1 18. 261. -261.

 hole 410 rotate a1=240

 media 20 1 1

 boundary 1

unit 46

 rhexprism 1 18. 261. -261.

 hole 410 rotate a1=300

 media 20 1 1

 boundary 1

'

'================ Control rods (Fig. 3.8, pag. 183 of [1]) =============

'

'============== Control rod section (Fig. 3.7, pag. 182 of [1]) =============

unit 9101

 cylinder 1 0.5 30. 1.

 cylinder 2 3.25 30. 1.

 cylinder 3 3.75 30. 1.

 cylinder 4 5.25 30. 1.

 cylinder 5 5.65 31. 0.

 cylinder 6 6.15 31. 0.

 hexprism 7 7. 31. 0.

 media 27 1 1

 media 21 1 2 -1

 media 27 1 3 -2

 media 26 1 4 -3

 media 27 1 5 -4

 media 21 1 6 -5

 media 20 1 7 -6

 boundary 7

'================ Control rod empty region =============

unit 9102

 cylinder 1 6.15 522. 0.

 hexprism 2 7. 522. 0.

 media 21 1 1

 media 20 1 2 -1

 boundary 2

'================ Central region in CR =============
A-19

unit 6001

 cone 1 2.5 29. 1. 15.5

 cylinder 2 1.5 20. 14.

 cylinder 3 2.25 14. 4.

 hexprism 4 2.5 29. -29.

 media 21 1 1 -2

 media 21 1 2

 media 21 1 3

 media 20 1 4 -1 -2 -3

 boundary 4

'================ CR Column 61: Central =================

unit 610

 cylinder 1 6.15 261. -155. origin x=-5.4 y=-9.353074

 cylinder 2 6.15 261. -155. origin x=10.8 y=0.

 cylinder 3 6.15 261. -155. origin x=-5.4 y=9.353074

 cylinder 4 2.3 261. -261.

 array 9101 1 place 1 1 2 -5.4 -9.353074 32.5

 array 9101 2 place 1 1 2 10.8 0. 32.5

 array 600 4 place 1 1 5 0.0 0.0 0.0

 rhexprism 5 17. 261. -261.

 media 21 1 3

 media 20 1 5 -1 -2 -3 -4

 boundary 5

'================ Central CR: place CR in central column =================

unit 61

 rhexprism 1 18. 261. -261.

 hole 610 rotate a1=0

 media 20 1 1

 boundary 1

'================ CR Column 62: R1, Column 1 =================

unit 620

 cylinder 1 6.15 261. -155. origin x=-10.8 y=0.

 cylinder 2 6.15 261. -155. origin x=5.4 y=-9.353074

 cylinder 3 6.15 261. -155. origin x=5.4 y=9.353074

 cylinder 4 2.3 261. -261.

 array 9101 1 place 1 1 2 -10.8 0. 32.5

 array 9101 2 place 1 1 2 5.4 -9.353074 32.5

array 600 4 place 1 1 5 0.0 0.0 0.0

 rhexprism 5 17. 261. -261.

 media 21 1 3

 media 20 1 5 -1 -2 -3 -4

 boundary 5

'================ Ring 1 CR: place CR in six columns =================

unit 62

 rhexprism 1 18. 261. -261.

 hole 620 rotate a1=0

 media 20 1 1

 boundary 1

unit 63

 rhexprism 1 18. 261. -261.

 hole 620 rotate a1=60

 media 20 1 1

 boundary 1

unit 64

 rhexprism 1 18. 261. -261.

 hole 620 rotate a1=120

 media 20 1 1

 boundary 1
A-20

unit 65

 rhexprism 1 18. 261. -261.

 hole 620 rotate a1=180

 media 20 1 1

 boundary 1

unit 66

 rhexprism 1 18. 261. -261.

 hole 620 rotate a1=240

 media 20 1 1

 boundary 1

unit 67

 rhexprism 1 18. 261. -261.

 hole 620 rotate a1=300

 media 20 1 1

 boundary 1

'================ CR Column 71: R2, Column 1 =================

unit 710

 cylinder 1 6.15 261. -155. origin x=-5.4 y=9.353074

 cylinder 2 6.15 261. -155. origin x=-5.4 y=-9.353074

 cylinder 3 6.15 261. -155. origin x=10.8 y=0.

 cylinder 4 2.3 261. -261.

 array 9101 1 place 1 1 2 -5.4 9.353074 32.5

 array 9101 2 place 1 1 2 -5.4 -9.353074 32.5

 array 600 4 place 1 1 5 0.0 0.0 0.0

 rhexprism 5 17. 261. -261.

 media 21 1 3

 media 20 1 5 -1 -2 -3 -4

 boundary 5

'================ Ring 2 CR: place CR in six columns =================

unit 71

 rhexprism 1 18. 261. -261.

 hole 710 rotate a1=0

 media 20 1 1

 boundary 1

unit 72

 rhexprism 1 18. 261. -261.

 hole 710 rotate a1=60

 media 20 1 1

 boundary 1

unit 74

 rhexprism 1 18. 261. -261.

 hole 710 rotate a1=120

 media 20 1 1

 boundary 1

unit 75

 rhexprism 1 18. 261. -261.

 hole 710 rotate a1=180

 media 20 1 1

 boundary 1

unit 77

 rhexprism 1 18. 261. -261.

 hole 710 rotate a1=240

 media 20 1 1

 boundary 1

unit 78

 rhexprism 1 18. 261. -261.

 hole 710 rotate a1=300

 media 20 1 1
A-21

 boundary 1

'================ CR Column 73: R3, Column 1 =================

unit 730

 cylinder 1 6.15 261. -155. origin x=-5.4 y=-9.353074

 cylinder 2 6.15 261. -155. origin x=10.8 y=0.

 cylinder 3 6.15 261. -155. origin x=-5.4 y=9.353074

 cylinder 4 2.3 261. -261.

 array 9101 1 place 1 1 2 -5.4 -9.353074 259.9

 array 9101 2 place 1 1 2 10.8 0.0 259.9

 array 600 4 place 1 1 5 0.0 0.0 0.0

 rhexprism 5 17. 261. -261.

 media 21 1 3

 media 20 1 5 -1 -2 -3 -4

 boundary 5

'================ Ring 3 CR: place CR in three columns =================

unit 73

 rhexprism 1 18. 261. -261.

 hole 730 rotate a1=0

 media 20 1 1

 boundary 1

unit 76

 rhexprism 1 18. 261. -261.

 hole 730 rotate a1=120

 media 20 1 1

 boundary 1

unit 79

 rhexprism 1 18. 261. -261.

 hole 730 rotate a1=240

 media 20 1 1

 boundary 1

'================ Instrumentation Block =================

unit 801

 cylinder 1 6.15 29. -29. origin x=-10.8 y=0.

 cylinder 2 6.15 29. -29. origin x=5.4 y=9.353074

 cylinder 3 6.15 29. -29. origin x=5.4 y=-9.353074

 cone 4 2.5 29. 1.5 20.

 cylinder 5 1.5 20. 14.

 cylinder 6 2.25 14. 4.

 cylinder 7 2.505 29. -29.

 rhexprism 8 18. 29. -29.

 media 21 1 1

 media 21 1 2

 media 21 1 3

 media 21 1 4

 media 21 1 5

 media 21 1 6

 media 20 1 7 -4 -5 -6

 media 20 1 8 -1 -2 -3 -7

 boundary 8

unit 802

 cone 4 2.5 29. 1.5 20.

 cylinder 5 1.5 20. 14.

 cylinder 6 2.25 14. 4.

 cylinder 7 2.505 29. -29.

 rhexprism 8 18. 29. -29.

 media 21 1 4

 media 21 1 5

 media 21 1 6
A-22

 media 20 1 7 -4 -5 -6

 media 20 1 8 -7

 boundary 8

unit 80

 rhexprism 1 18. 261. -261.

 array 80 1 place 1 1 5 0.0 0.0 0.0

 boundary 1

'================ RR Block not in fuel column =================

unit 900

 cone 1 2.5 29. 1.5 20.

 cylinder 2 1.5 20. 14.

 cylinder 3 2.25 14. 4.

 cylinder 4 2.505 29. -29.

 rhexprism 5 18. 29. -29.

 media 21 1 1

 media 21 1 2

 media 21 1 3

 media 20 1 4 -1 -2 -3

 media 20 1 5 -4

 boundary 5

unit 90

 rhexprism 1 18. 261. -261.

 array 90 1 place 1 1 5 0.0 0.0 0.0

 boundary 1

'================ Global Geometry =================

global unit 1

 cylinder 1 212.5 261. -261.

 array 1 1 place 10 10 1 0.0 0.0 0.0

 boundary 1

end geom

' ---------------------------------------------------------------------------

' --- Boundary conditions ---------------------------------------------------

read boun all=vacuum end boun

' ---------------------------------------------------------------------------

read array

 ara=1 nux=19 nuy=19 nuz=1 typ=rhexagonal

 fill

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 80 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 77 90 45 90 78 10 10 10 10 10 10 10

 10 10 10 10 10 76 90 54 35 66 55 36 90 79 10 10 10 10 10

 10 10 10 10 10 90 44 65 25 15 26 67 46 90 10 10 10 10 10

 10 10 10 10 10 75 34 24 14 61 16 21 56 71 10 10 10 10 10

 10 10 10 10 10 90 53 64 13 12 11 62 31 90 10 10 10 10 10

 10 10 10 10 10 80 43 33 23 63 22 51 41 80 10 10 10 10 10

 10 10 10 10 10 10 90 74 52 42 32 72 90 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 90 73 90 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
A-23

 end fill

' --- Columns arrays --------------------------------------------------------

 ara=10 nux=1 nuy=1 nuz=9 typ=rhexagonal

 fill 100 100 100 100 100 100 100 100 100 end fill

 ara=11 nux=1 nuy=1 nuz=9 typ=rhexagonal

 fill 111 111 161 161 151 141 131 111 111 end fill

 ara=21 nux=1 nuy=1 nuz=9 typ=rhexagonal

 fill 211 211 261 261 251 241 231 211 211 end fill

 ara=31 nux=1 nuy=1 nuz=9 typ=rhexagonal

 fill 311 311 361 361 351 341 331 311 311 end fill

 ara=41 nux=1 nuy=1 nuz=9 typ=rhexagonal

 fill 411 411 461 461 451 441 431 411 411 end fill

 ara=80 nux=1 nuy=1 nuz=9 typ=rhexagonal

 fill 802 801 801 801 801 801 801 801 801 end fill

 ara=90 nux=1 nuy=1 nuz=9 typ=rhexagonal

 fill 900 900 900 900 900 900 900 900 900 end fill

' --- Fuel block arrays -----------------------------------------------------

 ara=111 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1113 1113 1113 1116

 1116 1116 1116 1113 1113 1113 1113 1113 1116

 1116 1116 1113 1113 1113 1113 1113 1113 1116

 1116 1113 1113 1113 1114 1113 1113 1116 1116

 1116 1113 1113 1113 1113 1113 1113 1116 1116

 1116 1113 1113 1113 1113 1113 1116 1116 1116

 1116 1116 1113 1113 1113 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=131 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1312 1313 1313 1313 1116

 1116 1116 1116 1313 1313 1313 1313 1313 1116

 1116 1116 1313 1313 1313 1313 1313 1313 1116

 1116 1313 1313 1313 1114 1313 1313 1312 1116

 1116 1313 1313 1313 1313 1313 1313 1116 1116

 1116 1313 1313 1313 1313 1313 1116 1116 1116

 1116 1315 1313 1313 1313 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=141 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1412 1413 1413 1413 1116

 1116 1116 1116 1413 1413 1413 1413 1413 1116

 1116 1116 1413 1413 1413 1413 1413 1413 1116

 1116 1413 1413 1413 1114 1413 1413 1412 1116

 1116 1413 1413 1413 1413 1413 1413 1116 1116

 1116 1413 1413 1413 1413 1413 1116 1116 1116

 1116 1315 1413 1413 1413 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=151 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1412 1513 1513 1513 1116

 1116 1116 1116 1513 1513 1513 1513 1513 1116
A-24

 1116 1116 1513 1513 1513 1513 1513 1513 1116

 1116 1513 1513 1513 1114 1513 1513 1412 1116

 1116 1513 1513 1513 1513 1513 1513 1116 1116

 1116 1513 1513 1513 1513 1513 1116 1116 1116

 1116 1315 1513 1513 1513 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=161 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1312 1613 1613 1613 1116

 1116 1116 1116 1613 1613 1613 1613 1613 1116

 1116 1116 1613 1613 1613 1613 1613 1613 1116

 1116 1613 1613 1613 1114 1613 1613 1312 1116

 1116 1613 1613 1613 1613 1613 1613 1116 1116

 1116 1613 1613 1613 1613 1613 1116 1116 1116

 1116 1315 1613 1613 1613 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=211 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1113 1113 1113 1116 1116

 1116 1116 1116 1113 1113 1113 1113 1113 1116

 1116 1116 1113 1113 1113 1113 1113 1113 1116

 1116 1116 1113 1113 1114 1113 1113 1113 1116

 1116 1113 1113 1113 1113 1113 1113 1116 1116

 1116 1113 1113 1113 1113 1113 1116 1116 1116

 1116 1113 1113 1113 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=231 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 2313 2313 2313 1315 1116

 1116 1116 1116 2313 2313 2313 2313 2313 1116

 1116 1116 2313 2313 2313 2313 2313 2313 1116

 1116 1312 2313 2313 1114 2313 2313 2313 1116

 1116 2313 2313 2313 2313 2313 2313 1116 1116

 1116 2313 2313 2313 2313 2313 1116 1116 1116

 1116 2313 2313 2313 1312 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=241 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 2413 2413 2413 1315 1116

 1116 1116 1116 2413 2413 2413 2413 2413 1116

 1116 1116 2413 2413 2413 2413 2413 2413 1116

 1116 1412 2413 2413 1114 2413 2413 2413 1116

 1116 2413 2413 2413 2413 2413 2413 1116 1116

 1116 2413 2413 2413 2413 2413 1116 1116 1116

 1116 2413 2413 2413 1412 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=251 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116
A-25

 1116 1116 1116 1116 2513 2513 2513 1315 1116

 1116 1116 1116 2513 2513 2513 2513 2513 1116

 1116 1116 2513 2513 2513 2513 2513 2513 1116

 1116 1412 2513 2513 1114 2513 2513 2513 1116

 1116 2513 2513 2513 2513 2513 2513 1116 1116

 1116 2513 2513 2513 2513 2513 1116 1116 1116

 1116 2513 2513 2513 1412 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=261 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 2613 2613 2613 1315 1116

 1116 1116 1116 2613 2613 2613 2613 2613 1116

 1116 1116 2613 2613 2613 2613 2613 2613 1116

 1116 1312 2613 2613 1114 2613 2613 2613 1116

 1116 2613 2613 2613 2613 2613 2613 1116 1116

 1116 2613 2613 2613 2613 2613 1116 1116 1116

 1116 2613 2613 2613 1312 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=311 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1113 1113 1116 1116

 1116 1116 1116 1113 1113 1113 1113 1113 1116

 1116 1116 1113 1113 1113 1113 1113 1113 1116

 1116 1113 1113 1113 1114 1113 1113 1116 1116

 1116 1113 1113 1113 1113 1113 1113 1116 1116

 1116 1113 1113 1113 1113 1113 1116 1116 1116

 1116 1116 1113 1113 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=331 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1312 3313 3313 1116 1116

 1116 1116 1116 3313 3313 3313 3313 3313 1116

 1116 1116 3313 3313 3313 3313 3313 3313 1116

 1116 3313 3313 3313 1114 3313 3313 1315 1116

 1116 3313 3313 3313 3313 3313 3313 1116 1116

 1116 3313 3313 3313 3313 3313 1116 1116 1116

 1116 1312 3313 3313 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=341 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1412 3413 3413 1116 1116

 1116 1116 1116 3413 3413 3413 3413 3413 1116

 1116 1116 3413 3413 3413 3413 3413 3413 1116

 1116 3413 3413 3413 1114 3413 3413 1315 1116

 1116 3413 3413 3413 3413 3413 3413 1116 1116

 1116 3413 3413 3413 3413 3413 1116 1116 1116

 1116 1412 3413 3413 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=351 nux=9 nuy=9 nuz=1 typ=hexagonal
A-26

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1412 3513 3513 1116 1116

 1116 1116 1116 3513 3513 3513 3513 3513 1116

 1116 1116 3513 3513 3513 3513 3513 3513 1116

 1116 3513 3513 3513 1114 3513 3513 1315 1116

 1116 3513 3513 3513 3513 3513 3513 1116 1116

 1116 3513 3513 3513 3513 3513 1116 1116 1116

 1116 1412 3513 3513 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=361 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1312 3613 3613 1116 1116

 1116 1116 1116 3613 3613 3613 3613 3613 1116

 1116 1116 3613 3613 3613 3613 3613 3613 1116

 1116 3613 3613 3613 1114 3613 3613 1315 1116

 1116 3613 3613 3613 3613 3613 3613 1116 1116

 1116 3613 3613 3613 3613 3613 1116 1116 1116

 1116 1312 3613 3613 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=411 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1113 1113 1113 1116 1116

 1116 1116 1116 1113 1113 1113 1113 1113 1116

 1116 1116 1113 1113 1113 1113 1113 1113 1116

 1116 1116 1113 1113 1114 1113 1113 1116 1116

 1116 1113 1113 1113 1113 1113 1113 1116 1116

 1116 1113 1113 1113 1113 1113 1116 1116 1116

 1116 1116 1113 1113 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=431 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 4313 4313 4313 1312 1116

 1116 1116 1116 4313 4313 4313 4313 4313 1116

 1116 1116 4313 4313 4313 4313 4313 4313 1116

 1116 1312 4313 4313 1114 4313 4313 1116 1116

 1116 4313 4313 4313 4313 4313 4313 1116 1116

 1116 4313 4313 4313 4313 4313 1116 1116 1116

 1116 1116 4313 4313 1315 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=441 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 4413 4413 4413 1412 1116

 1116 1116 1116 4413 4413 4413 4413 4413 1116

 1116 1116 4413 4413 4413 4413 4413 4413 1116

 1116 1412 4413 4413 1114 4413 4413 1116 1116

 1116 4413 4413 4413 4413 4413 4413 1116 1116

 1116 4413 4413 4413 4413 4413 1116 1116 1116

 1116 1116 4413 4413 1315 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116
A-27

 end fill

 ara=451 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 4513 4513 4513 1412 1116

 1116 1116 1116 4513 4513 4513 4513 4513 1116

 1116 1116 4513 4513 4513 4513 4513 4513 1116

 1116 1412 4513 4513 1114 4513 4513 1116 1116

 1116 4513 4513 4513 4513 4513 4513 1116 1116

 1116 4513 4513 4513 4513 4513 1116 1116 1116

 1116 1116 4513 4513 1315 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=461 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 4613 4613 4613 1312 1116

 1116 1116 1116 4613 4613 4613 4613 4613 1116

 1116 1116 4613 4613 4613 4613 4613 4613 1116

 1116 1312 4613 4613 1114 4613 4613 1116 1116

 1116 4613 4613 4613 4613 4613 4613 1116 1116

 1116 4613 4613 4613 4613 4613 1116 1116 1116

 1116 1116 4613 4613 1315 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=600 nux=1 nuy=1 nuz=9 typ=hexagonal fill 9*6001 end fill

' --- Grains arrays ---------------------------------------------------------

 ara=1311 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*1311 end fill

 ara=1411 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*1411 end fill

 ara=1511 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*1511 end fill

 ara=1611 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*1611 end fill

 ara=2311 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*2311 end fill

 ara=2411 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*2411 end fill

 ara=2511 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*2511 end fill

 ara=2611 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*2611 end fill

 ara=3311 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*3311 end fill

 ara=3411 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*3411 end fill

 ara=3511 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*3511 end fill

 ara=3611 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*3611 end fill

 ara=4311 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*4311 end fill

 ara=4411 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*4411 end fill

 ara=4511 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*4511 end fill

 ara=4611 nux=25 nuy=25 nuz=495 typ=cuboidal fill 309375*4611 end fill

 ara=9101 nux=1 nuy=1 nuz=12 typ=hexagonal

 fill 9102 10*9101 9102 end fill

end array

' ---------------------------------------------------------------------------

' --- Energy splitting ------------------------------------------------------

read energy

 2e7 1.01e6 0.625 1e-5

end energy
A-28

' ---------------------------------------------------------------------------

' --- Plot cros-section -----------------------------------------------------

read plot

ttl='z=242 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=242.

