Use of Serpent Monte-Carlo code for

development of 3D full-core models of

Gen-IV fast-spectrum reactors and

preparation of group constants for

transient analyses with PARCS/TRACE

coupled system

LEVON K. GHASABYAN

Degree project in

Reactor Physics

Second cycle

Stockholm, Sweden 2013

Use of Serpent Monte-Carlo code for development of 3D full-core models of Gen-IV fast-spectrum reactors and

preparation of group constants for transient analyses with PARCS/TRACE coupled system

Master of Science Thesis presented by

Levon K. Ghasabyan

Thesis Promoters

(Royal Institute of Technology, KTH)

Waclaw Gudowski Vasily Arzhanov

Thesis Supervisors (Paul Scherrer Institute, PSI)

Konstantin Mikityuk Jiri Krepel

Sandro Pelloni

Division of Nuclear and Reactor Physics Department of Physics

Royal Institute of Technology

Stockholm 2013

II

Copyright Notice

The author gives the permission to use this thesis for consultation and to copy parts of it

for personal use. Every other use is subject to the copyright laws; more specifically the

source must be extensively specified when using results from this thesis.

February, 2013

Levon K. Ghasabyan

Paul Scherrer Institute

Reactorstrasse 1, Villigen PSI, Switzerland

(Email: levon.ghasabyan@psi.ch)

III

Abstract

Current work presents a methodology and a wrapper code, which uses Serpent MC code

for generating group constant database, compatible with U.S. NRC PARCS neutronics

simulator. The database contains all necessary beginning-of-life (BOL) group constants

and their derivatives necessary for transient analyses of fast spectrum reactors.

The applicability of the methodology was tested on the European Sodium-cooled Fast

Reactor (ESFR) design with an oxide fuel proposed by CEA (France). The results of

steady-state and single-effect calculations of the PARCS/TRACE coupled system were

compared with those of the Serpent MC code.

The k-effective, power peaking factors and safety parameters (such as Doppler constant,

coolant expansion coefficient, fuel axial expansion coefficient, diagrid expansion

coefficients and control rod worth) calculated by PARCS/TRACE were compared with the

Serpent MC calculation results. The comparison indicates overall reasonable agreement

between conceptually different (deterministic and stochastic) codes. The new

development makes it in principle possible to use Serpent for cross section generation

for PARCS to perform transient analyses of fast reactors. The advantages and limitations

of this methodology are discussed.

The appendix contains Serpent input file of an SFR core, the Matlab code of S2P

wrapper and the PARCS input file.

IV

Acknowledgements

This report is based on the thesis submitted by the first author to the Division of Nuclear

and Reactor Physics, in partial fulfillment of the requirements for the Degree of Master

of Science in Nuclear Energy Engineering at The Royal Institute of Technology (Swedish:

Kungliga Tekniska Högskolan).

I would like to express my appreciation to all members of the Fast Reactors Project

group (FAST) of Paul Scherrer Institute. It has been a privilege to work with you.

In particular, I am profoundly indebted to my main supervisor, Dr. Konstantin Mikityuk,

who was very generous with his time and knowledge and guided me in each step to

complete the thesis. Thank you for giving me the opportunity to be part of the FAST

team.

I am deeply grateful to Dr. Sandro Pelloni for guiding me and being constant source of

knowledge and inspiration. Thank you for supporting my endeavors.

Special thanks to Dr. Jiri Krepel who was readily available for any discussion and freewill

to answer my many questions.

I am greatly thankful to my present-day KTH supervisor, Prof. Waclaw Gudowski for

supporting my plans to do my thesis research in Switzerland. Prof. Gudowski gave me

the flexible schedule and freedom to complete the thesis without a rush.

My sincere gratitude goes to my KTH supervisor Dr. Vasily Arzhanov. Thank you for your

long lasting supervision, invaluable help and guidance during all these years at KTH. It

has been a privilege to work with you.

V

Special thanks to Dr. Kaichao Sun, who was always open for any kind of discussion and

forced me to start playing basketball. I must thank Vladimir Brankov, for helping with

accommodation and many other issues.

I also wish to thank all the professors, lecturers and academic staff of the Division of

Reactor Physics, KTH, for their on-going advice and support during the course of my MSc

studies.

And finally, last but not least, my utmost gratitude goes to my family who has been an

important and constant source of financial and spiritual support.

VI

Contents Figures ................................................................................................................... VII Tables ................................................................................................................... VIII 1. Introduction and Thesis Structure ................................................................. 1

1.1. Introduction .......................................................................................... 1 1.2. Motivation ............................................................................................. 2 1.3. Thesis Structure .................................................................................... 3

2. Thesis Background ......................................................................................... 4 2.1. Simulation tools .................................................................................... 4 2.2. Reactivity coefficients, thermal expansions and safety parameters .. 10 2.3. Reactor Core Design ............................................................................ 13

3. Methodology ................................................................................................ 16 3.1. Serpent Core model ............................................................................ 16 3.2. Generation of Group Constants .......................................................... 17 3.3. Multi-universe core mapping.............................................................. 19 3.4. Cross Sections and their derivatives ................................................... 21 3.5. S2P wrapper ........................................................................................ 27 3.6. Parcs model ......................................................................................... 28 3.7. Trace model ........................................................................................ 29 3.8. Calculating safety parameters with PARCS/TRACE ............................. 30

4. Results and Discussion ................................................................................. 32 5. Conclusions and Future Work ...................................................................... 37

5.1. Conclusions ......................................................................................... 37 5.2. Future Work ........................................................................................ 38

VII

A. S2P Wrapper ................................................................................................ 40 B. S2P case-list .................................................................................................. 54 C. SFR Parameterized Serpent Input ................................................................ 55 D. SFR Parcs Input ............................................................................................. 65 E. GFR Serpent Input ........................................................................................ 68 F. LFR Serpent Input ......................................................................................... 75 G. GFR ............................................................................................................... 86 H. ELSY .............................................................................................................. 87 I. Shannon Entropy.......................................................................................... 88 References ............................................................................................................ 90 List of Abbreviations ............................................................................................. 92

Figures

Figure 1: Comparison of core representation by Serpent MC and PARCS. ........................ 1 Figure 2: FAST assembly code, composed of different well known code systems. ........... 8 Figure 3: Flow chart of FAST code system. ......................................................................... 8 Figure 4: New modules of the FAST code system. .............................................................. 9 Figure 5: ESFR Working Horses core design ..................................................................... 13 Figure 6: Axial cross-section of the ESFR core as modeled in Serpent and PARCS/TRACE[14]. ............................................................................................................ 14 Figure 7: Radial (left) and axial (right) cut of ESFR fuel assembly. ................................... 16 Figure 8: Radial cut of CSD (left) and DSD (right) control rod assemblies. ....................... 17 Figure 9: Fuel assembly multi-universe mapping. ............................................................ 20 Figure 10: Universe map of ESFR core. ............................................................................. 21 Figure 11: Perturbation of fuel height inside fuel pins of ESFR FA-s. ............................... 22 Figure 12: Core radial expansion model. .......................................................................... 24 Figure 13: Control rod positioning in ESFR core. .............................................................. 25 Figure 14: The flowchart inside S2P Wrapper. ................................................................. 27 Figure 15: PARCS model, one sixth of the ESFR core. ....................................................... 28 Figure 16: Schematic of the TRACE model........................................................................ 29 Figure 17: Convergence of Shannon entropy and k-eff in the ESFR 3D full-core calculation. ........................................................................................................................ 33

VIII

Figure 18: Power peaking and relative error for CZP ESFR 3D core. ................................ 34 Figure 19: Statistical uncertainty of neutron flux of inner FA. ......................................... 35

Tables

Table 1: ESFR Working Horses core parameters. ............................................................. 15 Table 2: ECCO 33-group energy structure. ....................................................................... 17 Table 3: Equivalence table of Group Constants of Serpent and PARCS. .......................... 18 Table 4: Equivalence table of kinetic parameters of Serpent and PARCS. ....................... 18 Table 5: Calculation methodology of safety parameters and XS derivatives. .................. 26 Table 6: k-effective of ESFR 3D core for reference case at 300K calculated by Serpent MC and PARCS/TRACE codes. .................................................................................................. 34 Table 7: Safety parameters and their relative deviations calculated with Serpent MC and PARCS/TRACE for ESFR 3D core. ....................................................................................... 35 Table 8: GFR core parameters. ......................................................................................... 86 Table 9: Safety coefficients and their relative deviations calculated with Serpent MC. .. 86 Table 10: ELSY core parameters. ...................................................................................... 87 Table 11: Safety coefficients and their relative deviations calculated with Serpent MC. 87

1

1. Introduction and Thesis Structure

1.1. INTRODUCTION

To simulate real scale nuclear reactor one can use a Monte Carlo code or deterministic

code. The major advantages of Monte Carlo codes are complete geometry

representation, best available knowledge on neutron interactions and possibility to

generate group constants for any geometric region of any type of reactor core [1].

Figure 1: Comparison of core representation by Serpent MC and PARCS.

However, the apparent advantages of MC codes are counterweighted with the

disadvantages of high computational cost, which is a major limitation when complex

systems are considered. Another problem is the methodological conflict between

stochastic and deterministic methods based on a number of analytical approximations.