 XLR=213.0 YLR=-213.0 ZLR=242.

 NAX=1280 end

ttl='z=184 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=184.

 XLR=213.0 YLR=-213.0 ZLR=184.

 NAX=1280 end

ttl='z=126 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=126.

 XLR=213.0 YLR=-213.0 ZLR=126.

 NAX=1280 end

ttl='z=68 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=68.

 XLR=213.0 YLR=-213.0 ZLR=68.

 NAX=1280 end

ttl='z=10 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=10.

 XLR=213.0 YLR=-213.0 ZLR=10.

 NAX=1280 end

ttl='z=-48 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=-48.

 XLR=213.0 YLR=-213.0 ZLR=-48.

 NAX=1280 end

ttl='z=-106 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=-106.

 XLR=213.0 YLR=-213.0 ZLR=-106.

 NAX=1280 end

ttl='z=-164 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=-164.

 XLR=213.0 YLR=-213.0 ZLR=-164.

 NAX=1280 end

ttl='z=-222 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=-222.

 XLR=213.0 YLR=-213.0 ZLR=-222.

 NAX=1280 end

ttl='Vertical View of the HTTR Core'

 TYP=XZ

 XUL=-213. YUL=0. ZUL=265.

 XLR=213. YLR=0. ZLR=-265.

 UAX=1.0 WDN=-1.0 NAX=1280 end

end plot

end data
A-29

end

' ---------------------------------------------------------------------------

' --- End input deck --------------------------------------------------------
A-30
31

APPENDIX B. SCALE MULTIGROUP MODEL FOR HTTR
32
B-1

APPENDIX B. SCALE MULTIGROUP MODEL FOR HTTR

=csas26 parm=centrm 

Dan Ilas, 2009, 2010: HTTR core based on HTTR-GCR-RESR-001

v7-238

' ---------------------------------------------------------------------------

--

' --- References:

' [1] John D. Bess, Nozomu Fujimoto: Evaluation of the Start-up Core Physics

' Tests at Japan's High Temperature Engineering Test Reactor

' (Fully-Loaded Core), Revision 0, March, 2009

' ---------------------------------------------------------------------------

' --- Materials -------------------------------------------------------------

read comp 

' Material References (n is the enrichment or block type number):

' --------------------

' m=(n-1)*10+1 CFP fuel atom densities from Table 3.1, pag. 195 of [1]

' m=(n-1)*10+2 Buffer atom densities from Table 3.2, pag. 196 of [1]

' m=(n-1)*10+3 IPyC atom densities from Table 3.2, pag. 196 of [1]

' m=(n-1)*10+4 SiC atom densities from Table 3.2, pag. 196 of [1]

' m=(n-1)*10+5 OPyC atom densities from Table 3.2, pag. 196 of [1]

' m=(n-1)*10+6 Homogenized compact 

' Obtained by volumetric homogenization of materials 121 and 

130

' m=(n-1)*10+7 Sleeve atom densities from Table 3.4, pag. 196 of [1]

' m=(n-1)*10+8 IG-110 atom densities from Table 3.6, pag. 197 of [1]

' by multiplying with 1.005

' m=(n-1)*10+9 Helium coolant from 3.1.3.10, page 199 of [1]

' m=(n-1)*10+10 Pin homogenized fuel

' m=121 Generic helium coolant from 3.1.3.10, page 199 of [1]

' m=122 Disks atom densities in BP pins from Table 3.5, pag. 197 of 

[1]

' m=123 BP atom densities (2.0%) from Table 3.5, pag. 197 of [1]

' m=124 BP atom densities (2.5%) from Table 3.5, pag. 197 of [1]

' m=125 PGX Graphite from Table 3.9, pag. 199 of [1]

' m=126 Absorber Compacts in CR from Table 3.7, pag. 198 of [1]

' m=127 Alloy 800H Clad in CR from Table 3.8, pag. 198 of [1]

' m=128 Generic IG-110 atom densities from Table 3.6, pag. 197 of [1]

' m=129 Overcoat atom densities from Table 3.2, pag. 196 of [1]

' m=130 Compact atom densities from Table 3.3, pag. 196 of [1]

'

' 

=============================================================================

' --- Fuel Kernel, 3.4% enrichment: 

 U-234 1 0 6.0946E-06 293.65 end

 U-235 1 0 7.9784E-04 293.65 end

 U-238 1 0 2.2376E-02 293.65 end

 O-16 1 0 4.6343E-02 293.65 end

 B-10 1 0 1.7276E-07 293.65 end

' --- Buffer:

 C-graphite 2 0 5.5153E-02 293.65 end

 B-10 2 0 1.8290E-08 293.65 end

' --- IPyC:

 C-graphite 3 0 9.2758E-02 293.65 end

 B-10 3 0 3.0761E-08 293.65 end

' --- SiC:
B-2

 C-graphite 4 0 4.8061E-02 293.65 end

 Si 4 0 4.8061E-02 293.65 end

 B-10 4 0 5.3208E-08 293.65 end

' --- OPyC:

 C-graphite 5 0 9.2758E-02 293.65 end

 B-10 5 0 3.0761E-08 293.65 end

' --- Homogenized graphite compact (inner and outer helium embedded):

 He 6 0 5.8706E-06 293.65 end

 C-graphite 6 0 6.4909E-02 293.65 end

 B-10 6 0 1.1767E-08 293.65 end

' --- Graphite sleeve:

 C-graphite 7 0 8.8747E-02 293.65 end

 B-10 7 0 7.2596E-09 293.65 end

' --- IG-110 Graphite:

 C-graphite 8 0 8.8243E-02 293.65 end

 B-10 8 0 7.8036E-09 293.65 end

' --- Helium coolant:

 He 9 0 2.4616E-05 293.65 end

' --- Fuel Kernel, 3.9% enrichment: 

 U-234 11 0 6.9909E-06 293.65 end

 U-235 11 0 9.1517E-04 293.65 end

 U-238 11 0 2.2259E-02 293.65 end

 O-16 11 0 4.6343E-02 293.65 end

 B-10 11 0 1.7276E-07 293.65 end

' --- Buffer:

 C-graphite 12 0 5.5153E-02 293.65 end

 B-10 12 0 1.8290E-08 293.65 end

' --- IPyC:

 C-graphite 13 0 9.2758E-02 293.65 end

 B-10 13 0 3.0761E-08 293.65 end

' --- SiC:

 C-graphite 14 0 4.8061E-02 293.65 end

 Si 14 0 4.8061E-02 293.65 end

 B-10 14 0 5.3208E-08 293.65 end

' --- OPyC:

 C-graphite 15 0 9.2758E-02 293.65 end

 B-10 15 0 3.0761E-08 293.65 end

' --- Homogenized graphite compact (inner and outer helium embedded):

 He 16 0 5.8706E-06 293.65 end

 C-graphite 16 0 6.4909E-02 293.65 end

 B-10 16 0 1.1767E-08 293.65 end

' --- Graphite sleeve:

 C-graphite 17 0 8.8747E-02 293.65 end

 B-10 17 0 7.2596E-09 293.65 end

' --- IG-110 Graphite:

 C-graphite 18 0 8.8243E-02 293.65 end

 B-10 18 0 7.8036E-09 293.65 end

' --- Helium coolant:

 He 19 0 2.4616E-05 293.65 end

' --- Fuel Kernel, 4.3% enrichment: 

 U-234 21 0 7.7079E-06 293.65 end

 U-235 21 0 1.0090E-03 293.65 end

 U-238 21 0 2.2166E-02 293.65 end

 O-16 21 0 4.6343E-02 293.65 end

 B-10 21 0 1.7276E-07 293.65 end

' --- Buffer:

 C-graphite 22 0 5.5153E-02 293.65 end

 B-10 22 0 1.8290E-08 293.65 end

' --- IPyC
B-3

 C-graphite 23 0 9.2758E-02 293.65 end

 B-10 23 0 3.0761E-08 293.65 end

' --- SiC:

 C-graphite 24 0 4.8061E-02 293.65 end

 Si 24 0 4.8061E-02 293.65 end

 B-10 24 0 5.3208E-08 293.65 end

' --- OPyC:

 C-graphite 25 0 9.2758E-02 293.65 end

 B-10 25 0 3.0761E-08 293.65 end

' --- Homogenized graphite compact (inner and outer helium embedded):

 He 26 0 5.8706E-06 293.65 end

 C-graphite 26 0 6.4909E-02 293.65 end

 B-10 26 0 1.1767E-08 293.65 end

' --- Graphite sleeve:

 C-graphite 27 0 8.8747E-02 293.65 end

 B-10 27 0 7.2596E-09 293.65 end

' --- IG-110 Graphite:

 C-graphite 28 0 8.8243E-02 293.65 end

 B-10 28 0 7.8036E-09 293.65 end

' --- Helium coolant:

 He 29 0 2.4616E-05 293.65 end

' --- Fuel Kernel, 4.8% enrichment: 

 U-234 31 0 8.6041E-06 293.65 end

 U-235 31 0 1.1264E-03 293.65 end

 U-238 31 0 2.2049E-02 293.65 end

 O-16 31 0 4.6343E-02 293.65 end

 B-10 31 0 1.7276E-07 293.65 end

' --- Buffer:

 C-graphite 32 0 5.5153E-02 293.65 end

 B-10 32 0 1.8290E-08 293.65 end

' --- IPyC:

 C-graphite 33 0 9.2758E-02 293.65 end

 B-10 33 0 3.0761E-08 293.65 end

' --- SiC:

 C-graphite 34 0 4.8061E-02 293.65 end

 Si 34 0 4.8061E-02 293.65 end

 B-10 34 0 5.3208E-08 293.65 end

' --- OPyC:

 C-graphite 35 0 9.2758E-02 293.65 end

 B-10 35 0 3.0761E-08 293.65 end

' --- Homogenized graphite compact (inner and outer helium embedded):

 He 36 0 5.8706E-06 293.65 end

 C-graphite 36 0 6.4909E-02 293.65 end

 B-10 36 0 1.1767E-08 293.65 end

' --- Graphite sleeve:

 C-graphite 37 0 8.8747E-02 293.65 end

 B-10 37 0 7.2596E-09 293.65 end

' --- IG-110 Graphite:

 C-graphite 38 0 8.8243E-02 293.65 end

 B-10 38 0 7.8036E-09 293.65 end

' --- Helium coolant:

 He 39 0 2.4616E-05 293.65 end

' --- Fuel Kernel, 5.2% enrichment: 

 U-234 41 0 9.3211E-06 293.65 end

 U-235 41 0 1.2202E-03 293.65 end

 U-238 41 0 2.1955E-02 293.65 end

 O-16 41 0 4.6343E-02 293.65 end

 B-10 41 0 1.7276E-07 293.65 end

' --- Buffer:
B-4

 C-graphite 42 0 5.5153E-02 293.65 end

 B-10 42 0 1.8290E-08 293.65 end

' --- IPyC:

 C-graphite 43 0 9.2758E-02 293.65 end

 B-10 43 0 3.0761E-08 293.65 end

' --- SiC:

 C-graphite 44 0 4.8061E-02 293.65 end

 Si 44 0 4.8061E-02 293.65 end

 B-10 44 0 5.3208E-08 293.65 end

' --- OPyC:

 C-graphite 45 0 9.2758E-02 293.65 end

 B-10 45 0 3.0761E-08 293.65 end

' --- Homogenized graphite compact (inner and outer helium embedded):

 He 46 0 5.8706E-06 293.65 end

 C-graphite 46 0 6.4909E-02 293.65 end

 B-10 46 0 1.1767E-08 293.65 end

' --- Graphite sleeve:

 C-graphite 47 0 8.8747E-02 293.65 end

 B-10 47 0 7.2596E-09 293.65 end

' --- IG-110 Graphite:

 C-graphite 48 0 8.8243E-02 293.65 end

 B-10 48 0 7.8036E-09 293.65 end

' --- Helium coolant:

 He 49 0 2.4616E-05 293.65 end

' --- Fuel Kernel, 5.9% enrichment: 

 U-234 51 0 1.0576E-05 293.65 end

 U-235 51 0 1.3845E-03 293.65 end

 U-238 51 0 2.1792E-02 293.65 end

 O-16 51 0 4.6343E-02 293.65 end

 B-10 51 0 1.7276E-07 293.65 end

' --- Buffer:

 C-graphite 52 0 5.5153E-02 293.65 end

 B-10 52 0 1.8290E-08 293.65 end

' --- IPyC:

 C-graphite 53 0 9.2758E-02 293.65 end

 B-10 53 0 3.0761E-08 293.65 end

' --- SiC:

 C-graphite 54 0 4.8061E-02 293.65 end

 Si 54 0 4.8061E-02 293.65 end

 B-10 54 0 5.3208E-08 293.65 end

' --- OPyC:

 C-graphite 55 0 9.2758E-02 293.65 end

 B-10 55 0 3.0761E-08 293.65 end

' --- Homogenized graphite compact (inner and outer helium embedded):

 He 56 0 5.8706E-06 293.65 end

 C-graphite 56 0 6.4909E-02 293.65 end

 B-10 56 0 1.1767E-08 293.65 end

' --- Graphite sleeve:

 C-graphite 57 0 8.8747E-02 293.65 end

 B-10 57 0 7.2596E-09 293.65 end

' --- IG-110 Graphite:

 C-graphite 58 0 8.8243E-02 293.65 end

 B-10 58 0 7.8036E-09 293.65 end

' --- Helium coolant:

 He 59 0 2.4616E-05 293.65 end

' --- Fuel Kernel, 6.3% enrichment: 

 U-234 61 0 1.1293E-05 293.65 end

 U-235 61 0 1.4783E-03 293.65 end

 U-238 61 0 2.1699E-02 293.65 end
B-5

 O-16 61 0 4.6343E-02 293.65 end

 B-10 61 0 1.7276E-07 293.65 end

' --- Buffer:

 C-graphite 62 0 5.5153E-02 293.65 end

 B-10 62 0 1.8290E-08 293.65 end

' --- IPyC:

 C-graphite 63 0 9.2758E-02 293.65 end

 B-10 63 0 3.0761E-08 293.65 end

' --- SiC:

 C-graphite 64 0 4.8061E-02 293.65 end

 Si 64 0 4.8061E-02 293.65 end

 B-10 64 0 5.3208E-08 293.65 end

' --- OPyC:

 C-graphite 65 0 9.2758E-02 293.65 end

 B-10 65 0 3.0761E-08 293.65 end

' --- Homogenized graphite compact (inner and outer helium embedded):

 He 66 0 5.8706E-06 293.65 end

 C-graphite 66 0 6.4909E-02 293.65 end

 B-10 66 0 1.1767E-08 293.65 end

' --- Graphite sleeve:

 C-graphite 67 0 8.8747E-02 293.65 end

 B-10 67 0 7.2596E-09 293.65 end

' --- IG-110 Graphite:

 C-graphite 68 0 8.8243E-02 293.65 end

 B-10 68 0 7.8036E-09 293.65 end

' --- Helium coolant:

 He 69 0 2.4616E-05 293.65 end

' --- Fuel Kernel, 6.7% enrichment: 

 U-234 71 0 1.2010E-05 293.65 end

 U-235 71 0 1.5722E-03 293.65 end

 U-238 71 0 2.1605E-02 293.65 end

 O-16 71 0 4.6343E-02 293.65 end

 B-10 71 0 1.7276E-07 293.65 end

' --- Buffer:

 C-graphite 72 0 5.5153E-02 293.65 end

 B-10 72 0 1.8290E-08 293.65 end

' --- IPyC:

 C-graphite 73 0 9.2758E-02 293.65 end

 B-10 73 0 3.0761E-08 293.65 end

' --- SiC:

 C-graphite 74 0 4.8061E-02 293.65 end

 Si 74 0 4.8061E-02 293.65 end

 B-10 74 0 5.3208E-08 293.65 end

' --- OPyC:

 C-graphite 75 0 9.2758E-02 293.65 end

 B-10 75 0 3.0761E-08 293.65 end

' --- Homogenized graphite compact (inner and outer helium embedded):

 He 76 0 5.8706E-06 293.65 end

 C-graphite 76 0 6.4909E-02 293.65 end

 B-10 76 0 1.1767E-08 293.65 end

' --- Graphite sleeve:

 C-graphite 77 0 8.8747E-02 293.65 end

 B-10 77 0 7.2596E-09 293.65 end

' --- IG-110 Graphite:

 C-graphite 78 0 8.8243E-02 293.65 end

 B-10 78 0 7.8036E-09 293.65 end

' --- Helium coolant:

 He 79 0 2.4616E-05 293.65 end

' --- Fuel Kernel, 7.2% enrichment: 
B-6

 U-234 81 0 1.2906E-05 293.65 end

 U-235 81 0 1.6895E-03 293.65 end

 U-238 81 0 2.1489E-02 293.65 end

 O-16 81 0 4.6343E-02 293.65 end

 B-10 81 0 1.7276E-07 293.65 end

' --- Buffer:

 C-graphite 82 0 5.5153E-02 293.65 end

 B-10 82 0 1.8290E-08 293.65 end

' --- IPyC:

 C-graphite 83 0 9.2758E-02 293.65 end

 B-10 83 0 3.0761E-08 293.65 end

' --- SiC:

 C-graphite 84 0 4.8061E-02 293.65 end

 Si 84 0 4.8061E-02 293.65 end

 B-10 84 0 5.3208E-08 293.65 end

' --- OPyC:

 C-graphite 85 0 9.2758E-02 293.65 end

 B-10 85 0 3.0761E-08 293.65 end

' --- Homogenized graphite compact (inner and outer helium embedded):

 He 86 0 5.8706E-06 293.65 end

 C-graphite 86 0 6.4909E-02 293.65 end

 B-10 86 0 1.1767E-08 293.65 end

' --- Graphite sleeve:

 C-graphite 87 0 8.8747E-02 293.65 end

 B-10 87 0 7.2596E-09 293.65 end

' --- IG-110 Graphite:

 C-graphite 88 0 8.8243E-02 293.65 end

 B-10 88 0 7.8036E-09 293.65 end

' --- Helium coolant:

 He 89 0 2.4616E-05 293.65 end

' --- Fuel Kernel, 7.9% enrichment: 

 U-234 91 0 1.4161E-05 293.65 end

 U-235 91 0 1.8538E-03 293.65 end

 U-238 91 0 2.1325E-02 293.65 end

 O-16 91 0 4.6343E-02 293.65 end

 B-10 91 0 1.7276E-07 293.65 end

' --- Buffer:

 C-graphite 92 0 5.5153E-02 293.65 end

 B-10 92 0 1.8290E-08 293.65 end

' --- IPyC:

 C-graphite 93 0 9.2758E-02 293.65 end

 B-10 93 0 3.0761E-08 293.65 end

' --- SiC:

 C-graphite 94 0 4.8061E-02 293.65 end

 Si 94 0 4.8061E-02 293.65 end

 B-10 94 0 5.3208E-08 293.65 end

' --- OPyC:

 C-graphite 95 0 9.2758E-02 293.65 end

 B-10 95 0 3.0761E-08 293.65 end

' --- Homogenized graphite compact (inner and outer helium embedded):

 He 96 0 5.8706E-06 293.65 end

 C-graphite 96 0 6.4909E-02 293.65 end

 B-10 96 0 1.1767E-08 293.65 end

' --- Graphite sleeve:

 C-graphite 97 0 8.8747E-02 293.65 end

 B-10 97 0 7.2596E-09 293.65 end

' --- IG-110 Graphite:

 C-graphite 98 0 8.8243E-02 293.65 end

 B-10 98 0 7.8036E-09 293.65 end
B-7

' --- Helium coolant:

 He 99 0 2.4616E-05 293.65 end

' --- Fuel Kernel, 9.4% enrichment: 

 U-234 101 0 1.6850E-05 293.65 end

 U-235 101 0 2.2058E-03 293.65 end

 U-238 101 0 2.0975E-02 293.65 end

 O-16 101 0 4.6343E-02 293.65 end

 B-10 101 0 1.7276E-07 293.65 end

' --- Buffer:

 C-graphite 102 0 5.5153E-02 293.65 end

 B-10 102 0 1.8290E-08 293.65 end

' --- IPyC:

 C-graphite 103 0 9.2758E-02 293.65 end

 B-10 103 0 3.0761E-08 293.65 end

' --- SiC:

 C-graphite 104 0 4.8061E-02 293.65 end

 Si 104 0 4.8061E-02 293.65 end

 B-10 104 0 5.3208E-08 293.65 end

' --- OPyC:

 C-graphite 105 0 9.2758E-02 293.65 end

 B-10 105 0 3.0761E-08 293.65 end

' --- Homogenized graphite compact (inner and outer helium embedded):

 He 106 0 5.8706E-06 293.65 end

 C-graphite 106 0 6.4909E-02 293.65 end

 B-10 106 0 1.1767E-08 293.65 end

' --- Graphite sleeve:

 C-graphite 107 0 8.8747E-02 293.65 end

 B-10 107 0 7.2596E-09 293.65 end

' --- IG-110 Graphite:

 C-graphite 108 0 8.8243E-02 293.65 end

 B-10 108 0 7.8036E-09 293.65 end

' --- Helium coolant:

 He 109 0 2.4616E-05 293.65 end

' --- Fuel Kernel, 9.9% enrichment: 

 U-234 111 0 1.7746E-05 293.65 end

 U-235 111 0 2.3231E-03 293.65 end

 U-238 111 0 2.0858E-02 293.65 end

 O-16 111 0 4.6343E-02 293.65 end

 B-10 111 0 1.7276E-07 293.65 end

' --- Buffer:

 C-graphite 112 0 5.5153E-02 293.65 end

 B-10 112 0 1.8290E-08 293.65 end

' --- IPyC:

 C-graphite 113 0 9.2758E-02 293.65 end

 B-10 113 0 3.0761E-08 293.65 end

' --- SiC:

 C-graphite 114 0 4.8061E-02 293.65 end

 Si 114 0 4.8061E-02 293.65 end

 B-10 114 0 5.3208E-08 293.65 end

' --- OPyC:

 C-graphite 115 0 9.2758E-02 293.65 end

 B-10 115 0 3.0761E-08 293.65 end

' --- Homogenized graphite compact (inner and outer helium embedded):

 He 116 0 5.8706E-06 293.65 end

 C-graphite 116 0 6.4909E-02 293.65 end

 B-10 116 0 1.1767E-08 293.65 end

' --- Graphite sleeve:

 C-graphite 117 0 8.8747E-02 293.65 end

 B-10 117 0 7.2596E-09 293.65 end
B-8

' --- IG-110 Graphite:

 C-graphite 118 0 8.8243E-02 293.65 end

 B-10 118 0 7.8036E-09 293.65 end

' --- Helium coolant:

 He 119 0 2.4616E-05 293.65 end

' --- Helium coolant used in CR to mark the CR placement:

 He 121 0 2.4616E-05 293.65 end

' --- Graphite disks:

 C-graphite 122 0 8.8747E-02 293.65 end

 B-10 122 0 7.2596E-09 293.65 end

' --- Burnable poison (2.0wt%):

 C-graphite 123 0 8.8446E-02 293.65 end

 B-10 123 0 3.9906E-04 293.65 end

 B-11 123 0 1.6063E-03 293.65 end

' --- Burnable poison (2.5wt%):

 C-graphite 124 0 8.7995E-02 293.65 end

 B-10 124 0 4.9882E-04 293.65 end

 B-11 124 0 2.0078E-03 293.65 end

' --- PGX Graphite:

 C-graphite 125 0 8.6134E-02 293.65 end

 B-10 125 0 3.6372E-08 293.65 end

' --- Absorber Compacts in CR:

 C-graphite 126 0 6.6685E-02 293.65 end

 B-10 126 0 6.8220E-03 293.65 end

 B-11 126 0 2.4974E-02 293.65 end

' --- Alloy 800H Clad in CR:

 C-graphite 127 0 3.2210E-04 293.65 end

 Al 127 0 6.7209E-04 293.65 end

 Si 127 0 6.0263E-04 293.65 end

 P 127 0 3.1225E-05 293.65 end

 S 127 0 1.5081E-05 293.65 end

 Ti 127 0 3.7884E-04 293.65 end

 Cr 127 0 1.9530E-02 293.65 end

 Mn 127 0 8.8022E-04 293.65 end

 Fe 127 0 3.8092E-02 293.65 end

 Ni 127 0 2.6777E-02 293.65 end

 Cu 127 0 2.2830E-04 293.65 end

' --- IG-110 Graphite:

 C-graphite 128 0 8.8243E-02 293.65 end

 B-10 128 0 7.8036E-09 293.65 end

' --- Graphite overcoat:

 C-graphite 129 0 8.5237E-02 293.65 end

 B-10 129 0 2.8267E-08 293.65 end

' --- Graphite compact:

 C-graphite 130 0 8.5237E-02 293.65 end

 B-10 130 0 1.5452E-08 293.65 end

end comp

' ---------------------------------------------------------------------------

' --- Cell data -------------------------------------------------------------

read celldata

doublehet fuelmix=10 end

 gfd=0.06 1

 coatr=0.036 2

 coatr=0.039 3

 coatr=0.0415 4

 coatr=0.046 5

matrix=6

numpar=12987 end grain
B-9

rod triangpitch right_bdy=white left_bdy=reflected

pitch=5.15 8 fuelr=1.325 fuelh=3.9 gapd=3.4 7 cladd=4.1 9 end

doublehet fuelmix=20 end

 gfd=0.06 11

 coatr=0.036 12

 coatr=0.039 13

 coatr=0.0415 14

 coatr=0.046 15

matrix=16

numpar=12987 end grain

rod triangpitch right_bdy=white left_bdy=reflected

pitch=5.15 18 fuelr=1.325 fuelh=3.9 gapd=3.4 17 cladd=4.1 19 end

doublehet fuelmix=30 end

 gfd=0.06 21

 coatr=0.036 22

 coatr=0.039 23

 coatr=0.0415 24

 coatr=0.046 25

matrix=26

numpar=12987 end grain

rod triangpitch right_bdy=white left_bdy=reflected

pitch=5.15 28 fuelr=1.325 fuelh=3.9 gapd=3.4 27 cladd=4.1 29 end

doublehet fuelmix=40 end

 gfd=0.06 31

 coatr=0.036 32

 coatr=0.039 33

 coatr=0.0415 34

 coatr=0.046 35

matrix=36

numpar=12987 end grain

rod triangpitch right_bdy=white left_bdy=reflected

pitch=5.15 38 fuelr=1.325 fuelh=3.9 gapd=3.4 37 cladd=4.1 39 end

doublehet fuelmix=50 end

 gfd=0.06 41

 coatr=0.036 42

 coatr=0.039 43

 coatr=0.0415 44

 coatr=0.046 45

matrix=46

numpar=12987 end grain

rod triangpitch right_bdy=white left_bdy=reflected

pitch=5.15 48 fuelr=1.325 fuelh=3.9 gapd=3.4 47 cladd=4.1 49 end

doublehet fuelmix=60 end

 gfd=0.06 51

 coatr=0.036 52

 coatr=0.039 53

 coatr=0.0415 54

 coatr=0.046 55

matrix=56

numpar=12987 end grain

rod triangpitch right_bdy=white left_bdy=reflected

pitch=5.15 58 fuelr=1.325 fuelh=3.9 gapd=3.4 57 cladd=4.1 59 end

doublehet fuelmix=70 end
B-10

 gfd=0.06 61

 coatr=0.036 62

 coatr=0.039 63

 coatr=0.0415 64

 coatr=0.046 65

matrix=66

numpar=12987 end grain

rod triangpitch right_bdy=white left_bdy=reflected

pitch=5.15 68 fuelr=1.325 fuelh=3.9 gapd=3.4 67 cladd=4.1 69 end

doublehet fuelmix=80 end

 gfd=0.06 71

 coatr=0.036 72

 coatr=0.039 73

 coatr=0.0415 74

 coatr=0.046 75

matrix=76

numpar=12987 end grain

rod triangpitch right_bdy=white left_bdy=reflected

pitch=5.15 78 fuelr=1.325 fuelh=3.9 gapd=3.4 77 cladd=4.1 79 end

doublehet fuelmix=90 end

 gfd=0.06 81

 coatr=0.036 82

 coatr=0.039 83

 coatr=0.0415 84

 coatr=0.046 85

matrix=86

numpar=12987 end grain

rod triangpitch right_bdy=white left_bdy=reflected

pitch=5.15 88 fuelr=1.325 fuelh=3.9 gapd=3.4 87 cladd=4.1 89 end

doublehet fuelmix=100 end

 gfd=0.06 91

 coatr=0.036 92

 coatr=0.039 93

 coatr=0.0415 94

 coatr=0.046 95

matrix=96

numpar=12987 end grain

rod triangpitch right_bdy=white left_bdy=reflected

pitch=5.15 98 fuelr=1.325 fuelh=3.9 gapd=3.4 97 cladd=4.1 99 end

doublehet fuelmix=110 end

 gfd=0.06 101

 coatr=0.036 102

 coatr=0.039 103

 coatr=0.0415 104

 coatr=0.046 105

matrix=106

numpar=12987 end grain

rod triangpitch right_bdy=white left_bdy=reflected

pitch=5.15 108 fuelr=1.325 fuelh=3.9 gapd=3.4 107 cladd=4.1 109 end

doublehet fuelmix=120 end

 gfd=0.06 111

 coatr=0.036 112

 coatr=0.039 113

 coatr=0.0415 114
B-11

 coatr=0.046 115

matrix=116

numpar=12987 end grain

rod triangpitch right_bdy=white left_bdy=reflected

pitch=5.15 118 fuelr=1.325 fuelh=3.9 gapd=3.4 117 cladd=4.1 119 end

end celldata

' ---------------------------------------------------------------------------

' --- Parameters ------------------------------------------------------------

read parm 

 gen=1100

 npg=100000

 nsk=100

 tba=100

 htm=no

 flx=yes

 fdn=yes

 res=1100

 wrs=35

end parm

' ---------------------------------------------------------------------------

' --- Geometry --------------------------------------------------------------

read geom

' Dimensions for block and pin details based on Figure 1.52 page 68 of [1]

' Counting of pins starts at the lower left corner, going horizontally and

' then vertically

' Dimensions for grain cells based on Figure 3.1 page 176 of [1]

'

' Numbering scheme for cells that make up fuel block units:

' zlb1 fuel grain

' zlb2 BP pin

' zlb3 fuel pin

' zlb4 central hole

' zlb5 empty pin

' zlb6 graphite

' zlb block

'

' Block numbering (Fig. 3.15, page 190 of [1]):

' Each block is numbered according to the scheme 100*z+10*l+b, where:

' z=1,...,8 zone number

' **Fuel: z=1,2 for zones 1 and 2, respectively

' z=3,5 alternatively as one goes 

counterclockwise

' for zone 3, z=4 for zone 4

' **Replaceable Reflectors in fuel columns follow the 

same

' pattern as fuel blocks, but with different l: 

l=1,2,8,9

' **CR: z=6 for "C" (b=1) and "R1" (b=2,...,7)

' z=7 for "R2" and "R3" (b=1,...,9, going 

' counterclockwise)

' **Instrumentation Blocks have z=8 (b=1,2,3)

' l=1,...,9 layer number from top to bottom

' (fuel blocks in layers 3 to 7 from top)

' b=1,...,bmax(z) block number (starting from positive x, counterclockwise)

' bmax(1)=...=bmax(5)=6

' bmax(6)=7, bmax(7)=9

' bmax(8)=3
B-12

' Replaceable Reflector (RR) blocks that are not in fuel columns are assigned

' block# 900

' Graphite blocks to make up the Permanent Reflector are assigned block# 100

'

'================ Graphite Block =================

unit 100

 rhexprism 1 18. 29. -29.

 media 125 1 1

 boundary 1

unit 10

 rhexprism 1 18. 261. -261.

 array 10 1 place 1 1 5 0.0 0.0 0.0

 boundary 1

'================ Fuel Column: Zone 1 Block 1 =================

'================ Block 111 =================

unit 1113

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 121 1 5

 media 128 1 6 -5

 boundary 6

unit 1114

 cone 1 2.5 29. 1.5 20.

 cylinder 2 1.5 20. 14.

 cylinder 3 2.25 14. 4.

 cylinder 4 2.505 29. -29.

 hexprism 5 2.575 29. -29.

 media 121 1 1

 media 121 1 2

 media 121 1 3

 media 128 1 4 -1 -2 -3

 media 128 1 5 -4

 boundary 5

unit 1116

 hexprism 1 2.575 29. -29.

 media 128 1 1

 boundary 1

unit 111

 rhexprism 1 18. 29. -29.

 array 111 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 131 =================

unit 1312

 cylinder 1 0.7 5.2 -4.8

 cylinder 2 0.7 25.2 -24.8

 cylinder 3 0.75 25.2 -24.8

 cylinder 4 0.75 29. -29. 

 hexprism 5 2.575 29. -29.

 media 122 1 1

 media 123 1 2 -1

 media 79 1 3 -2

 media 78 1 4 -3

 media 78 1 5 -4

 boundary 5

unit 1313

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 
B-13

 hexprism 6 2.575 29. -29.

 media 80 1 2

 media 79 1 3 -2

 media 77 1 4 -3

 media 79 1 5 -4

 media 78 1 6 -5

 boundary 6

unit 1315

 cylinder 1 0.75 25.2 -24.8

 cylinder 2 0.75 29. -29. 

 hexprism 3 2.575 29. -29.

 media 79 1 1

 media 78 1 2 -1

 media 78 1 3 -2

 boundary 3

unit 131

 rhexprism 1 18. 29. -29.

 array 131 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 141 =================

unit 1412

 cylinder 1 0.7 5.2 -4.8

 cylinder 2 0.7 25.2 -24.8

 cylinder 3 0.75 25.2 -24.8

 cylinder 4 0.75 29. -29. 

 hexprism 5 2.575 29. -29.

 media 122 1 1

 media 124 1 2 -1

 media 49 1 3 -2

 media 48 1 4 -3

 media 48 1 5 -4

 boundary 5

unit 1413

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 50 1 2

 media 49 1 3 -2

 media 47 1 4 -3

 media 49 1 5 -4

 media 48 1 6 -5

 boundary 6

unit 141

 rhexprism 1 18. 29. -29.

 array 141 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 151 =================

unit 1513

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 30 1 2

 media 29 1 3 -2

 media 27 1 4 -3

 media 29 1 5 -4
B-14

 media 28 1 6 -5

 boundary 6

unit 151

 rhexprism 1 18. 29. -29.

 array 151 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 161 =================

unit 1613

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 10 1 2

 media 9 1 3 -2

 media 7 1 4 -3

 media 9 1 5 -4

 media 8 1 6 -5

 boundary 6

unit 161

 rhexprism 1 18. 29. -29.