On the other hand, deterministic codes provide exact results (without standard

deviations) and are computationally less demanding, which guarantees the possibility of

performing long transient calculations. Nonetheless, these advantages of deterministic

PARCS

Diffusion Theory

Simplification

Serpent

Transport Theory

Detailed Geometry + isotopic composition

REFLECTOR

FISSION GAS

FUEL

SODIUM

WRAPPER

Simplified Geometry+ Homogenized Macro XS

2

codes are compensated with simplified geometry and transport/diffusion physics

(Figure 1).

Current work presents the use of both modern stochastic (Serpent MC) and

deterministic (PARCS/TRACE) codes for 3D fast reactor core simulations. This approach

guarantees superposition of advantages and best practices of conceptually different

stochastic and deterministic methods.

In our study the Serpent MC code was used to simulate multiple real scale ESFR

reactor cores with perturbed geometries, densities and temperatures. From these

simulations safety parameters of ESFR core were calculated.

Afterwards, a special methodology was developed and used to analyze Serpent

generated group constants and convert the data to PARCS compatible database.

Subsequently, single-effect transient simulations were performed with PARCS/TRACE

coupled system and major safety parameters were calculated and compared with those

of Serpent [2].

1.2. MOTIVATION

The motivation of this research came out of ongoing effort of Fast Reactors group at PSI

to assemble a general purpose tool which is capable of performing both core statics and

dynamics simulation of advanced fast-spectrum concepts with different coolants.

A code system of this complexity is attractive in the framework of safety related

studies aimed at establishing the basic viability of the advanced critical fast reactors

suggested by the Generation IV International Forum. This general purpose code system

will be able to evaluate, in a systematic manner, a wide variety of transients.

3

Furthermore, via modeling of the entire power plant, we will be able to assess the

complex phenomena which depend, not only on the core behavior of next generation

reactor types, but also on the interaction between the primary and secondary systems.

The motivation of this project lies in the fact that: (a) an integrated system for

the analysis of a broad range of proposed scenarios for advanced fast-spectrum reactors

is not available currently, and (b) the stand-alone codes being foreseen as part of the

package are state-of-the-art as regards a certain domain of applications, but are either

not coupled together or qualified and tested for advanced fast-spectrum system analysis

[3].

1.3. THESIS STRUCTURE

The thesis is organized in five chapters. Following this introductory chapter, the second

chapter shortly describes simulation tools, the physics of the safety parameters in fast-

spectrum reactors and the ESFR core design.

Chapter 3 describes in detail the methodology used for modeling the ESFR core

in Serpent. The methodology of multiple geometric perturbations, necessary for

calculating safety coefficients and XS derivatives, is presented. Afterwards,

PARCS/TRACE model is described with the methodology used to simulate single effect

transient feedbacks.

The main simulation results are presented in Chapter 4. The recommendations

for future work and concluding remarks are summarized in Chapter 5.

4

2. Thesis Background

There are two basic types of nuclear simulation codes, stochastic and deterministic. The

combined usage of these codes has proved to be advantageous vs. single use of any of

them. In the present study we have used the SERPENT MC code to generate detailed XS-

s for a number of scenarios. Generated XS-s from multiple simulations were analyzed

and converted into PARCS compatible XSEC database file which contains all group

constants, their derivatives and kinetic parameters necessary to simulate transient

calculations with PARCS/TRACE. A special wrapper code was developed to automate and

simplify the simulation of XSEC database.

In Section 2.1 we present a short description of calculation tools used for

simulation of sodium-cooled fast reactor. Section 2.2 describes those reactivity effects

and safety parameters which were calculated during our research. Finally, Section 2.3

presents the ESFR core design which was used to model and calculate integral and

safety parameters both in Serpent MC and PARCS/TRACE.

2.1. SIMULATION TOOLS

Serpent

Serpent (version 1.1.18) is a 3D continuous-energy Monte Carlo calculation code

developed and optimized for reactor physics applications since 2004. Serpent code uses

Woodcock delta-tracking [4] and unionized energy grid [5], which significantly improves

the code performance in time at the expense of computer memory space. The main

intended use of this code is the generation of homogenized multi-group constants for

deterministic 3D core analysis. The code is capable to calculate homogenized multi-

group cross sections, scattering matrixes, kinetic parameters, etc. for any energy group

5

structure and region of interest. Serpent also has a built-in decay and burnup routine

which is capable to generate time-dependent isotopic compositions and spent-fuel

characteristics including radioactivity and decay heat. Presently, a newer version of

Serpent code (Serpent 2) is being developed which will extend the burnup capability to

the full 3D core problems without any limitations in parallelization of multi-core CPU’s.

Reasonably short calculation time and capability to generate multi-group

constants makes Serpent one of the most attractive MC codes for lattice physics

calculations. The code is distributed by RSICC and the OECD/NEA Data Bank and is

currently used in 26 countries [6].