 array 161 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Generic fuel column for ring 1 =================

unit 110

 rhexprism 1 17. 261. -261.

 array 11 1 place 1 1 5 0.0 0.0 0.0

 boundary 1

'============= Ring 1: place the above-defined fuel column in six places ====

unit 11

 rhexprism 1 18. 261. -261.

 hole 110 rotate a1=0

 media 128 1 1

 boundary 1

unit 12

 rhexprism 1 18. 261. -261.

 hole 110 rotate a1=60

 media 128 1 1

 boundary 1

unit 13

 rhexprism 1 18. 261. -261.

 hole 110 rotate a1=120

 media 128 1 1

 boundary 1

unit 14

 rhexprism 1 18. 261. -261.

 hole 110 rotate a1=180

 media 128 1 1

 boundary 1

unit 15

 rhexprism 1 18. 261. -261.

 hole 110 rotate a1=240

 media 128 1 1

 boundary 1

unit 16

 rhexprism 1 18. 261. -261.

 hole 110 rotate a1=300

 media 128 1 1

 boundary 1
B-15

'================ Fuel Column: Zone 2 Block 1 =================

'================ Block 211 =================

unit 211

 rhexprism 1 18. 29. -29.

 array 211 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 231 =================

unit 2313

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 100 1 2

 media 99 1 3 -2

 media 97 1 4 -3

 media 99 1 5 -4

 media 98 1 6 -5

 boundary 6

unit 231

 rhexprism 1 18. 29. -29.

 array 231 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 241 =================

unit 2413

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 70 1 2

 media 69 1 3 -2

 media 67 1 4 -3

 media 69 1 5 -4

 media 68 1 6 -5

 boundary 6

unit 241

 rhexprism 1 18. 29. -29.

 array 241 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 251 =================

unit 2513

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 50 1 2

 media 49 1 3 -2

 media 47 1 4 -3

 media 49 1 5 -4

 media 48 1 6 -5

 boundary 6

unit 251

 rhexprism 1 18. 29. -29.

 array 251 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 261 =================

unit 2613
B-16

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

media 20 1 2

 media 19 1 3 -2

 media 17 1 4 -3

 media 19 1 5 -4

 media 18 1 6 -5

 boundary 6

unit 261

 rhexprism 1 18. 29. -29.

 array 261 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Generic fuel column for ring 2 =================

unit 210

 rhexprism 1 17. 261. -261.

 array 21 1 place 1 1 5 0.0 0.0 0.0

 boundary 1

'============= Ring 2: place the above-defined fuel column in six places ====

unit 21

 rhexprism 1 18. 261. -261.

 hole 210 rotate a1=0

 media 128 1 1

 boundary 1

unit 22

 rhexprism 1 18. 261. -261.

 hole 210 rotate a1=60

 media 128 1 1

 boundary 1

unit 23

 rhexprism 1 18. 261. -261.

 hole 210 rotate a1=120

 media 128 1 1

 boundary 1

unit 24

 rhexprism 1 18. 261. -261.

 hole 210 rotate a1=180

 media 128 1 1

 boundary 1

unit 25

 rhexprism 1 18. 261. -261.

 hole 210 rotate a1=240

 media 128 1 1

 boundary 1

unit 26

 rhexprism 1 18. 261. -261.

 hole 210 rotate a1=300

 media 128 1 1

 boundary 1

'================ Fuel Column: Zone 3 Block 1.1 =================

'================ Block 311 =================

unit 311

 rhexprism 1 18. 29. -29.

 array 311 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 331 =================

unit 3313
B-17

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 110 1 2

 media 109 1 3 -2

 media 107 1 4 -3

 media 109 1 5 -4

 media 108 1 6 -5

 boundary 6

unit 331

 rhexprism 1 18. 29. -29.

 array 331 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 341 =================

unit 3413

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 90 1 2

 media 89 1 3 -2

 media 87 1 4 -3

 media 89 1 5 -4

 media 88 1 6 -5

 boundary 6

unit 341

 rhexprism 1 18. 29. -29.

 array 341 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 351 =================

unit 3513

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 60 1 2

 media 59 1 3 -2

media 57 1 4 -3

 media 59 1 5 -4

 media 58 1 6 -5

 boundary 6

unit 351

 rhexprism 1 18. 29. -29.

 array 351 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 361 =================

unit 3613

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 30 1 2

 media 29 1 3 -2

 media 27 1 4 -3
B-18

 media 29 1 5 -4

 media 28 1 6 -5

 boundary 6

unit 361

 rhexprism 1 18. 29. -29.

 array 361 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Generic fuel column for ring 3 =================

unit 310

 rhexprism 1 17. 261. -261.

 array 31 1 place 1 1 5 0.0 0.0 0.0

 boundary 1

'============= Ring 3: place the above-defined fuel column in twelve places =

unit 31

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=0

 media 128 1 1

 boundary 1

unit 51

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=120

 media 128 1 1

 boundary 1

unit 32

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=60

 media 128 1 1

 boundary 1

unit 52

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=180

 media 128 1 1

 boundary 1

unit 33

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=120

 media 128 1 1

 boundary 1

unit 53

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=240

 media 128 1 1

 boundary 1

unit 34

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=180

 media 128 1 1

 boundary 1

unit 54

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=300

 media 128 1 1

 boundary 1

unit 35

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=240

 media 128 1 1

 boundary 1

unit 55
B-19

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=0

 media 128 1 1

 boundary 1

unit 36

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=300

 media 128 1 1

 boundary 1

unit 56

 rhexprism 1 18. 261. -261.

 hole 310 rotate a1=60

 media 128 1 1

 boundary 1

'================ Fuel Column: Zone 4 Block 1 =================

'================ Block 411 =================

unit 411

 rhexprism 1 18. 29. -29.

 array 411 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 431 =================

unit 4313

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 120 1 2

 media 119 1 3 -2

 media 117 1 4 -3

 media 119 1 5 -4

 media 118 1 6 -5

 boundary 6

unit 431

 rhexprism 1 18. 29. -29.

 array 431 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 441 =================

unit 4413

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 100 1 2

 media 99 1 3 -2

 media 97 1 4 -3

 media 99 1 5 -4

 media 98 1 6 -5

 boundary 6

unit 441

 rhexprism 1 18. 29. -29.

 array 441 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 451 =================

unit 4513

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85
B-20

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 70 1 2

 media 69 1 3 -2

media 67 1 4 -3

 media 69 1 5 -4

 media 68 1 6 -5

 boundary 6

unit 451

 rhexprism 1 18. 29. -29.

 array 451 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Block 461 =================

unit 4613

 cylinder 2 1.325 27.3 -27.3

 cylinder 3 1.325 27.45 -27.45

 cylinder 4 1.7 28.85 -28.85

 cylinder 5 2.05 29. -29. 

 hexprism 6 2.575 29. -29.

 media 40 1 2

 media 39 1 3 -2

 media 37 1 4 -3

 media 39 1 5 -4

 media 38 1 6 -5

 boundary 6

unit 461

 rhexprism 1 18. 29. -29.

 array 461 1 place 5 5 1 0.0 0.0 0.0

 boundary 1

'================ Generic fuel column for ring 4 =================

unit 410

 rhexprism 1 17. 261. -261.

 array 41 1 place 1 1 5 0.0 0.0 0.0

 boundary 1

'============= Ring 4: place the above-defined fuel column in six places ====

unit 41

 rhexprism 1 18. 261. -261.

 hole 410 rotate a1=0

 media 128 1 1

 boundary 1

unit 42

 rhexprism 1 18. 261. -261.

 hole 410 rotate a1=60

 media 128 1 1

 boundary 1

unit 43

 rhexprism 1 18. 261. -261.

 hole 410 rotate a1=120

 media 128 1 1

 boundary 1

unit 44

 rhexprism 1 18. 261. -261.

 hole 410 rotate a1=180

 media 128 1 1

 boundary 1

unit 45

 rhexprism 1 18. 261. -261.

 hole 410 rotate a1=240

 media 128 1 1
B-21

 boundary 1

unit 46

 rhexprism 1 18. 261. -261.

 hole 410 rotate a1=300

 media 128 1 1

 boundary 1

'

'================ Control rods (Fig. 3.8, pag. 183 of [1]) =============

'

'============== Control rod section (Fig. 3.7, pag. 182 of [1]) =============

unit 9101

 cylinder 1 0.5 30. 1.

 cylinder 2 3.25 30. 1.

 cylinder 3 3.75 30. 1.

 cylinder 4 5.25 30. 1.

 cylinder 5 5.65 31. 0.

 cylinder 6 6.15 31. 0.

 hexprism 7 7. 31. 0.

 media 127 1 1

 media 121 1 2 -1

 media 127 1 3 -2

 media 126 1 4 -3

 media 127 1 5 -4

 media 121 1 6 -5

 media 128 1 7 -6

 boundary 7

'================ Control rod empty region =============

unit 9102

 cylinder 1 6.15 522. 0.

 hexprism 2 7. 522. 0.

 media 121 1 1

 media 128 1 2 -1

 boundary 2

'================ Central region in CR =============

unit 6001

 cone 1 2.5 29. 1. 15.5

 cylinder 2 1.5 20. 14.

 cylinder 3 2.25 14. 4.

 hexprism 4 2.5 29. -29.

 media 121 1 1 -2

 media 121 1 2

 media 121 1 3

 media 128 1 4 -1 -2 -3

 boundary 4

'================ CR Column 61: Central =================

unit 610

 cylinder 1 6.15 261. -155. origin x=-5.4 y=-9.353074

 cylinder 2 6.15 261. -155. origin x=10.8 y=0.

 cylinder 3 6.15 261. -155. origin x=-5.4 y=9.353074

 cylinder 4 2.3 261. -261.

 array 9101 1 place 1 1 2 -5.4 -9.353074 32.5

 array 9101 2 place 1 1 2 10.8 0. 32.5

 array 600 4 place 1 1 5 0.0 0.0 0.0

 rhexprism 5 17. 261. -261.

 media 121 1 3

 media 128 1 5 -1 -2 -3 -4

 boundary 5

'================ Central CR: place CR in central column =================

unit 61
B-22

 rhexprism 1 18. 261. -261.

 hole 610 rotate a1=0

 media 128 1 1

 boundary 1

'================ CR Column 62: R1, Column 1 =================

unit 620

 cylinder 1 6.15 261. -155. origin x=-10.8 y=0.

 cylinder 2 6.15 261. -155. origin x=5.4 y=-9.353074

 cylinder 3 6.15 261. -155. origin x=5.4 y=9.353074

 cylinder 4 2.3 261. -261.

 array 9101 1 place 1 1 2 -10.8 0. 32.5

 array 9101 2 place 1 1 2 5.4 -9.353074 32.5

 array 600 4 place 1 1 5 0.0 0.0 0.0

 rhexprism 5 17. 261. -261.

 media 121 1 3

 media 128 1 5 -1 -2 -3 -4

 boundary 5

'================ Ring 1 CR: place CR in six columns =================

unit 62

 rhexprism 1 18. 261. -261.

 hole 620 rotate a1=0

 media 128 1 1

 boundary 1

unit 63

 rhexprism 1 18. 261. -261.

 hole 620 rotate a1=60

 media 128 1 1

 boundary 1

unit 64

 rhexprism 1 18. 261. -261.

 hole 620 rotate a1=120

 media 128 1 1

 boundary 1

unit 65

 rhexprism 1 18. 261. -261.

 hole 620 rotate a1=180

 media 128 1 1

 boundary 1

unit 66

 rhexprism 1 18. 261. -261.

 hole 620 rotate a1=240

 media 128 1 1

 boundary 1

unit 67

 rhexprism 1 18. 261. -261.

 hole 620 rotate a1=300

 media 128 1 1

 boundary 1

'================ CR Column 71: R2, Column 1 =================

unit 710

 cylinder 1 6.15 261. -155. origin x=-5.4 y=9.353074

 cylinder 2 6.15 261. -155. origin x=-5.4 y=-9.353074

 cylinder 3 6.15 261. -155. origin x=10.8 y=0.

 cylinder 4 2.3 261. -261.

 array 9101 1 place 1 1 2 -5.4 9.353074 32.5

 array 9101 2 place 1 1 2 -5.4 -9.353074 32.5

 array 600 4 place 1 1 5 0.0 0.0 0.0

 rhexprism 5 17. 261. -261.

 media 121 1 3
B-23

 media 128 1 5 -1 -2 -3 -4

 boundary 5

'================ Ring 2 CR: place CR in six columns =================

unit 71

 rhexprism 1 18. 261. -261.

 hole 710 rotate a1=0

 media 128 1 1

 boundary 1

unit 72

 rhexprism 1 18. 261. -261.

 hole 710 rotate a1=60

 media 128 1 1

 boundary 1

unit 74

 rhexprism 1 18. 261. -261.

 hole 710 rotate a1=120

 media 128 1 1

 boundary 1

unit 75

 rhexprism 1 18. 261. -261.

 hole 710 rotate a1=180

 media 128 1 1

 boundary 1

unit 77

 rhexprism 1 18. 261. -261.

 hole 710 rotate a1=240

 media 128 1 1

 boundary 1

unit 78

 rhexprism 1 18. 261. -261.

 hole 710 rotate a1=300

 media 128 1 1

 boundary 1

'================ CR Column 73: R3, Column 1 =================

unit 730

 cylinder 1 6.15 261. -155. origin x=-5.4 y=-9.353074

 cylinder 2 6.15 261. -155. origin x=10.8 y=0.

 cylinder 3 6.15 261. -155. origin x=-5.4 y=9.353074

 cylinder 4 2.3 261. -261.

 array 9101 1 place 1 1 2 -5.4 -9.353074 259.9

 array 9101 2 place 1 1 2 10.8 0.0 259.9

 array 600 4 place 1 1 5 0.0 0.0 0.0

 rhexprism 5 17. 261. -261.

 media 121 1 3

 media 128 1 5 -1 -2 -3 -4

 boundary 5

'================ Ring 3 CR: place CR in three columns =================

unit 73

 rhexprism 1 18. 261. -261.

 hole 730 rotate a1=0

 media 128 1 1

 boundary 1

unit 76

 rhexprism 1 18. 261. -261.

 hole 730 rotate a1=120

 media 128 1 1

 boundary 1

unit 79

 rhexprism 1 18. 261. -261.
B-24

 hole 730 rotate a1=240

 media 128 1 1

 boundary 1

'================ Instrumentation Block =================

unit 801

 cylinder 1 6.15 29. -29. origin x=-10.8 y=0.

 cylinder 2 6.15 29. -29. origin x=5.4 y=9.353074

 cylinder 3 6.15 29. -29. origin x=5.4 y=-9.353074

 cone 4 2.5 29. 1.5 20.

 cylinder 5 1.5 20. 14.

 cylinder 6 2.25 14. 4.

 cylinder 7 2.505 29. -29.

 rhexprism 8 18. 29. -29.

 media 121 1 1

 media 121 1 2

 media 121 1 3

 media 121 1 4

 media 121 1 5

 media 121 1 6

 media 128 1 7 -4 -5 -6

 media 128 1 8 -1 -2 -3 -7

 boundary 8

unit 802

 cone 4 2.5 29. 1.5 20.

 cylinder 5 1.5 20. 14.

 cylinder 6 2.25 14. 4.

 cylinder 7 2.505 29. -29.

 rhexprism 8 18. 29. -29.

 media 121 1 4

 media 121 1 5

 media 121 1 6

 media 128 1 7 -4 -5 -6

 media 128 1 8 -7

 boundary 8

unit 80

 rhexprism 1 18. 261. -261.

 array 80 1 place 1 1 5 0.0 0.0 0.0

 boundary 1

'================ RR Block not in fuel column =================

unit 900

 cone 1 2.5 29. 1.5 20.

 cylinder 2 1.5 20. 14.

 cylinder 3 2.25 14. 4.

 cylinder 4 2.505 29. -29.

 rhexprism 5 18. 29. -29.

 media 121 1 1

 media 121 1 2

 media 121 1 3

 media 128 1 4 -1 -2 -3

 media 128 1 5 -4

 boundary 5

unit 90

 rhexprism 1 18. 261. -261.

 array 90 1 place 1 1 5 0.0 0.0 0.0

 boundary 1

'================ Global Geometry =================

global unit 1

 cylinder 1 212.5 261. -261.

 array 1 1 place 10 10 1 0.0 0.0 0.0
B-25

 boundary 1

end geom

' ---------------------------------------------------------------------------

' --- Boundary conditions ---------------------------------------------------

read boun all=vacuum end boun

' ---------------------------------------------------------------------------

read array

 ara=1 nux=19 nuy=19 nuz=1 typ=rhexagonal

 fill

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 80 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 77 90 45 90 78 10 10 10 10 10 10 10

 10 10 10 10 10 76 90 54 35 66 55 36 90 79 10 10 10 10 10

 10 10 10 10 10 90 44 65 25 15 26 67 46 90 10 10 10 10 10

 10 10 10 10 10 75 34 24 14 61 16 21 56 71 10 10 10 10 10

 10 10 10 10 10 90 53 64 13 12 11 62 31 90 10 10 10 10 10

 10 10 10 10 10 80 43 33 23 63 22 51 41 80 10 10 10 10 10

 10 10 10 10 10 10 90 74 52 42 32 72 90 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 90 73 90 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

 end fill

' --- Columns arrays --------------------------------------------------------

 ara=10 nux=1 nuy=1 nuz=9 typ=rhexagonal

 fill 100 100 100 100 100 100 100 100 100 end fill

 ara=11 nux=1 nuy=1 nuz=9 typ=rhexagonal

 fill 111 111 161 161 151 141 131 111 111 end fill

 ara=21 nux=1 nuy=1 nuz=9 typ=rhexagonal

 fill 211 211 261 261 251 241 231 211 211 end fill

 ara=31 nux=1 nuy=1 nuz=9 typ=rhexagonal

 fill 311 311 361 361 351 341 331 311 311 end fill

 ara=41 nux=1 nuy=1 nuz=9 typ=rhexagonal

 fill 411 411 461 461 451 441 431 411 411 end fill

 ara=80 nux=1 nuy=1 nuz=9 typ=rhexagonal

 fill 802 801 801 801 801 801 801 801 801 end fill

 ara=90 nux=1 nuy=1 nuz=9 typ=rhexagonal

 fill 900 900 900 900 900 900 900 900 900 end fill

' --- Fuel block arrays -----------------------------------------------------

 ara=111 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1113 1113 1113 1116

 1116 1116 1116 1113 1113 1113 1113 1113 1116

 1116 1116 1113 1113 1113 1113 1113 1113 1116

 1116 1113 1113 1113 1114 1113 1113 1116 1116

 1116 1113 1113 1113 1113 1113 1113 1116 1116

 1116 1113 1113 1113 1113 1113 1116 1116 1116

 1116 1116 1113 1113 1113 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill
B-26

 ara=131 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1312 1313 1313 1313 1116