SerpentXS

SerpentXS is a Python-based wrapper code, developed by Bryan Herman [7] for Serpent

MC and has been the inspiration of the S2P wrapper concept. The code has the

capability of performing automated branch case simulations for 3D fuel assemblies.

SerpentXS generates a PMAXS formatted cross section database which is compatible

with PARCS [8].

PARCS

PARCS is a 3D reactor core simulator which solves the steady-state and time dependent,

multi-group neutron diffusion and SP3 transport equations in square and hexagonal

geometries [9]. PARCS can be coupled with the thermal-hydraulics code TRACE.

PARCS/TRACE coupling allows 3D core transient simulation.

The PARCS code uses macroscopic XS-s for a reference state and their

derivatives, with respect to state variable, to account for the reactivity feedbacks. It is

based on the following XS parameterization:

6

( ) ( )

( ) ( ) ( ) ( )

0

0

0 0

0 00 0

0

0 0M

ΣΣ , , , , Σ

Σ Σ Σ Σρ B Z

f

M M

f M M f ff T

M M M MB ZM T

T T B Z T TT

T T B B Z ZT

ρ

ρ

ρ ρ

∂ = + − +∂

∂ ∂ ∂ ∂ − + − + − + − ∂ ∂ ∂ ∂

(1)

where 0Σ is the reference microscopic XS, fT – fuel temperature, MT – moderator

temperature, Mρ – average moderator density, B – boron concentration and Z –

control rod position. The parameters with subscript '0' refer to reference state.

Originally developed for thermal-spectrum applications, the XS parameterization

was modified for fast-neutron spectrum analyses at the FAST group of PSI [3]. The

macroscopic cross-sections during transient calculations are parameterized according to

equation (2).

( ) ( ) ( )

( ) ( ) ( )

0

0

0 0 0

0 0c

0 0 0

Σ ΣΣ , , , , Σ ln lnln ρ

Σ Σ ΣR H Z

cf

f c f f c cf T

R H Z

T R H Z T TT

R R H H Z Z

ρ

ρ ρ ρ ∂ ∂

= + − + − + ∂ ∂

∂ ∂ ∂ − + − + − ∂ ∂ ∂

(2)

where fT – fuel temperature, Cρ – average coolant density, R – average core radius,

H – average fuel height and Z – control rod position.

TRACE

TRACE is a modernized thermal-hydraulics code developed by U.S. Nuclear Regulatory

Commission (NRC). Formerly called TRAC-M, TRAC/RELAP Advanced Computation

Engine is the latest in a series of advanced, best-estimate reactor system codes.

It combines the capabilities of the NRC’s four main systems codes (TRAC-P,

TRAC-B, RELAP5 and RAMONA) into a single modernized computational tool.

7

TRACE has been originally designed to perform best-estimate analyses of loss-of-

coolant accidents (LOCAs), operational transients, and other accident scenarios in PWRs

and BWRs. Furthermore, its versatility allows one to model a wide variety of thermal-

hydraulics experiments in reduced-scale facilities. It is able to analyze nuclear reactor

(PWRs and BWRs) system transients in both 1D and 3D geometries.

The code’s computer execution time is highly problem dependent and is a

function of the total number of mesh cells, the maximum size of the allowable time-step

and the rate of change of the neutronics and thermal-hydraulics phenomena being

evaluated [10].

Additional updates have been made to the TRACE code at PSI. A thermal-

mechanics FRED code has been incorporated into TRACE which essentially improved the

transient simulation of the fuel rod [3]. Furthermore, the TRACE code has been modified

to allow sodium two-phase flow simulation [11].

FAST Code System

The FAST (Fast-spectrum Advanced Systems for power production and resource

managemenT) Code System [12] is used by the Fast Reactors Group at PSI with an

objective to analyze whole fast-spectrum reactor system (including Accelerator-Driven

Systems) with different coolants and fuel types. This unique code system is assembled

from several state-of-the-art codes (Figure 2). The ERANOS code is used for static

neutronics, PARCS for reactor kinetics, TRACE for system thermal-hydraulics, and FRED

for thermal mechanics. ETOP (ERANOS TO PARCS) is a wrapper code which converts

group constants generated by ERANOS code into PARCS compatible database file. This

database file contains all group constants (such as XS-s, scattering matrixes and XS

derivatives) and kinetic parameters necessary for the PARCS code to perform 3D steady-

8

state and transient calculations. The flowchart of the FAST code system is shown in

Figure 3.

Figure 2: FAST assembly code, composed of different well known code systems.

Figure 3: Flow chart of FAST code system.