 1116 1116 1116 1313 1313 1313 1313 1313 1116

 1116 1116 1313 1313 1313 1313 1313 1313 1116

 1116 1313 1313 1313 1114 1313 1313 1312 1116

 1116 1313 1313 1313 1313 1313 1313 1116 1116

 1116 1313 1313 1313 1313 1313 1116 1116 1116

 1116 1315 1313 1313 1313 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=141 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1412 1413 1413 1413 1116

 1116 1116 1116 1413 1413 1413 1413 1413 1116

 1116 1116 1413 1413 1413 1413 1413 1413 1116

 1116 1413 1413 1413 1114 1413 1413 1412 1116

 1116 1413 1413 1413 1413 1413 1413 1116 1116

 1116 1413 1413 1413 1413 1413 1116 1116 1116

 1116 1315 1413 1413 1413 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=151 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1412 1513 1513 1513 1116

 1116 1116 1116 1513 1513 1513 1513 1513 1116

 1116 1116 1513 1513 1513 1513 1513 1513 1116

 1116 1513 1513 1513 1114 1513 1513 1412 1116

 1116 1513 1513 1513 1513 1513 1513 1116 1116

 1116 1513 1513 1513 1513 1513 1116 1116 1116

 1116 1315 1513 1513 1513 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=161 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1312 1613 1613 1613 1116

 1116 1116 1116 1613 1613 1613 1613 1613 1116

 1116 1116 1613 1613 1613 1613 1613 1613 1116

 1116 1613 1613 1613 1114 1613 1613 1312 1116

 1116 1613 1613 1613 1613 1613 1613 1116 1116

 1116 1613 1613 1613 1613 1613 1116 1116 1116

 1116 1315 1613 1613 1613 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=211 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1113 1113 1113 1116 1116

 1116 1116 1116 1113 1113 1113 1113 1113 1116

 1116 1116 1113 1113 1113 1113 1113 1113 1116

 1116 1116 1113 1113 1114 1113 1113 1113 1116

 1116 1113 1113 1113 1113 1113 1113 1116 1116

 1116 1113 1113 1113 1113 1113 1116 1116 1116

 1116 1113 1113 1113 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116
B-27

 end fill

 ara=231 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 2313 2313 2313 1315 1116

 1116 1116 1116 2313 2313 2313 2313 2313 1116

 1116 1116 2313 2313 2313 2313 2313 2313 1116

 1116 1312 2313 2313 1114 2313 2313 2313 1116

 1116 2313 2313 2313 2313 2313 2313 1116 1116

 1116 2313 2313 2313 2313 2313 1116 1116 1116

 1116 2313 2313 2313 1312 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=241 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 2413 2413 2413 1315 1116

 1116 1116 1116 2413 2413 2413 2413 2413 1116

 1116 1116 2413 2413 2413 2413 2413 2413 1116

 1116 1412 2413 2413 1114 2413 2413 2413 1116

 1116 2413 2413 2413 2413 2413 2413 1116 1116

 1116 2413 2413 2413 2413 2413 1116 1116 1116

 1116 2413 2413 2413 1412 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=251 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 2513 2513 2513 1315 1116

 1116 1116 1116 2513 2513 2513 2513 2513 1116

 1116 1116 2513 2513 2513 2513 2513 2513 1116

 1116 1412 2513 2513 1114 2513 2513 2513 1116

 1116 2513 2513 2513 2513 2513 2513 1116 1116

 1116 2513 2513 2513 2513 2513 1116 1116 1116

 1116 2513 2513 2513 1412 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=261 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 2613 2613 2613 1315 1116

 1116 1116 1116 2613 2613 2613 2613 2613 1116

 1116 1116 2613 2613 2613 2613 2613 2613 1116

 1116 1312 2613 2613 1114 2613 2613 2613 1116

 1116 2613 2613 2613 2613 2613 2613 1116 1116

 1116 2613 2613 2613 2613 2613 1116 1116 1116

 1116 2613 2613 2613 1312 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=311 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1113 1113 1116 1116

 1116 1116 1116 1113 1113 1113 1113 1113 1116

 1116 1116 1113 1113 1113 1113 1113 1113 1116

 1116 1113 1113 1113 1114 1113 1113 1116 1116

 1116 1113 1113 1113 1113 1113 1113 1116 1116

 1116 1113 1113 1113 1113 1113 1116 1116 1116

 1116 1116 1113 1113 1116 1116 1116 1116 1116
B-28

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=331 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1312 3313 3313 1116 1116

 1116 1116 1116 3313 3313 3313 3313 3313 1116

 1116 1116 3313 3313 3313 3313 3313 3313 1116

 1116 3313 3313 3313 1114 3313 3313 1315 1116

 1116 3313 3313 3313 3313 3313 3313 1116 1116

 1116 3313 3313 3313 3313 3313 1116 1116 1116

 1116 1312 3313 3313 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=341 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1412 3413 3413 1116 1116

 1116 1116 1116 3413 3413 3413 3413 3413 1116

 1116 1116 3413 3413 3413 3413 3413 3413 1116

 1116 3413 3413 3413 1114 3413 3413 1315 1116

 1116 3413 3413 3413 3413 3413 3413 1116 1116

 1116 3413 3413 3413 3413 3413 1116 1116 1116

 1116 1412 3413 3413 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=351 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1412 3513 3513 1116 1116

 1116 1116 1116 3513 3513 3513 3513 3513 1116

 1116 1116 3513 3513 3513 3513 3513 3513 1116

 1116 3513 3513 3513 1114 3513 3513 1315 1116

 1116 3513 3513 3513 3513 3513 3513 1116 1116

 1116 3513 3513 3513 3513 3513 1116 1116 1116

 1116 1412 3513 3513 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=361 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1312 3613 3613 1116 1116

 1116 1116 1116 3613 3613 3613 3613 3613 1116

 1116 1116 3613 3613 3613 3613 3613 3613 1116

 1116 3613 3613 3613 1114 3613 3613 1315 1116

 1116 3613 3613 3613 3613 3613 3613 1116 1116

 1116 3613 3613 3613 3613 3613 1116 1116 1116

 1116 1312 3613 3613 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=411 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1113 1113 1113 1116 1116

 1116 1116 1116 1113 1113 1113 1113 1113 1116

 1116 1116 1113 1113 1113 1113 1113 1113 1116

 1116 1116 1113 1113 1114 1113 1113 1116 1116

 1116 1113 1113 1113 1113 1113 1113 1116 1116

 1116 1113 1113 1113 1113 1113 1116 1116 1116
B-29

 1116 1116 1113 1113 1116 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=431 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 4313 4313 4313 1312 1116

 1116 1116 1116 4313 4313 4313 4313 4313 1116

 1116 1116 4313 4313 4313 4313 4313 4313 1116

 1116 1312 4313 4313 1114 4313 4313 1116 1116

 1116 4313 4313 4313 4313 4313 4313 1116 1116

 1116 4313 4313 4313 4313 4313 1116 1116 1116

 1116 1116 4313 4313 1315 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=441 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 4413 4413 4413 1412 1116

 1116 1116 1116 4413 4413 4413 4413 4413 1116

 1116 1116 4413 4413 4413 4413 4413 4413 1116

 1116 1412 4413 4413 1114 4413 4413 1116 1116

 1116 4413 4413 4413 4413 4413 4413 1116 1116

 1116 4413 4413 4413 4413 4413 1116 1116 1116

 1116 1116 4413 4413 1315 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=451 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 4513 4513 4513 1412 1116

 1116 1116 1116 4513 4513 4513 4513 4513 1116

 1116 1116 4513 4513 4513 4513 4513 4513 1116

 1116 1412 4513 4513 1114 4513 4513 1116 1116

 1116 4513 4513 4513 4513 4513 4513 1116 1116

 1116 4513 4513 4513 4513 4513 1116 1116 1116

 1116 1116 4513 4513 1315 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=461 nux=9 nuy=9 nuz=1 typ=hexagonal

 fill

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 1116 1116 1116 1116 4613 4613 4613 1312 1116

 1116 1116 1116 4613 4613 4613 4613 4613 1116

 1116 1116 4613 4613 4613 4613 4613 4613 1116

 1116 1312 4613 4613 1114 4613 4613 1116 1116

 1116 4613 4613 4613 4613 4613 4613 1116 1116

 1116 4613 4613 4613 4613 4613 1116 1116 1116

 1116 1116 4613 4613 1315 1116 1116 1116 1116

 1116 1116 1116 1116 1116 1116 1116 1116 1116

 end fill

 ara=600 nux=1 nuy=1 nuz=9 typ=hexagonal fill 9*6001 end fill

 ara=9101 nux=1 nuy=1 nuz=12 typ=hexagonal

 fill 9102 10*9101 9102 end fill

end array

' ---------------------------------------------------------------------------
B-30

' --- Energy splitting ------------------------------------------------------

read energy

 2e7 1.01e6 0.625 1e-5

end energy

' ---------------------------------------------------------------------------

' --- Plot cros-section -----------------------------------------------------

read plot

ttl='z=242 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=242.

 XLR=213.0 YLR=-213.0 ZLR=242.

 NAX=1280 end

ttl='z=184 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=184.

 XLR=213.0 YLR=-213.0 ZLR=184.

 NAX=1280 end

ttl='z=126 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=126.

 XLR=213.0 YLR=-213.0 ZLR=126.

 NAX=1280 end

ttl='z=68 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=68.

 XLR=213.0 YLR=-213.0 ZLR=68.

 NAX=1280 end

ttl='z=10 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=10.

 XLR=213.0 YLR=-213.0 ZLR=10.

 NAX=1280 end

ttl='z=-48 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=-48.

 XLR=213.0 YLR=-213.0 ZLR=-48.

 NAX=1280 end

ttl='z=-106 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=-106.

 XLR=213.0 YLR=-213.0 ZLR=-106.

 NAX=1280 end

ttl='z=-164 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=-164.

 XLR=213.0 YLR=-213.0 ZLR=-164.

 NAX=1280 end

ttl='z=-222 cm'

 TYP=XY

 XUL=-213.0 YUL=213.0 ZUL=-222.

 XLR=213.0 YLR=-213.0 ZLR=-222.

 NAX=1280 end

ttl='Vertical View of the HTTR Core'

 TYP=XZ

 XUL=-213. YUL=0. ZUL=265.

 XLR=213. YLR=0. ZLR=-265.