ETOP

PARCSv.2.8

FREDv. 1.0

TRACEv. 5.0RC

ERANOSv.2.2

9

In this study, ERANOS code and ETOP wrapper have been substituted with

Serpent MC and S2P wrapper (Figure 4). The methodology implemented inside S2P is

presented in Chapter 3. The advantages and limitations of these new modules in FAST

code system are discussed in Chapter 4.

Figure 4: New modules of the FAST code system.

S2P

PARCSv.2.8

FREDv. 1.0

TRACEv. 5.0RC

SERPENT MCv.1.1.18

10

2.2. REACTIVITY COEFFICIENTS, THERMAL EXPANSIONS AND SAFETY PARAMETERS

The nuclear fission process in a fast reactor can be influenced by a number of physical

phenomena that affect core reactivity. These phenomena include both nuclear physics

and material expansions. To measure the effect that a variation in parameter (such as

increase in temperature) will have on the reactivity of the core, reactivity coefficients

are used. Reactivity coefficients can be described with the following equation:

ΔΔx x x

ρ ρα ∂≈

∂≡ (3)

where ρ∆ is called reactivity defect which stands for the total reactivity change caused

by a variation in parameter x by x∆ .

The detailed methodology used for simulating these reactivity feedbacks both in

Serpent MC and PARCS/TRACE codes are described in Chapter 3.

Simulated feedback mechanisms are briefly introduced below.

Doppler coefficient and Doppler constant: It is crucial to have a prompt negative

reactivity feedback that reverses a power transient if the reactor becomes prompt

critical. The Doppler feedback provides this prompt negative reactivity feedback for a

fast reactor fueled with ceramic fuel. In a power excursion, excess fission energy quickly

raises the fuel to a high temperature. The increase of fuel temperature results in large

increase in the effective parasitic capture cross section in the principal 238U fertile

isotope. This provides a strong negative reactivity effect.

The Doppler coefficient Dα is defined as the derivative of reactivity ρ with

respect to fuel temperature fT :

DfTρα ∂

≡∂

(4)

In oxide fuel fast reactors, reactivity drops logarithmically with fuel temperature [13].

11

( ) ( )00

ln ff f D

f

TT T K

Tρ ρ

= +

(5)

where DK is the Doppler constant which characterizes the Doppler feedback for fast

oxide reactors. From equations (4) and (5) follows that

ln lnD

f f

dKd T T

ρ ρ∆= ≈

∆ (6)

and

DD

f

KT

α = (7)

In this report the Doppler constant has the unit of pcm.

Axial fuel expansion coefficient: Increase of fuel temperature results in thermal

expansion of the fuel pellets and decrease of fuel density inside fuel pins. Overall the

expansion causes increase of fuel average height and decrease of fuel smeared density.

Consequently the fuel region becomes more transparent and this results in increase of

neutron leakage in radial direction. Other effects are the increase of scattering in

coolant and more parasitic absorption in the cladding. Overall, fuel axial expansion

results in negative reactivity feedback and is calculated as follows:

fuel fuelAFEC

fuel fuel fuel fuel fuel

H HH T H T Tρ ρ ρα

∂ ∆∂ ∆ ∆≡ ≈ =∂ ∂ ∆ ∆ ∆

(8)

Where ρ∆ stands for reactivity change due to T∆ change in fuel temperature, fuelH∆ is

the change of fuel average height.

Radial expansion coefficient: Neutron mean free path in fast systems is much

longer than for thermal systems. This brings stronger dependence of reactivity from

core radius [13]. Increase of coolant inlet temperature causes thermal expansion of core

diagrid (grid on which Fuel Assemblies are installed). The increase of effective core

radius is accompanied by more coolant in inter-assembly channels. Therefore, neutrons

12

experience more scattering and these effect sums up to spectral softening. Overall, the

effect of diagrid expansion is negative. Core radial expansion coefficient is calculated as

0RECp p

p T p T Tρ ρ ρα ∂ ∂ ∆ ∆ ∆

≡ ≈ = <∂ ∂ ∆ ∆ ∆

(9)

where p∆ is the change of the inter-assembly pitch (diagrid pitch), T∆ is the change of

the core inlet coolant temperature.

Coolant expansion coefficient: The change in reactivity due to change of the

average coolant density is called the coolant expansion coefficient. In particular,

increase in coolant temperature reduces coolant density. As a result neutrons

experience less scattering in the coolant. Overall the system experiences hardening of

the spectrum with positive reactivity and increase of leakage with negative reactivity.

The effect of coolant density varies across the core. It is positive in the center were

spectral hardening is dominant and less positive (can be even negative) in the periphery,

where the leakage effect is stronger [13]. For large reactor cores coolant expansion

coefficient is positive, because the hardening effect is dominant over leakage. In small

cores the coefficient can be negative, because of the dominance of leakage effect. The

coolant expansion coefficient is calculated as

CTC T T Tρ γ ρ γ ραγ γ∂ ∂ ∆ ∆ ∆

≡ ≈ =∂ ∂ ∆ ∆ ∆

(10)

where γ∆ is the change of average coolant density due to T∆ change of average

coolant temperature.

Control rod worth: Control rod worth is the total worth of control rods

altogether and is calculated as the difference of reactivities between fully inserted and

fully withdrawn positions as CRworth CRout CRinρ ρ ρ∆ = − .

13

2.3. REACTOR CORE DESIGN

Three Gen-IV Reactor designs were considered for this research, namely ESFR (European

Sodium-cooled Fast Reactor), ELSY (European Lead-cooled SYstem) and GFR (Gas-cooled

Fast Reactor). For each of these reactor designs Serpent MC input was prepared and

calculations were performed to calculate safety coefficients. However, only ESFR core

simulations were coupled with PARCS/TRACE code system. This document describes in

detail simulation results of ESFR core with both Serpent MC and PARCS/TRACE.

General core design parameters and Serpent MC simulation results of GFR and ELSY

reactor cores are described in Appendix G and Appendix H respectively.

From these three designs SFR technology can be considered the most mature (400

reactor years) and promising candidate for implementation of fast reactor technology in

the near future.

Figure 5: ESFR Working Horses core design reference core design (left), modified core design, 60° symmetry (right). yellow – inner fuel zone, red – outer fuel zone, blue – reflector, green – control rods.

14

In our study the core design of the European Sodium-cooled Fast Reactor

Working Horses (ESFR WH) was used (Figure 5). This design was developed in the

framework of the Collaborative Project on the ESFR (CP ESFR) realized under the aegis of

the EUROATOM 7th Framework Program [14].

Figure 6: Axial cross-section of the ESFR core as modeled in Serpent and PARCS/TRACE[14].

Two core designs are proposed by CEA for the 3600 MWth SFR concept: one

with oxide fuel and the other with carbide fuel. This study was performed on slightly

modified oxide-fuel ESFR core. The official CEA design has 120 degree symmetry. The

core was adjusted to 60 degree symmetry, which resulted in decrease of the number of

inner fuel assemblies by 3 and increase of DSDs (Diverse Shutdown Devices) by 3 (Figure

5, Table 1). This modification enabled simulation of 60⁰ PARCS core and 30⁰ TRACE core

models. Major core design parameters are given in Figure 6 and Table 1. Present study

was performed for a core with fresh fuel, i.e. beginning of life (BOL) core.

15

Table 1: ESFR Working Horses core parameters.

Parameters Reference core Modified core Reactor thermal power (MWth) 3600 Ave/Max core burnup (GWd/t) 100/145 Power density (W/cm3) 206 CSD / DSD 24 / 9 24 / 12 I/O FA 225 / 228 222 / 228 PuO2 content in I/O FA (wt%) 14.05/ 16.35 10B inside B4C in CSD / DSD* 19.9%/ 90% Fuel residence time (EFPD†) 2050

* CSD – Control and Shutdown Device, DSD – Diverse Shutdown Device † Equivalent Full Power Days

16

3. Methodology

3.1. SERPENT CORE MODEL

One of the great advantages of Monte Carlo codes, such as Serpent MC, is the ability to

simulate heterogeneous 3D geometries at the level of realistic neutron interactions

within reasonable time. All parts except radial reflector assemblies of ESFR Core were

modeled heterogeneously. It should be noted that self-shielding effect‡ in non-

multiplying regions, such as reflector, is negligible in fast spectrum [15]. Heterogeneous

structure of fuel assemblies is shown in Figure 7. Serpent models of CSD and DSD

control rod structures are shown in Figure 8.

Figure 7: Radial (left) and axial (right) cut of ESFR fuel assembly. ‡ The degree of self-shielding effect is a temperature dependent measure of anti-

correlation between the reaction cross section and neutron flux in energy and in space.

In technical terms, if the reaction cross section xΣ becomes large, the flux Φ decreases

roughly in inverse proportion so that to limit the reaction rate xΣ Φ . With regard to

space, it can be construed that the external layers of a material, such as fuel, protect the

internal layers, giving rise to the term “self-shielding”.

REFLECTOR

FISSION GAS

FUEL

SODIUM

WRAPPER

Bot

tom

Top

17

Figure 8: Radial cut of CSD (left) and DSD (right) control rod assemblies.

3.2. GENERATION OF GROUP CONSTANTS

Serpent calculations were employed with JEFF-3.1 continuous energy cross

section library with unresolved resonance probability tables. Energy grid with 33-group

structure was used to generate necessary group constants for PARCS (Table 2).

Table 2: ECCO 33-group energy structure.