 UAX=1.0 WDN=-1.0 NAX=1280 end

end plot
B-31

end data

end

' ---------------------------------------------------------------------------

' --- End input deck --------------------------------------------------------

33

APPENDIX C. SCALE MULTIGROUP MODEL FOR HTR-10

APPENDIX C. SCALE MULTIGROUP MODEL FOR HTR-10

'============================================================================

' HTR-10 model for first critical core

' based on IRPhE 2009 high-fidelity benchmark specifications

' Authors: Eva Sunny and Germina Ilas

' Date: January 2010

'============================================================================

=csas6

HTR-10

'============================================================================

v7-238

'============================================================================

' Material composition data based on Tables 3.5.a, 3.5.b, 3.6, 3.7, and 3.8

'============================================================================

read composition

'----------------------------------------------------------------------------

' boronated carbon bricks

'----------------------------------------------------------------------------

c-graphite 1 0 7.29410e-02 300 end

b-10 1 0 6.53026e-02 300 end

b-11 1 0 2.64508e-03 300 end

n-14 1 0 1.86679e-06 300 end

o-16 1 0 5.00805e-07 300 end

ar-40 1 0 1.11653e-08 300 end

h-1 1 0 4.09691e-08 300 end

o-16 1 0 2.04846e-08 300 end

'----------------------------------------------------------------------------

' top graphite reflector

'----------------------------------------------------------------------------

c-graphite 2 0 8.51462e-02 300 end

b-10 2 0 9.05153e-08 300 end

b-11 2 0 3.66633e-07 300 end

n-14 2 0 1.37155e-06 300 end

o-16 2 0 3.67947e-07 300 end

ar-40 2 0 8.20327e-09 300 end

h-1 2 0 3.01005e-08 300 end

o-16 2 0 1.50502e-08 300 end

'----------------------------------------------------------------------------

' cold coolant chamber

'----------------------------------------------------------------------------

c-graphite 3 0 1.45350e-02 300 end

b-10 3 0 1.54516e-08 300 end

b-11 3 0 6.25868e-08 300 end

n-14 3 0 3.26568e-05 300 end

o-16 3 0 8.76083e-06 300 end

ar-40 3 0 1.95320e-07 300 end

h-1 3 0 7.16694e-07 300 end

o-16 3 0 3.58347e-07 300 end

'----------------------------------------------------------------------------

' top reflector

'----------------------------------------------------------------------------

c-graphite 4 0 8.02916e-02 300 end

b-10 4 0 8.53546e-08 300 end

b-11 4 0 3.45729e-07 300 end
C-2

n-14 4 0 3.52247e-06 300 end

o-16 4 0 9.44972e-07 300 end

ar-40 4 0 2.10679e-08 300 end

h-1 4 0 7.73049e-08 300 end

o-16 4 0 3.86524e-08 300 end

'----------------------------------------------------------------------------

' top core cavity

'----------------------------------------------------------------------------

n-14 5 0 3.90968e-05 300 end

o-16 5 0 1.04885e-05 300 end

ar-40 5 0 2.33838e-07 300 end

h-1 5 0 8.58028e-07 300 end

o-16 5 0 4.29014e-07 300 end

'----------------------------------------------------------------------------

' dummy pebbles

'----------------------------------------------------------------------------

c-graphite 6 0 5.72501e-02 300 end

b-10 6 0 5.50210e-10 300 end

b-11 6 0 2.22863e-09 300 end

n-14 6 0 1.52478e-05 300 end

o-16 6 0 4.09052e-06 300 end

ar-40 6 0 9.11968e-08 300 end

h-1 6 0 3.34631e-07 300 end

o-16 6 0 1.67315e-07 300 end

'----------------------------------------------------------------------------

c-graphite 7 0 5.72501e-02 300 end

b-10 7 0 5.50210e-10 300 end

b-11 7 0 2.22863e-09 300 end

n-14 7 0 1.52478e-05 300 end

o-16 7 0 4.09052e-06 300 end

ar-40 7 0 9.11968e-08 300 end

h-1 7 0 3.34631e-07 300 end

o-16 7 0 1.67315e-07 300 end

'----------------------------------------------------------------------------

' bottom reflector structures

'----------------------------------------------------------------------------

c-graphite 8 0 7.81408e-02 300 end

b-10 8 0 8.30683e-08 300 end

b-11 8 0 3.36469e-07 300 end

n-14 8 0 4.47541e-06 300 end

o-16 8 0 1.20062e-06 300 end

ar-40 8 0 2.67674e-08 300 end

h-1 8 0 9.82185e-08 300 end

o-16 8 0 4.91092e-08 300 end

'----------------------------------------------------------------------------

c-graphite 9 0 8.23751e-02 300 end

b-10 9 0 8.75697e-08 300 end

b-11 9 0 3.54701e-07 300 end

n-14 9 0 2.59931e-06 300 end

o-16 9 0 6.97317e-07 300 end

ar-40 9 0 1.55465e-08 300 end

h-1 9 0 5.70451e-08 300 end

o-16 9 0 2.85226e-08 300 end

'----------------------------------------------------------------------------

c-graphite 10 0 8.43647e-02 300 end

b-10 10 0 5.91038e-05 300 end

b-11 10 0 2.39400e-04 300 end
C-3

n-14 10 0 1.58577e-06 300 end

o-16 10 0 4.25414e-07 300 end

ar-40 10 0 9.48447e-09 300 end

h-1 10 0 3.48016e-08 300 end

o-16 10 0 1.74008e-08 300 end

'----------------------------------------------------------------------------

c-graphite 11 0 8.17101e-02 300 end

b-10 11 0 3.09704e-05 300 end

b-11 11 0 1.25446e-04 300 end

n-14 11 0 2.82486e-06 300 end

o-16 11 0 7.57826e-07 300 end

ar-40 11 0 1.68955e-08 300 end

h-1 11 0 6.19951e-08 300 end

o-16 11 0 3.09975e-08 300 end

'----------------------------------------------------------------------------

c-graphite 12 0 8.50790e-02 300 end

b-10 12 0 4.14002e-05 300 end

b-11 12 0 1.67692e-04 300 end

n-14 12 0 1.30888e-06 300 end

o-16 12 0 3.51134e-07 300 end

ar-40 12 0 7.82843e-09 300 end

h-1 12 0 2.87251e-08 300 end

o-16 12 0 1.43625e-08 300 end

'----------------------------------------------------------------------------

c-graphite 13 0 8.19167e-02 300 end

b-10 13 0 7.09887e-06 300 end

b-11 13 0 2.87540e-05 300 end

n-14 13 0 2.78674e-06 300 end

o-16 13 0 7.47599e-07 300 end

ar-40 13 0 1.66675e-08 300 end

h-1 13 0 6.11585e-08 300 end

o-16 13 0 3.05793e-08 300 end

'----------------------------------------------------------------------------

c-graphite 14 0 5.41118e-02 300 end

b-10 14 0 1.14336e-05 300 end

b-11 14 0 4.63120e-05 300 end

n-14 14 0 1.50964e-05 300 end

o-16 14 0 4.04992e-06 300 end

ar-40 14 0 9.02919e-08 300 end

h-1 14 0 3.31310e-07 300 end

o-16 14 0 1.65655e-07 300 end

'----------------------------------------------------------------------------

c-graphite 15 0 3.32110e-02 300 end

b-10 15 0 3.53052e-08 300 end

b-11 15 0 1.43004e-07 300 end

n-14 15 0 2.43823e-05 300 end

o-16 15 0 6.54105e-06 300 end

ar-40 15 0 1.45831e-07 300 end

h-1 15 0 5.35101e-07 300 end

o-16 15 0 2.67550e-07 300 end

'----------------------------------------------------------------------------

c-graphite 16 0 8.81811e-02 300 end

b-10 16 0 7.10555e-06 300 end

b-11 16 0 2.87811e-05 300 end

n-14 16 0 1.12208e-08 300 end

o-16 16 0 3.01020e-09 300 end

ar-40 16 0 6.71115e-11 300 end
C-4

h-1 16 0 2.46254e-10 300 end

o-16 16 0 1.23127e-10 300 end

'----------------------------------------------------------------------------

' boronated carbon bricks

'----------------------------------------------------------------------------

c-graphite 17 0 7.65984e-02 300 end

b-10 17 0 6.85771e-04 300 end

b-11 17 0 2.77772e-03 300 end

'----------------------------------------------------------------------------

' carbon bricks

'----------------------------------------------------------------------------

c-graphite 18 0 7.97184e-02 300 end

'----------------------------------------------------------------------------

' boronated carbon bricks

'----------------------------------------------------------------------------

c-graphite 19 0 7.61157e-02 300 end

b-10 19 0 6.81449e-04 300 end

b-11 19 0 2.76021e-03 300 end

n-14 19 0 2.46380e-07 300 end

o-16 19 0 6.60950e-08 300 end

ar-40 19 0 1.47360e-09 300 end

h-1 19 0 5.40704e-09 300 end

o-16 19 0 2.70352e-09 300 end

'----------------------------------------------------------------------------

' graphite reflector structures

'----------------------------------------------------------------------------

c-graphite 20 0 8.78374e-02 300 end

b-10 20 0 9.33762e-08 300 end

b-11 20 0 3.78221e-07 300 end

n-14 20 0 1.79180e-07 300 end

o-16 20 0 4.80680e-08 300 end

ar-40 20 0 1.07170e-09 300 end

h-1 20 0 3.93226e-09 300 end

o-16 20 0 1.96613e-09 300 end

'----------------------------------------------------------------------------

c-graphite 21 0 5.79696e-02 300 end

b-10 21 0 6.16251e-08 300 end

b-11 21 0 2.49613e-07 300 end

n-14 21 0 1.34130e-05 300 end

o-16 21 0 3.59820e-06 300 end

ar-40 21 0 8.02200e-08 300 end

h-1 21 0 2.94355e-07 300 end

o-16 21 0 1.47178e-07 300 end

'----------------------------------------------------------------------------

c-graphite 22 0 8.82418e-02 300 end

b-10 22 0 9.38063e-08 300 end

b-11 22 0 3.79963e-07 300 end

c-graphite 23 0 8.82418e-02 300 end

b-10 23 0 9.38063e-08 300 end

b-11 23 0 3.79963e-07 300 end

'----------------------------------------------------------------------------

c-graphite 24 0 8.79541e-02 300 end

b-10 24 0 3.33371e-05 300 end

b-11 24 0 1.35032e-04 300 end

n-14 24 0 5.30930e-08 300 end

o-16 24 0 1.42430e-08 300 end

ar-40 24 0 3.17550e-10 300 end
C-5

h-1 24 0 1.16520e-09 300 end

o-16 24 0 5.82601e-10 300 end

'----------------------------------------------------------------------------

c-graphite 25 0 8.82418e-04 300 end

b-10 25 0 9.38063e-08 300 end

b-11 25 0 3.79963e-07 300 end

'----------------------------------------------------------------------------

c-graphite 26 0 8.82418e-04 300 end

b-10 26 0 9.38063e-08 300 end

b-11 26 0 3.79963e-07 300 end

'----------------------------------------------------------------------------

' boronated carbon bricks

'----------------------------------------------------------------------------

c-graphite 27 0 7.65984e-02 300 end

b-10 27 0 6.85771e-04 300 end

b-11 27 0 2.77772e-03 300 end

'----------------------------------------------------------------------------

' graphite reflector structures

'----------------------------------------------------------------------------

c-graphite 28 0 8.82418e-02 300 end

b-10 28 0 9.38063e-08 300 end

b-11 28 0 3.79963e-07 300 end

'----------------------------------------------------------------------------

c-graphite 29 0 5.24843e-02 300 end

b-10 29 0 3.60299e-06 300 end

b-11 29 0 1.45939e-05 300 end

n-14 29 0 9.01730e-06 300 end

o-16 29 0 2.41910e-06 300 end

ar-40 29 0 5.39320e-08 300 end

h-1 29 0 1.97896e-07 300 end

o-16 29 0 9.89478e-08 300 end

'----------------------------------------------------------------------------

c-graphite 30 0 8.82418e-02 300 end

b-10 30 0 9.38063e-08 300 end

b-11 30 0 3.79963e-07 300 end

'----------------------------------------------------------------------------

' graphite reflector, control rods borin regions

'----------------------------------------------------------------------------

c-graphite 31 0 8.82418e-02 300 end

b-10 31 0 9.38063e-08 300 end

b-11 31 0 3.79963e-07 300 end

'----------------------------------------------------------------------------

' graphite reflector structures

'----------------------------------------------------------------------------

c-graphite 42 0 8.79637e-02 300 end

b-10 42 0 3.22548e-05 300 end

b-11 42 0 1.30648e-04 300 end

n-14 42 0 1.58430e-05 300 end

o-16 42 0 4.25010e-06 300 end

ar-40 42 0 9.47560e-08 300 end

h-1 42 0 3.47690e-07 300 end

o-16 42 0 1.73845e-07 300 end

'----------------------------------------------------------------------------

c-graphite 43 0 8.82418e-02 300 end

b-10 43 0 9.38063e-08 300 end

b-11 43 0 3.79963e-07 300 end

'----------------------------------------------------------------------------
C-6

c-graphite 44 0 8.82418e-02 300 end

b-10 44 0 9.38063e-08 300 end

b-11 44 0 3.79963e-07 300 end

'----------------------------------------------------------------------------

' boronated carbon bricks

'----------------------------------------------------------------------------

c-graphite 46 0 7.65984e-02 300 end

b-10 46 0 6.85771e-04 300 end

b-11 46 0 2.77772e-03 300 end

'----------------------------------------------------------------------------

' carbon bricks

'----------------------------------------------------------------------------

c-graphite 47 0 7.97184e-02 300 end

'----------------------------------------------------------------------------

' graphite reflector structures

'----------------------------------------------------------------------------

c-graphite 53 0 8.82418e-02 300 end

b-10 53 0 9.38063e-08 300 end

b-11 53 0 3.79963e-07 300 end

'----------------------------------------------------------------------------

c-graphite 57 0 7.28262e-02 300 end

b-10 57 0 7.74186e-08 300 end

b-11 57 0 3.13584e-07 300 end

n-14 57 0 1.32800e-05 300 end

o-16 57 0 3.56250e-06 300 end

ar-40 57 0 7.94250e-08 300 end

h-1 57 0 2.91438e-07 300 end

o-16 57 0 1.45719e-07 300 end

'----------------------------------------------------------------------------

' graphite reflector, cold coolant flow region

'----------------------------------------------------------------------------

c-graphite 58 0 8.82418e-02 300 end

b-10 58 0 9.38063e-08 300 end

b-11 58 0 3.79963e-07 300 end

'----------------------------------------------------------------------------

c-graphite 60 0 8.79538e-02 300 end

b-10 60 0 3.33371e-05 300 end

b-11 60 0 1.35032e-04 300 end

n-14 60 0 6.83020e-06 300 end

o-16 60 0 1.83230e-06 300 end

ar-40 60 0 4.08510e-08 300 end

h-1 60 0 1.49897e-07 300 end

o-16 60 0 7.49487e-08 300 end

'----------------------------------------------------------------------------

c-graphite 62 0 8.82418e-02 300 end

b-10 62 0 9.38063e-08 300 end

b-11 62 0 3.79963e-07 300 end

'----------------------------------------------------------------------------

' boronated carbon bricks

'----------------------------------------------------------------------------

c-graphite 64 0 7.65984e-02 300 end

b-10 64 0 6.85771e-04 300 end

b-11 64 0 2.77772e-03 300 end

'----------------------------------------------------------------------------

' carbon bricks

'----------------------------------------------------------------------------

c-graphite 65 0 7.97184e-02 300 end
C-7

'----------------------------------------------------------------------------

' graphite reflector structures

'----------------------------------------------------------------------------

c-graphite 66 0 5.82699e-02 300 end

b-10 66 0 6.19443e-08 300 end

b-11 66 0 2.50906e-07 300 end

n-14 66 0 1.23220e-07 300 end

o-16 66 0 3.30560e-08 300 end

ar-40 66 0 7.36960e-10 300 end

h-1 66 0 2.70416e-09 300 end

o-16 66 0 1.35208e-09 300 end

'----------------------------------------------------------------------------

c-graphite 70 0 8.82418e-02 300 end

b-10 70 0 9.38063e-08 300 end

b-11 70 0 3.79963e-07 300 end

'----------------------------------------------------------------------------

' boronated carbon bricks

'----------------------------------------------------------------------------

c-graphite 77 0 7.65984e-02 300 end

b-10 77 0 6.85771e-04 300 end

b-11 77 0 2.77772e-03 300 end

'----------------------------------------------------------------------------

' dummy pebbles

'----------------------------------------------------------------------------

c-graphite 81 0 8.47872e-02 300 end

n-14 81 0 1.52480e-05 300 end

o-16 81 0 4.09050e-06 300 end

ar-40 81 0 9.11970e-08 300 end

h-1 81 0 3.34631e-07 300 end

o-16 81 0 1.67315e-07 300 end

'----------------------------------------------------------------------------

' bottom reflector with hot coolant flow borings

'----------------------------------------------------------------------------

c-graphite 83 0 8.51047e-02 300 end

b-10 83 0 9.04713e-08 300 end

b-11 83 0 3.66455e-07 300 end

n-14 83 0 1.38993e-06 300 end

o-16 83 0 3.72877e-07 300 end

ar-40 83 0 8.31317e-09 300 end

h-1 83 0 3.05038e-08 300 end

o-16 83 0 1.52519e-08 300 end

'----------------------------------------------------------------------------

' dummy pebbles

'----------------------------------------------------------------------------

c-graphite 91 0 5.72501e-02 300 end

b-10 91 0 5.50210e-10 300 end

b-11 91 0 2.22863e-09 300 end

n-14 91 0 1.52478e-05 300 end

o-16 91 0 4.09052e-06 300 end

ar-40 91 0 9.11968e-08 300 end

h-1 91 0 3.34631e-07 300 end

o-16 91 0 1.67315e-07 300 end

'----------------------------------------------------------------------------

' coolant - saturated air at 15C

'----------------------------------------------------------------------------

n-14 96 0 3.95901e-05 300 end

o-16 96 0 1.06209e-05 300 end
C-8

ar-40 96 0 2.36778e-07 300 end

h-1 96 0 8.58028e-07 300 end

o-16 96 0 4.29014e-07 300 end

'----------------------------------------------------------------------------

' fuel kernel

'----------------------------------------------------------------------------

u-235 99 0 3.99198e-03 300 end

u-238 99 0 1.92441e-02 300 end

o-16 99 0 4.64720e-02 300 end

b-10 99 0 4.06384e-07 300 end

b-11 99 0 1.63575e-06 300 end

'----------------------------------------------------------------------------

' 1st coating - buffer

'----------------------------------------------------------------------------

c-graphite 101 0 5.51511e-02 300 end

b-10 101 0 1.58513e-08 300 end

b-11 101 0 6.38035e-08 300 end

'----------------------------------------------------------------------------

' 2nd coating - inner pyrolitic carbon

'----------------------------------------------------------------------------

c-graphite 102 0 9.52610e-02 300 end

b-10 102 0 2.73795e-08 300 end

b-11 102 0 1.10206e-07 300 end

'----------------------------------------------------------------------------

' 3rd coating - SiC

'----------------------------------------------------------------------------

c 103 0 4.77597e-02 300 end

si-28 103 0 4.77597e-02 300 end

'----------------------------------------------------------------------------

' 4th coating - outer pyrolitic carbon

'----------------------------------------------------------------------------

c-graphite 104 0 8.67377e-02 300 end

b-10 104 0 2.49298e-08 300 end

b-11 104 0 1.00345e-07 300 end

'----------------------------------------------------------------------------

' graphite matrix

'----------------------------------------------------------------------------

c-graphite 105 0 8.67377e-02 300 end

b-10 105 0 2.49298e-08 300 end

b-11 105 0 1.00345e-07 300 end

'----------------------------------------------------------------------------

' pebble shell - graphite

'----------------------------------------------------------------------------

c-graphite 106 0 8.67377e-02 300 end

b-10 106 0 2.49298e-08 300 end

b-11 106 0 1.00345e-07 300 end

'----------------------------------------------------------------------------

' dummy pebbles - graphite

'----------------------------------------------------------------------------

c-graphite 107 0 9.22528e-02 300 end

b-10 107 0 2.54951e-09 300 end

b-11 107 0 1.02621e-08 300 end

end composition

'============================================================================

' Unit cell data - use DOUBLEHET option

'============================================================================

read celldata
C-9

doublehet fuelmix=100 end

 gfr=0.025 99 

 coatr=0.034 101

 coatr=0.038 102 

 coatr=0.0415 103

 coatr=0.0455 104 

 numpar=8335 

 matrix=105 end grain

pebble sphtriangp right_bdy=white 

 hpitch=3.859776 96

 fuelr=2.5 

 cladr=3.0 106 end

end celldata

'============================================================================

' Beginning of KENO model section 

'============================================================================

'----------------------------------------------------------------------------

' parameter data

'----------------------------------------------------------------------------

read parameter

gen=1100

npg=10000

nsk=100

htm=no

flx=no

end parameter

'----------------------------------------------------------------------------

' geometry data

'----------------------------------------------------------------------------

read geometry

'----------------------------------------------------------------------------

unit 13

com='unit 13'

hexprism 30 8.1962 9.798 0

sphere 21 2.999

sphere 22 2.999 origin x=5.196152 y=3 z=0

sphere 23 2.999 origin x=-5.196152 y=3 z=0

sphere 24 2.999 origin x=0 y=-6 z=0

sphere 25 2.999 origin x=0 y=6 z=0

sphere 26 2.999 origin x=5.196152 y=-3 z=0

sphere 27 2.999 origin x=-5.196152 y=-3 z=0

sphere 41 2.999 origin x=3.4641 y=0 z=4.899

sphere 42 2.999 origin x=-1.7321 y=3 z=4.899

sphere 43 2.999 origin x=-1.7321 y=-3 z=4.899

sphere 44 2.999 origin x=3.4641 y=6 z=4.899

sphere 45 2.999 origin x=3.4641 y=-6 z=4.899

sphere 46 2.999 origin x=-6.9283 y=0 z=4.899

sphere 47 2.999 origin x=9.4641 y=0 z=4.899

sphere 48 2.999 origin x=-4.7321 y=-8.1962 z=4.899

sphere 49 2.999 origin x=-4.7321 y=8.1962 z=4.899

sphere 61 2.999 origin x=0 y=0 z=9.798

sphere 62 2.999 origin x=5.196152 y=3 z=9.798

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C-173

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C-174

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'----------------------------------------------------------------------------

unit 47

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C-175

media 106 1 49 -39

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boundary 30

'---------------------------------------------------------------------------

unit 48

com='unit 48'

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boundary 30

'---------------------------------------------------------------------------

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sphere 49 2.999 origin x=-4.7321 y=8.1962 z=4.899
C-176

sphere 51 2.5 origin x=0 y=0 z=9.798

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media 100 1 12

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media 107 1 25

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media 106 1 48 -38

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'---------------------------------------------------------------------------

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C-177

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media 100 1 12

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media 100 1 33

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media 100 1 35

media 100 1 36

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media 106 1 43 -33

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media 106 1 45 -35

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media 100 1 52

media 100 1 53

media 106 1 61 -51
C-178

media 106 1 62 -52

media 106 1 63 -53

media 107 1 64

media 107 1 65

media 107 1 66

media 107 1 67

media 96 1 30 -21 -22 -23 -24 -25 -26 -27 -41 -42 -43 -44 -45 -46 -47 -49 

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boundary 30

'----------------------------------------------------------------------------

unit 51

com='unit 51'

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media 106 1 23 -13

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media 107 1 65

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boundary 30

'----------------------------------------------------------------------------

unit 52

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media 106 1 22 -12

media 107 1 25

media 100 1 34

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media 106 1 44 -34

media 106 1 49 -39

media 100 1 52
C-179

media 106 1 62 -52

media 107 1 65

media 96 1 30 -22 -25 -44 -49 -62 -65

boundary 30

'----------------------------------------------------------------------------

unit 53

com='unit 53'

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media 100 1 11

media 100 1 12

media 100 1 13

media 106 1 21 -11

media 106 1 22 -12

media 106 1 23 -13

media 107 1 25

media 100 1 32

media 100 1 34

media 100 1 36

media 100 1 39

media 106 1 42 -32

media 106 1 44 -34

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media 106 1 49 -39

media 100 1 51

media 100 1 52

media 100 1 53

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media 106 1 62 -52

media 106 1 63 -53

media 107 1 65

media 96 1 30 -21 -22 -23 -25 -42 -44 -46 -49 -61 -62 -63 -65

boundary 30

'----------------------------------------------------------------------------

unit 54

com='unit 54'
C-180

hexprism 30 8.1962 9.798 0

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sphere 22 2.999 origin x=5.196152 y=3 z=0

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sphere 42 2.999 origin x=-1.7321 y=3 z=4.899

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sphere 49 2.999 origin x=-4.7321 y=8.1962 z=4.899

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sphere 52 2.5 origin x=5.196152 y=3 z=9.798

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media 100 1 12

media 100 1 13

media 106 1 21 -11

media 106 1 22 -12

media 106 1 23 -13

media 107 1 25

media 100 1 31

media 100 1 32

media 100 1 34

media 100 1 37

media 100 1 39

media 106 1 41 -31

media 106 1 42 -32

media 106 1 44 -34

media 106 1 47 -37

media 106 1 49 -39

media 100 1 51

media 100 1 52

media 100 1 53

media 106 1 61 -51

media 106 1 62 -52

media 106 1 63 -53

media 107 1 65

media 96 1 30 -21 -22 -23 -25 -41 -42 -44 -47 -49 -61 -62 -63 -65

boundary 30

'----------------------------------------------------------------------------

unit 55

com='unit 55'

hexprism 30 8.1962 9.798 0

sphere 11 2.5

sphere 12 2.5 origin x=5.196152 y=3 z=0
C-181

sphere 13 2.5 origin x=-5.196152 y=3 z=0

sphere 21 2.999

sphere 22 2.999 origin x=5.196152 y=3 z=0

sphere 23 2.999 origin x=-5.196152 y=3 z=0

sphere 25 2.999 origin x=0 y=6 z=0

sphere 31 2.5 origin x=3.4641 y=0 z=4.899

sphere 32 2.5 origin x=-1.7321 y=3 z=4.899

sphere 34 2.5 origin x=3.4641 y=6 z=4.899

sphere 36 2.5 origin x=-6.9283 y=0 z=4.899

sphere 37 2.5 origin x=9.4641 y=0 z=4.899

sphere 39 2.5 origin x=-4.7321 y=8.1962 z=4.899

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sphere 42 2.999 origin x=-1.7321 y=3 z=4.899

sphere 44 2.999 origin x=3.4641 y=6 z=4.899

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sphere 47 2.999 origin x=9.4641 y=0 z=4.899