EM10 STEEL

SODIUMODS STEEL

B4C NATURAL

HELIUM

Group number

Upper energy boundary (MeV)

Group number

Upper energy boundary (MeV)

Group number

Upper energy boundary (MeV)

1 1.96E+01 12 6.74E-02 23 3.04E-04 2 1.00E+01 13 4.09E-02 24 1.49E-04 3 6.07E+00 14 2.48E-02 25 9.17E-05 4 3.68E+00 15 1.50E-02 26 6.79E-05 5 2.23E+00 16 9.12E-03 27 4.02E-05 6 1.35E+00 17 5.53E-03 28 2.26E-05 7 8.21E-01 18 3.35E-03 29 1.37E-05 8 4.98E-01 19 2.03E-03 30 8.32E-06 9 3.02E-01 20 1.23E-03 31 4.00E-06 10 1.83E-01 21 7.49E-04 32 5.40E-07 11 1.11E-01 22 4.54E-04 33 1.00E-07

18

The group constants and kinetic parameters generated by Serpent which were used in

PARCS XSEC database file are listed in Table 3 and Table 4. For the sake of completeness,

the structure of XSEC block is shown in Appendix D.

Table 3: Equivalence table of Group Constants of Serpent and PARCS.

Parameter Units PARCS XSEC Serpent

Transport XS, Σ𝑡𝑟, 1/cm SIGTR P1_TRANSPXS

Absorption XS, Σ𝑎, 1/cm SIGA RABSXS

Production XS, νΣ𝑓𝑖𝑠𝑠 1/cm SIGNF NSF

Kappa-Fission XS, 𝜅Σ𝑓𝑖𝑠𝑠 J/cm SIGKF FISSE×FISSXS×C§

Scattering Matrix XS, Σ𝑠,𝑖→𝑗 1/cm - GPRODXS

Fission Spectrum - FISS_SPEC CHI

Table 4: Equivalence table of kinetic parameters of Serpent and PARCS.

Parameter Units PARCS XSEC Serpent Number of delayed neutron precursor groups - DNP_NGRP PRECURSOR_GROUPS

Delayed neutron fraction - DNP_BETA BETA_EFF Delayed neutron precursor decay constant 1/s DNP_LAMBDA DECAY_CONSTANT

Neutron velocity cm/s NEUT_VELO RECIPVEL**

Kappa-fission XS is the multiplication of 𝜅 (kappa), which is average energy release per

fission event (units: J/fission) and fission-XS Σ𝑓. Kappa-fission XS can be calculated from

Serpent parameters FISSE and FISSXS as FISSE×FISSXS×C, where FISSE is 𝜅 in units of

§ C = 1.60219E-13 J/MeV. ** reciprocal velocity, units s/cm.

19

MeV/fission and FISSXS is fission-XS Σ𝑓. C constant converts the unit of FISSE from MeV

to Joules.

3.3. MULTI-UNIVERSE CORE MAPPING

The Serpent code uses a universe-based geometry. This implies that the geometry is

divided into independent simple geometric objects which are easy to model using basic

and derived surface types. Then these objects are nested inside one another. As a result

universe-based structure allows modeling of complicated reactor geometries.

In each of the universes Serpent code can calculate homogenized group

constants. It can be specified in the input file as follows.

set gcu < U1 >< U2 > ⋯

where < U1 >, < U2 >, … are the universe numbers. The homogenization is performed

on all geometric objects nested inside the universe. Homogenized group constants are

generated according to the multi-energy group structure specified with the following

entry in Serpent

set nfg < 𝑛𝑒 > < 𝐸1 > < 𝐸2 > ⋯

where < ne > is the number of energy groups, < E1 > , < E2 >, … are the group

boundaries.

To generate detailed homogenized group constants the ESFR reactor core was modeled

as a multi-universe structure. Four basic building blocks were used to model ESFR core,

namely inner FA, outer FA, CA (Control Assembly) and RA (Reflector Assembly).

Universe-wise mapping of Fuel Assemblies

Fuel Assembly (FA) universe-wise structure is shown in Figure 9. Inner FA is

encapsulated inside universe 1000, and outer FA inside universe 2000 (Figure 10). On a

20

lower universe level each physical zone of the FA is encapsulated into a universe, which

allows generation of group constants in each physically distinct zone of the assembly,

such as upper and lower axial reflector zones, fuel zone, upper and lower fission gas

plenum zones.

Figure 9: Fuel assembly multi-universe mapping.