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sphere 53 2.5 origin x=-5.196152 y=3 z=9.798

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media 100 1 12

media 100 1 13

media 106 1 21 -11

media 106 1 22 -12

media 106 1 23 -13

media 107 1 25

media 100 1 31

media 100 1 32

media 100 1 34

media 100 1 36

media 100 1 37

media 100 1 39

media 106 1 41 -31

media 106 1 42 -32

media 106 1 44 -34

media 106 1 46 -36

media 106 1 47 -37

media 106 1 49 -39

media 100 1 51

media 100 1 52

media 100 1 53

media 106 1 61 -51

media 106 1 62 -52

media 106 1 63 -53

media 107 1 65

media 96 1 30 -21 -22 -23 -25 -41 -42 -44 -46 -47 -49 -61 -62 -63 -65

boundary 30

'----------------------------------------------------------------------------

' control channels units

'----------------------------------------------------------------------------

unit 3

com='hot gas duct'
C-182

xcylinder 117 15 190 90 origin x=0 y=0 z=480

media 96 1 117

boundary 117

unit 4

com='elliptical klak'

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cylinder 115 3 258.764 0 origin x=5 y=0 z=0

cuboid 116 8 -8 3 -3 258.764 0

media 96 1 113

media 96 1 114 -113

media 96 1 115 -113

media 31 1 116 -113 -114 -115

boundary 116

unit 5

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cylinder 112 3 221.236 0

media 96 1 112

boundary 112

unit 6

com='upper circular klak channel'

cylinder 112 3 130 0

media 96 1 112

boundary 112

unit 7

com='control rod channel'

cylinder 111 6.5 450 0

media 96 1 111

boundary 111

unit 8

com='irradiation channels'

cylinder 111 6.5 450 0

media 96 1 111

boundary 111

unit 9

com='coolant channel'

cylinder 110 4 505 0

media 96 1 110

boundary 110

'----------------------------------------------------------------------------

' central 90cm radius column

'----------------------------------------------------------------------------

unit 2

com='central 90cm column'

cylinder 10 90 40 0

cylinder 20 90 95 0

cylinder 30 90 105 0

cylinder 40 90 130 0

cylinder 50 90 228.244 0

cylinder 60 90 351.818 0

cylinder 61 90 351.818 228.244

cylinder 70 90 388.764 0

cone 71 25 388.764 90 351.818

cylinder 72 25 388.764 0

cylinder 73 25 494.988 388.764

cylinder 80 90 402 0

cylinder 90 90 430 0
C-183

cylinder 91 41.75 430 0

cylinder 100 90 450 0

cylinder 101 41.75 450 0

cylinder 110 90 465 0

cylinder 111 70.75 465 0

cylinder 120 90 495 0

cylinder 121 70.75 495 0

cylinder 122 41.75 495 0

cylinder 123 25 494.988 0

cylinder 130 90 510 0

cylinder 131 41.75 510 0

cylinder 140 90 540 0

cylinder 141 25 540 0

cylinder 150 90 610 0

cylinder 151 25 610 0

array 1 61 place 7 7 1 0 0 228.244

array 2 71 place 7 7 1 0 0 351.818

array 3 73 place 7 7 1 0 0 388.764

media 1 1 10

media 2 1 20 -10

media 3 1 30 -20

media 4 1 40 -30

media 5 1 50 -40 -61

media 83 1 70 -71 -60

media 7 1 141 -123

media 81 1 151 -141

media 8 1 80 -70 -123

media 9 1 90 -80 -123

media 10 1 101 -91 -123

media 11 1 100 -90 -131

media 12 1 131 -101 -141

media 13 1 110 -100 -131

media 14 1 121 -111 -131

media 15 1 120 -110 -121

media 16 1 130 -120 -131

media 17 1 140 -130 -141

media 18 1 150 -140 -151

boundary 150

'----------------------------------------------------------------------------

' global unit 

'----------------------------------------------------------------------------

global unit 1

com='annular regions between radii 90 and 95.6 cm'

cylinder 10 95.6 610 0

cylinder 11 95.6 40 0

cylinder 12 95.6 95 0

cylinder 13 95.6 105 0

cylinder 14 95.6 388.74 0

cylinder 15 95.6 430 0

cylinder 16 95.6 450 0

cylinder 17 95.6 465 0

cylinder 18 95.6 495 0

cylinder 19 95.6 510 0

cylinder 20 95.6 540 0

cylinder 30 108.6 610 0

cylinder 31 108.6 40 0

cylinder 32 108.6 95 0
C-184

cylinder 33 108.6 105 0

cylinder 34 108.6 114.7 0

cylinder 35 108.6 130 0

cylinder 36 108.6 388.74 0

cylinder 37 108.6 430 0

cylinder 38 108.6 450 0

cylinder 39 108.6 465 0

cylinder 40 108.6 495 0

cylinder 41 108.6 510 0

cylinder 42 108.6 540 0

cylinder 50 140.6 610 0

cylinder 51 140.6 40 0

cylinder 52 140.6 95 0

cylinder 53 140.6 105 0

cylinder 54 140.6 388.74 0

cylinder 55 140.6 430 0

cylinder 56 140.6 450 0

cylinder 57 140.6 465 0

cylinder 58 140.6 495 0

cylinder 59 140.6 510 0

cylinder 60 140.6 540 0

cylinder 70 148.6 610 0

cylinder 71 148.6 40 0

cylinder 72 148.6 95 0

cylinder 73 148.6 105 0

cylinder 74 148.6 388.74 0

cylinder 75 148.6 430 0

cylinder 76 148.6 450 0

cylinder 77 148.6 465 0

cylinder 78 148.6 495 0

cylinder 79 148.6 510 0

cylinder 80 148.6 540 0

cylinder 90 167.793 610 0

cylinder 91 167.793 40 0

cylinder 92 167.793 388.74 0

cylinder 93 167.793 430 0

cylinder 94 167.793 450 0

cylinder 95 167.793 465 0

cylinder 96 167.793 495 0

cylinder 97 167.793 510 0

cylinder 98 167.793 540 0

cylinder 100 190 610 0

cylinder 101 190 40 0

cylinder 102 190 465 0

cylinder 103 190 495 0

cylinder 104 190 540 0

cuboid 105 191 -191 191 -191 611 0

hole 9 origin x=22.62042 y=142.8197 z=105

hole 9 origin x=65.64703 y=128.8395 z=105

hole 9 origin x=102.2476 y=102.2476 z=105

hole 9 origin x=128.8395 y=65.64703 z=105

hole 9 origin x=142.8197 y=22.62042 z=105

hole 9 origin x=142.8197 y=-22.62042 z=105

hole 9 origin x=128.8395 y=-65.64703 z=105

hole 9 origin x=102.2476 y=-102.2476 z=105

hole 9 origin x=65.64703 y=-128.8395 z=105

hole 9 origin x=22.62042 y=-142.8197 z=105
C-185

hole 9 origin x=-22.62042 y=-142.8197 z=105

hole 9 origin x=-65.64703 y=-128.8395 z=105

hole 9 origin x=-102.2476 y=-102.2476 z=105

hole 9 origin x=-128.8395 y=-65.64703 z=105

hole 9 origin x=-142.8197 y=-22.62042 z=105

hole 9 origin x=-142.8197 y=22.62042 z=105

hole 9 origin x=-128.8395 y=65.64703 z=105

hole 9 origin x=-102.2476 y=102.2476 z=105

hole 9 origin x=-65.64703 y=128.8395 z=105

hole 9 origin x=-22.62042 y=142.8197 z=105

hole 8 origin x=100.843 y=15.97196 z=0

hole 8 origin x=-15.97196 y=-100.843 z=0

hole 8 origin x=-100.843 y=-15.97196 z=0

hole 7 origin x=46.35243 y=90.97177 z=0

hole 7 origin x=90.97177 y=46.35243 z=0

hole 7 origin x=100.843 y=-15.97196 z=0

hole 7 origin x=72.1956 y=-72.1956 z=0

hole 7 origin x=15.97196 y=-100.843 z=0

hole 7 origin x=-46.35243 y=-90.97177 z=0

hole 7 origin x=-90.97177 y=-46.35243 z=0

hole 7 origin x=-100.843 y=15.97196 z=0

hole 7 origin x=-72.1956 y=72.1956 z=0

hole 7 origin x=-15.97196 y=100.843 z=0

hole 6 origin x=15.42444 y=97.38607 z=0

hole 6 origin x=69.72073 y=69.72073 z=0

hole 6 origin x=87.85324 y=-44.76346 z=0

hole 6 origin x=44.76346 y=-87.85324 z=0

hole 6 origin x=-69.72073 y=-69.72073 z=0

hole 6 origin x=-87.85324 y=44.76346 z=0

hole 6 origin x=-44.76346 y=87.85324 z=0

hole 5 origin x=15.42444 y=97.38607 z=388.764

hole 5 origin x=69.72073 y=69.72073 z=388.764

hole 5 origin x=87.85324 y=-44.76346 z=388.764

hole 5 origin x=44.76346 y=-87.85324 z=388.764

hole 5 origin x=-69.72073 y=-69.72073 z=388.764

hole 5 origin x=-87.85324 y=44.76346 z=388.764

hole 5 origin x=-44.76346 y=87.85324 z=388.764

hole 4 origin x=15.42444 y=97.38607 z=130 rotate a1=351 a2=0 a3=0

hole 4 origin x=69.72073 y=69.72073 z=130 rotate a1=315 a2=0 a3=0

hole 4 origin x=87.85324 y=-44.76346 z=130 rotate a1=243 a2=0 a3=0

hole 4 origin x=44.76346 y=-87.85324 z=130 rotate a1=207 a2=0 a3=0

hole 4 origin x=-69.72073 y=-69.72073 z=130 rotate a1=135 a2=0 a3=0

hole 4 origin x=-87.85324 y=44.76346 z=130 rotate a1=63 a2=0 a3=0

hole 4 origin x=-44.76346 y=87.85324 z=130 rotate a1=27 a2=0 a3=0

hole 3

hole 2

media 19 1 11

media 20 1 12 -11

media 21 1 13 -12

media 22 1 14 -13

media 22 1 15 -14

media 24 1 16 -15

media 22 1 17 -16

media 26 1 18 -17

media 22 1 19 -18

media 17 1 20 -19

media 18 1 10 -20
C-186

media 27 1 31 -10

media 28 1 32 -31 -10

media 29 1 33 -32 -10

media 28 1 34 -33 -10

media 30 1 35 -34 -10

media 31 1 36 -35 -10

media 30 1 37 -36 -10

media 42 1 38 -37 -10

media 43 1 39 -38 -10

media 44 1 40 -39 -10

media 43 1 41 -40 -10

media 46 1 42 -41 -10

media 47 1 30 -42 -10

media 17 1 51 -30

media 22 1 52 -51 -30

media 66 1 53 -52 -30

media 22 1 54 -53 -30

media 22 1 55 -54 -30

media 24 1 56 -55 -30

media 22 1 57 -56 -30

media 53 1 58 -57 -30

media 22 1 59 -58 -30

media 17 1 60 -59 -30

media 18 1 50 -60 -30

media 17 1 71 -50

media 22 1 72 -71 -50

media 57 1 73 -72 -50

media 58 1 74 -73 -50

media 58 1 75 -74 -50

media 60 1 76 -75 -50

media 58 1 77 -76 -50

media 62 1 78 -77 -50

media 58 1 79 -78 -50

media 64 1 80 -79 -50

media 65 1 70 -80 -50

media 17 1 91 -70

media 22 1 92 -91 -70

media 22 1 93 -92 -70

media 24 1 94 -93 -70

media 22 1 95 -94 -70

media 70 1 96 -95 -70

media 22 1 97 -96 -70

media 17 1 98 -97 -70

media 18 1 90 -98 -70

media 17 1 101 -90

media 17 1 102 -101 -90

media 77 1 103 -102 -90

media 17 1 104 -103 -90

media 17 1 100 -104 -90

media 0 1 105 -100

boundary 105

end geometry

'----------------------------------------------------------------------------

' array data

'----------------------------------------------------------------------------

read array

'----------------------------------------------------------------------------
C-187

' active core region array

'----------------------------------------------------------------------------

ara=1 nux=13 nuy=13 nuz=14 typ=shexagonal

fill

 215 215 215 215 252 254 255 253 251 215 215 215 215

 215 215 248 250 210 210 210 210 249 247 215 215 215

 215 215 246 210 210 210 210 210 210 210 245 215 215

 215 244 210 210 210 210 210 210 210 210 243 215 215

 215 242 210 210 210 210 210 210 210 210 210 241 215

 240 210 210 210 210 210 210 210 210 210 210 239 215

 215 220 210 210 210 210 210 210 210 210 210 221 215

 222 210 210 210 210 210 210 210 210 210 210 223 215

 215 224 210 210 210 210 210 210 210 210 210 225 215

 215 226 210 210 210 210 210 210 210 210 227 215 215

 215 215 228 210 210 210 210 210 210 210 229 215 215

 215 215 230 232 210 210 210 210 233 231 215 215 215

 215 215 215 215 234 236 238 237 235 215 215 215 215

 15 15 15 15 52 54 55 53 51 15 15 15 15

 15 15 48 50 10 10 10 10 49 47 15 15 15

 15 15 46 10 10 10 10 10 10 10 45 15 15

 15 44 10 10 10 10 10 10 10 10 43 15 15

 15 42 10 10 10 10 10 10 10 10 10 41 15

 40 10 10 10 10 10 10 10 10 10 10 39 15

 15 20 10 10 10 10 10 10 10 10 10 21 15

 22 10 10 10 10 10 10 10 10 10 10 23 15

 15 24 10 10 10 10 10 10 10 10 10 25 15

 15 26 10 10 10 10 10 10 10 10 27 15 15

 15 15 28 10 10 10 10 10 10 10 29 15 15

 15 15 30 32 10 10 10 10 33 31 15 15 15

 15 15 15 15 34 36 38 37 35 15 15 15 15

 15 15 15 15 52 54 55 53 51 15 15 15 15

 15 15 48 50 10 10 10 10 49 47 15 15 15

 15 15 46 10 10 10 10 10 10 10 45 15 15

 15 44 10 10 10 10 10 10 10 10 43 15 15

 15 42 10 10 10 10 10 10 10 10 10 41 15

 40 10 10 10 10 10 10 10 10 10 10 39 15

 15 20 10 10 10 10 10 10 10 10 10 21 15

 22 10 10 10 10 10 10 10 10 10 10 23 15

 15 24 10 10 10 10 10 10 10 10 10 25 15

 15 26 10 10 10 10 10 10 10 10 27 15 15

 15 15 28 10 10 10 10 10 10 10 29 15 15

 15 15 30 32 10 10 10 10 33 31 15 15 15

 15 15 15 15 34 36 38 37 35 15 15 15 15

 15 15 15 15 52 54 55 53 51 15 15 15 15

 15 15 48 50 10 10 10 10 49 47 15 15 15

 15 15 46 10 10 10 10 10 10 10 45 15 15

 15 44 10 10 10 10 10 10 10 10 43 15 15

 15 42 10 10 10 10 10 10 10 10 10 41 15

 40 10 10 10 10 10 10 10 10 10 10 39 15

 15 20 10 10 10 10 10 10 10 10 10 21 15

 22 10 10 10 10 10 10 10 10 10 10 23 15

 15 24 10 10 10 10 10 10 10 10 10 25 15

 15 26 10 10 10 10 10 10 10 10 27 15 15

 15 15 28 10 10 10 10 10 10 10 29 15 15

 15 15 30 32 10 10 10 10 33 31 15 15 15

 15 15 15 15 34 36 38 37 35 15 15 15 15

 15 15 15 15 52 54 55 53 51 15 15 15 15
C-188

 15 15 48 50 10 10 10 10 49 47 15 15 15

 15 15 46 10 10 10 10 10 10 10 45 15 15

 15 44 10 10 10 10 10 10 10 10 43 15 15

 15 42 10 10 10 10 10 10 10 10 10 41 15

 40 10 10 10 10 10 10 10 10 10 10 39 15

 15 20 10 10 10 10 10 10 10 10 10 21 15

 22 10 10 10 10 10 10 10 10 10 10 23 15

 15 24 10 10 10 10 10 10 10 10 10 25 15

 15 26 10 10 10 10 10 10 10 10 27 15 15

 15 15 28 10 10 10 10 10 10 10 29 15 15

 15 15 30 32 10 10 10 10 33 31 15 15 15

 15 15 15 15 34 36 38 37 35 15 15 15 15

 15 15 15 15 52 54 55 53 51 15 15 15 15

 15 15 48 50 10 10 10 10 49 47 15 15 15

 15 15 46 10 10 10 10 10 10 10 45 15 15

 15 44 10 10 10 10 10 10 10 10 43 15 15

 15 42 10 10 10 10 10 10 10 10 10 41 15

 40 10 10 10 10 10 10 10 10 10 10 39 15

 15 20 10 10 10 10 10 10 10 10 10 21 15

 22 10 10 10 10 10 10 10 10 10 10 23 15

 15 24 10 10 10 10 10 10 10 10 10 25 15

 15 26 10 10 10 10 10 10 10 10 27 15 15

 15 15 28 10 10 10 10 10 10 10 29 15 15

 15 15 30 32 10 10 10 10 33 31 15 15 15

 15 15 15 15 34 36 38 37 35 15 15 15 15

 15 15 15 15 52 54 55 53 51 15 15 15 15

 15 15 48 50 10 10 10 10 49 47 15 15 15

 15 15 46 10 10 10 10 10 10 10 45 15 15

 15 44 10 10 10 10 10 10 10 10 43 15 15

 15 42 10 10 10 10 10 10 10 10 10 41 15

 40 10 10 10 10 10 10 10 10 10 10 39 15

 15 20 10 10 10 10 10 10 10 10 10 21 15

 22 10 10 10 10 10 10 10 10 10 10 23 15

 15 24 10 10 10 10 10 10 10 10 10 25 15

 15 26 10 10 10 10 10 10 10 10 27 15 15

 15 15 28 10 10 10 10 10 10 10 29 15 15

 15 15 30 32 10 10 10 10 33 31 15 15 15

 15 15 15 15 34 36 38 37 35 15 15 15 15

 15 15 15 15 52 54 55 53 51 15 15 15 15

 15 15 48 50 10 10 10 10 49 47 15 15 15

 15 15 46 10 10 10 10 10 10 10 45 15 15

 15 44 10 10 10 10 10 10 10 10 43 15 15

 15 42 10 10 10 10 10 10 10 10 10 41 15

 40 10 10 10 10 10 10 10 10 10 10 39 15

 15 20 10 10 10 10 10 10 10 10 10 21 15

 22 10 10 10 10 10 10 10 10 10 10 23 15

 15 24 10 10 10 10 10 10 10 10 10 25 15

 15 26 10 10 10 10 10 10 10 10 27 15 15

 15 15 28 10 10 10 10 10 10 10 29 15 15

 15 15 30 32 10 10 10 10 33 31 15 15 15

 15 15 15 15 34 36 38 37 35 15 15 15 15

 15 15 15 15 52 54 55 53 51 15 15 15 15

 15 15 48 50 10 10 10 10 49 47 15 15 15

 15 15 46 10 10 10 10 10 10 10 45 15 15

 15 44 10 10 10 10 10 10 10 10 43 15 15

 15 42 10 10 10 10 10 10 10 10 10 41 15

 40 10 10 10 10 10 10 10 10 10 10 39 15
C-189

 15 20 10 10 10 10 10 10 10 10 10 21 15

 22 10 10 10 10 10 10 10 10 10 10 23 15

 15 24 10 10 10 10 10 10 10 10 10 25 15

 15 26 10 10 10 10 10 10 10 10 27 15 15

 15 15 28 10 10 10 10 10 10 10 29 15 15

 15 15 30 32 10 10 10 10 33 31 15 15 15

 15 15 15 15 34 36 38 37 35 15 15 15 15

 15 15 15 15 52 54 55 53 51 15 15 15 15

 15 15 48 50 10 10 10 10 49 47 15 15 15

 15 15 46 10 10 10 10 10 10 10 45 15 15

 15 44 10 10 10 10 10 10 10 10 43 15 15

 15 42 10 10 10 10 10 10 10 10 10 41 15

 40 10 10 10 10 10 10 10 10 10 10 39 15

 15 20 10 10 10 10 10 10 10 10 10 21 15

 22 10 10 10 10 10 10 10 10 10 10 23 15

 15 24 10 10 10 10 10 10 10 10 10 25 15

 15 26 10 10 10 10 10 10 10 10 27 15 15

 15 15 28 10 10 10 10 10 10 10 29 15 15

 15 15 30 32 10 10 10 10 33 31 15 15 15

 15 15 15 15 34 36 38 37 35 15 15 15 15

 15 15 15 15 52 54 55 53 51 15 15 15 15

 15 15 48 50 10 10 10 10 49 47 15 15 15

 15 15 46 10 10 10 10 10 10 10 45 15 15

 15 44 10 10 10 10 10 10 10 10 43 15 15

 15 42 10 10 10 10 10 10 10 10 10 41 15

 40 10 10 10 10 10 10 10 10 10 10 39 15

 15 20 10 10 10 10 10 10 10 10 10 21 15

 22 10 10 10 10 10 10 10 10 10 10 23 15

 15 24 10 10 10 10 10 10 10 10 10 25 15

 15 26 10 10 10 10 10 10 10 10 27 15 15

 15 15 28 10 10 10 10 10 10 10 29 15 15

 15 15 30 32 10 10 10 10 33 31 15 15 15

 15 15 15 15 34 36 38 37 35 15 15 15 15

 15 15 15 15 52 54 55 53 51 15 15 15 15

 15 15 48 50 10 10 10 10 49 47 15 15 15

 15 15 46 10 10 10 10 10 10 10 45 15 15

 15 44 10 10 10 10 10 10 10 10 43 15 15

 15 42 10 10 10 10 10 10 10 10 10 41 15

 40 10 10 10 10 10 10 10 10 10 10 39 15

 15 20 10 10 10 10 10 10 10 10 10 21 15

 22 10 10 10 10 10 10 10 10 10 10 23 15

 15 24 10 10 10 10 10 10 10 10 10 25 15

 15 26 10 10 10 10 10 10 10 10 27 15 15

 15 15 28 10 10 10 10 10 10 10 29 15 15

 15 15 30 32 10 10 10 10 33 31 15 15 15

 15 15 15 15 34 36 38 37 35 15 15 15 15

 15 15 15 15 52 54 55 53 51 15 15 15 15

 15 15 48 50 10 10 10 10 49 47 15 15 15

 15 15 46 10 10 10 10 10 10 10 45 15 15

 15 44 10 10 10 10 10 10 10 10 43 15 15

 15 42 10 10 10 10 10 10 10 10 10 41 15

 40 10 10 10 10 10 10 10 10 10 10 39 15

 15 20 10 10 10 10 10 10 10 10 10 21 15

 22 10 10 10 10 10 10 10 10 10 10 23 15

 15 24 10 10 10 10 10 10 10 10 10 25 15

 15 26 10 10 10 10 10 10 10 10 27 15 15

 15 15 28 10 10 10 10 10 10 10 29 15 15
C-190

 15 15 30 32 10 10 10 10 33 31 15 15 15

 15 15 15 15 34 36 38 37 35 15 15 15 15

 115 115 115 115 152 154 155 153 151 115 115 115 115

 115 115 148 150 110 110 110 110 149 147 115 115 115

 115 115 146 110 110 110 110 110 110 110 145 115 115

 115 144 110 110 110 110 110 110 110 110 143 115 115

 115 142 110 110 110 110 110 110 110 110 110 141 115

 140 110 110 110 110 110 110 110 110 110 110 139 115

 115 120 110 110 110 110 110 110 110 110 110 121 115

 122 110 110 110 110 110 110 110 110 110 110 123 115

 115 124 110 110 110 110 110 110 110 110 110 125 115

 115 126 110 110 110 110 110 110 110 110 127 115 115

 115 115 128 110 110 110 110 110 110 110 129 115 115

 115 115 130 132 110 110 110 110 133 131 115 115 115

 115 115 115 115 134 136 138 137 135 115 115 115 115

end fill

'----------------------------------------------------------------------------

' conical section of the discharge tube (region 91 in Fig. 3.3)

' 351.818cm - 388.764cm 

'----------------------------------------------------------------------------

ara=2 nux=13 nuy=13 nuz=5 typ=shexagonal

fill

 315 315 315 315 315 615 333 613 315 315 315 315 315

 315 315 315 332 341 310 310 341 331 315 315 315 315

 315 315 617 339 310 310 310 310 310 340 611 315 315

 315 330 310 310 310 310 310 310 310 310 329 315 315

 315 619 310 310 310 310 310 310 310 310 310 609 315

 315 334 310 310 310 310 310 310 310 310 335 315 315

 315 320 310 310 310 310 310 310 310 310 310 321 315

 315 334 310 310 310 310 310 310 310 310 335 315 315

 315 621 310 310 310 310 310 310 310 310 310 607 315

 315 324 310 310 310 310 310 310 310 310 325 315 315

 315 315 623 337 310 310 310 310 310 338 605 315 315

 315 315 315 326 336 310 310 336 327 315 315 315 315

 315 315 315 315 315 601 328 603 315 315 315 315 315

 18 18 18 18 18 616 433 614 18 18 18 18 18

 18 18 18 432 450 451 452 700 431 18 18 18 18

 18 18 618 448 454 516 517 518 455 449 612 18 18

 18 430 446 514 13 13 13 13 515 447 429 18 18

 18 620 444 512 13 13 13 13 13 513 445 610 18

 18 434 510 13 13 13 13 13 13 511 435 18 18

 18 420 456 13 13 13 13 13 13 13 457 421 18

 18 434 508 13 13 13 13 13 13 509 435 18 18

 18 622 443 506 13 13 13 13 13 507 441 608 18

 18 424 442 504 13 13 13 13 505 440 425 18 18

 18 18 624 437 458 501 502 503 459 439 606 18 18

 18 18 18 426 460 436 453 438 427 18 18 18 18

 18 18 18 18 18 602 428 604 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 461 498 499 500 462 18 18 18 18

 18 18 18 492 493 494 495 496 497 18 18 18 18

 18 18 18 490 487 13 13 13 488 491 18 18 18

 18 18 486 487 13 13 13 13 488 489 18 18 18

 18 18 463 484 13 13 13 13 13 485 464 18 18

 18 18 480 477 13 13 13 13 478 483 18 18 18

 18 18 18 476 477 13 13 13 478 479 18 18 18
C-191

 18 18 18 470 471 472 473 474 475 18 18 18 18

 18 18 18 18 465 467 468 469 466 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 530 531 532 533 18 18 18 18 18

 18 18 18 18 528 534 535 536 529 18 18 18 18

 18 18 18 528 537 13 13 538 529 18 18 18 18

 18 18 18 526 539 13 13 13 540 527 18 18 18

 18 18 18 524 541 13 13 542 525 18 18 18 18

 18 18 18 18 524 543 544 545 525 18 18 18 18

 18 18 18 18 520 521 522 523 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 16 16 16 16 16 16 16 16 16 16 16 16 16

 16 16 16 16 16 16 16 16 16 16 16 16 16

 16 16 16 16 16 16 16 16 16 16 16 16 16

 16 16 16 16 16 16 16 16 16 16 16 16 16

 16 16 16 16 16 546 547 548 16 16 16 16 16

 16 16 16 16 549 558 559 550 16 16 16 16 16

 16 16 16 16 551 560 11 561 552 16 16 16 16

 16 16 16 16 553 562 563 554 16 16 16 16 16

 16 16 16 16 16 555 556 557 16 16 16 16 16

 16 16 16 16 16 16 16 16 16 16 16 16 16

 16 16 16 16 16 16 16 16 16 16 16 16 16

 16 16 16 16 16 16 16 16 16 16 16 16 16

 16 16 16 16 16 16 16 16 16 16 16 16 16

end fill

'----------------------------------------------------------------------------

' cylindrical section of the discharge tube (region 6 in Fig. 3.3)

' 388.764cm - 495.0cm 

'----------------------------------------------------------------------------

ara=3 nux=13 nuy=13 nuz=12 typ=shexagonal

fill

 17 17 17 17 17 17 17 17 17 17 17 17 17

 17 17 17 17 17 17 17 17 17 17 17 17 17

 17 17 17 17 17 17 17 17 17 17 17 17 17

 17 17 17 17 17 17 17 17 17 17 17 17 17

 17 17 17 17 17 17 564 17 17 17 17 17 17

 17 17 17 17 565 570 571 566 17 17 17 17 17

 17 17 17 17 17 572 12 573 17 17 17 17 17

 17 17 17 17 567 574 575 568 17 17 17 17 17

 17 17 17 17 17 17 569 17 17 17 17 17 17

 17 17 17 17 17 17 17 17 17 17 17 17 17

 17 17 17 17 17 17 17 17 17 17 17 17 17

 17 17 17 17 17 17 17 17 17 17 17 17 17

 17 17 17 17 17 17 17 17 17 17 17 17 17

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 576 18 18 18 18 18 18

 18 18 18 18 577 582 583 578 18 18 18 18 18

 18 18 18 18 18 584 13 585 18 18 18 18 18
C-192

 18 18 18 18 579 586 587 580 18 18 18 18 18

 18 18 18 18 18 18 581 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 576 18 18 18 18 18 18

 18 18 18 18 577 582 583 578 18 18 18 18 18

 18 18 18 18 18 584 13 585 18 18 18 18 18

 18 18 18 18 579 586 587 580 18 18 18 18 18

 18 18 18 18 18 18 581 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 576 18 18 18 18 18 18

 18 18 18 18 577 582 583 578 18 18 18 18 18

 18 18 18 18 18 584 13 585 18 18 18 18 18

 18 18 18 18 579 586 587 580 18 18 18 18 18

 18 18 18 18 18 18 581 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 576 18 18 18 18 18 18

 18 18 18 18 577 582 583 578 18 18 18 18 18

 18 18 18 18 18 584 13 585 18 18 18 18 18

 18 18 18 18 579 586 587 580 18 18 18 18 18

 18 18 18 18 18 18 581 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 576 18 18 18 18 18 18

 18 18 18 18 577 582 583 578 18 18 18 18 18

 18 18 18 18 18 584 13 585 18 18 18 18 18

 18 18 18 18 579 586 587 580 18 18 18 18 18

 18 18 18 18 18 18 581 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18
C-193

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 576 18 18 18 18 18 18

 18 18 18 18 577 582 583 578 18 18 18 18 18

 18 18 18 18 18 584 13 585 18 18 18 18 18

 18 18 18 18 579 586 587 580 18 18 18 18 18

 18 18 18 18 18 18 581 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 576 18 18 18 18 18 18

 18 18 18 18 577 582 583 578 18 18 18 18 18

 18 18 18 18 18 584 13 585 18 18 18 18 18

 18 18 18 18 579 586 587 580 18 18 18 18 18

 18 18 18 18 18 18 581 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 576 18 18 18 18 18 18

 18 18 18 18 577 582 583 578 18 18 18 18 18

 18 18 18 18 18 584 13 585 18 18 18 18 18

 18 18 18 18 579 586 587 580 18 18 18 18 18

 18 18 18 18 18 18 581 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 576 18 18 18 18 18 18

 18 18 18 18 577 582 583 578 18 18 18 18 18

 18 18 18 18 18 584 13 585 18 18 18 18 18

 18 18 18 18 579 586 587 580 18 18 18 18 18

 18 18 18 18 18 18 581 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18
C-194

 18 18 18 18 18 18 576 18 18 18 18 18 18

 18 18 18 18 577 582 583 578 18 18 18 18 18

 18 18 18 18 18 584 13 585 18 18 18 18 18

 18 18 18 18 579 586 587 580 18 18 18 18 18

 18 18 18 18 18 18 581 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 18 18 18 18 18 18 18 18 18 18 18 18 18

 19 19 19 19 19 19 19 19 19 19 19 19 19

 19 19 19 19 19 19 19 19 19 19 19 19 19

 19 19 19 19 19 19 19 19 19 19 19 19 19

 19 19 19 19 19 19 19 19 19 19 19 19 19

 19 19 19 19 19 19 588 19 19 19 19 19 19

 19 19 19 19 589 594 595 590 19 19 19 19 19

 19 19 19 19 19 596 14 597 19 19 19 19 19

 19 19 19 19 591 598 599 592 19 19 19 19 19

 19 19 19 19 19 19 593 19 19 19 19 19 19

 19 19 19 19 19 19 19 19 19 19 19 19 19

 19 19 19 19 19 19 19 19 19 19 19 19 19

 19 19 19 19 19 19 19 19 19 19 19 19 19

 19 19 19 19 19 19 19 19 19 19 19 19 19

end fill

'----------------------------------------------------------------------------

end array

'----------------------------------------------------------------------------

' source (start) data

'----------------------------------------------------------------------------

read start

nst=0

xsm=-90

xsp=90

ysm=-90

ysp=90

zsm=228.244

zsp=388.764

end start

'----------------------------------------------------------------------------

' volume data

'----------------------------------------------------------------------------

read volume

 type=random

 batches=1000

 points=1000000

end volume

'----------------------------------------------------------------------------

end data

end

'============================================================================

'end of model

'============================================================================
BIBLIOGRAPHIC DATA SHEET

(See instructions on the reverse)

NRC FORM 335

(12-2010)

NRCMD 3.7

U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NUMBER

 (Assigned by NRC, Add Vol., Supp., Rev.,

 and Addendum Numbers, if any.)

NUREG/CR-7107

3. DATE REPORT PUBLISHED

MONTH

July

YEAR

2012

4. FIN OR GRANT NUMBER

N6842

2. TITLE AND SUBTITLE

Validation of SCALE for High Temperature Gas-Cooled Reactor Analysis

5. AUTHOR(S)

Germina Ilas

Dan Ilas

Ryan P. Kelly

Eva E. Sunny

6. TYPE OF REPORT

NUREG/CR

7. PERIOD COVERED (Inclusive Dates)

8. PERFORMING ORGANIZATION - NAME AND ADDRESS (If NRC, provide Division, Office or Region, U.S. Nuclear Regulatory Commission, and mailing address; if contractor,

Oak Ridge National Laboratory

9. SPONSORING ORGANIZATION - NAME AND ADDRESS (If NRC, type "Same as above"; if contractor, provide NRC Division, Office or Region, U.S. Nuclear Regulatory Commission, 

Division of Systems Analysis

provide name and mailing address.)

and mailing address.)

10. SUPPLEMENTARY NOTES

n/a

11. ABSTRACT (200 words or less)

This report documents verification and validation studies carried out to assess the performance of the SCALE code system

methods and nuclear data for modeling and analysis of High Temperature Gas-Cooled Reactor (HTGR) configurations.

Validation data were available form the International Handbook of Evaluated Reactor Physics Benchmark Experiments, IRPhE,

prepared by the International Reactor Physics Experiment Evaluation Project, for two different HTGR designs: prismatic and

pebble bed. SCALE models have been developed for HTTR, a prismatic fuel design reactor operated in Japan and HTR-10, a

pebble bed reactor operated in China. The models were based on benchmark specifications included in the 2009, 2010 and

2011 releases of the IRPhE Handbook. SCALE models for the HTR-PROTEUS pebble bed configuration at the PROTEUS

critical facility in Switzerland have also been developed, based on benchmark specifications included in a 2009 IRPhE draft

benchmark. The development of the SCALE models has involved a series of investigations to identify particular issues

associated with modeling the physics of HTGRs and to understand and quantify the effect of particular modeling assumptions on

calculation-to-experiment comparisons.

12. KEY WORDS/DESCRIPTORS (List words or phrases that will assist researchers in locating the report.)

HTGR, SCALE 14. SECURITY CLASSIFICATION

13. AVAILABILITY STATEMENT

unlimited

(This Page)

unclassified

(This Report)

unclassified

15. NUMBER OF PAGES

16. PRICE

NRC FORM 335 (12-2010)

Managed by UT-Batelle, LLC

Oak Ridge, TN 37831-6170

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, D.C. 20555-0001


UNITED STATES 

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

--------------------

OFFICIAL BUSINESS
 

 

NUREG/CR-7107 Validation of SCALE for High Temperature Gas-Cooled Reactor Analysis