To generate detailed cross sections of the inner FA one needs to specify all the

universes inside FA with a following entry:

set gcu 98 99 100 101 102

Universe-wise mapping of Control and Reflector Assemblies

There are three rings of Control Assemblies (CA) inside ESFR core. Assemblies in each

ring were encapsulated into separate universes (Figure 10). The reason for using this

structure is to incorporate the effect of different fission spectra at the location of each

CA ring. CA-s consist of two parts: Control Rod (CR) and Control Rod Follower (CRF). In

our ESFR model CR-s of inner, central and outer rings are encapsulated into universes

#60, #70 and #80 accordingly. CRF-s of inner central and outer rings are encapsulated

202

201

200

199

198

102

101

100

99

98

UPPER AXIAL REFLECTOR

UPPER FISSION GAS PLENUM

LOWER FISSION GAS PLENUM

LOWER AXIAL REFLECTOR

I/O FUEL

21

into universes #61, #71 and #81 accordingly. RA (Reflector Assembly) is designed

homogeneously and is wrapped inside universe #50.

Figure 10: Universe map of ESFR core. 1000 – inner FA, 2000 – outer FA, 600, 700, 800 – inner central and outer CA-s. 60, 70, 80 – inner central and outer CR-s. 61, 71, 81 – inner, central and outer CRF-s. RA – 50.

3.4. CROSS SECTIONS AND THEIR DERIVATIVES

Parcs deterministic code accounts for the reactivity feedbacks assuming a linear

dependency of the different effects. The code was modified at PSI to enable fast

neutron spectrum analyses [3] according to equation (2).

These partial derivatives inside (2) were approximated by first order forward

differencing:

0 0

0

Σ X H X

XX H+Σ −Σ∂ ≈ ∂

(11)

To calculate safety coefficients, control rod worth and XS derivatives one needs to

perform at least six different input simulations in Serpent, which are listed in Table 5.

Each of these simulation cases are described below.

700

70

71

800

80

81

50

50

600

60

61

202

201

200

199

198

2000

102

101

100

99

98

1000

22

Case A: Reference

Reference case calculations were performed for cold zero power (CZP) core. This

calculation provides all the reference parameters presented in Table 3 and Table 4.

Case B: Doppler constant

To calculate Doppler constant KD and fuel temperature derivative [∂Σ/ ∂lnTf]Tf0 we use

simulation results of the reference case (Table 5, input A) and the perturbed case (Table

5, input B).

Calculations performed with these two input files is sufficient to calculate Doppler

constant as follows:

ln ln ln ln

A BD

f f A B

dKd T T T T

ρ ρρ ρ −∆= ≈ =

∆ − (12)

where ,A Bρ ρ stand for reactivity (in pcm), 𝑇𝐴,𝑇𝐵-fuel nuclides temperatures (in K).

Case C: Axial Fuel Expansion

To calculate Axial Fuel Expansion coefficient AFECα and fuel expansion derivative

[ ]0

Σ / HH

∂ ∂ we use simulation results of the reference case (Table 5, input A) and the

perturbed case (Figure 11, Table 5, input C).

Figure 11: Perturbation of fuel height inside fuel pins of ESFR FA-s.

REFLECTORFISSION GAS

FUEL

SODIUMWRAPPER

a)

b)

h∆

bott

om

top

)( AA TH

)( BB TH

23

The basic steps to model this effect in Serpent are:

1. increase fuel height

2. decrease fuel density

The fuel height is perturbed as

( ) [ ]( ) 1 ( )C C A A C AH T H T T Tα= + − (13)

where CT is temperature of the fuel at which fuel height is equal to CH ,α is the

material average linear expansion coefficient.

The decrease of fuel density should be performed in a way that total fuel mass is

conserved. Perturbed fuel density is calculated from

( ) ( )1 ( )

A AC C

C A

TT

T Tγ

γα

=+ −

(14)

Where Cγ is the fuel density at fuel temperature CT .

For the tabulated data of linear expansion coefficient one can calculate

1

1

Δ

Δ

Ni ii

Nii

T

T

αα =

=

= ∑∑

(15)

where 1i i iT T T −∆ = − is the temperature difference between two tabulated data points

of iα and 1iα − .

Fuel temperature 𝑇𝐶 is necessary to calculate perturbed fuel height 𝐻𝐶 and fuel density

𝛾𝐶. At the same time, the only changes requiring modification inside Serpent input file

are fuel height 𝐻𝐶 and fuel density 𝛾𝐶.

Simultaneous changes of fuel temperatures, fuel height and fuel density will result in

coupling of the fuel expansion effect with the Doppler effect.

24

Case D: Core Radial Expansion

To calculate Core Radial Expansion coefficient 𝛼𝐶𝑅𝐸𝐶 and radial expansion derivative

[∂Σ/ ∂R]𝑅0 we use simulation results of the reference case (Table 5, input A) and the

perturbed case (Table 5, input D). There are two parameters which need to be modified

inside Serpent input file.

1. Radius of the coolant channel around the assembly. FA Wrapper radius

stays unchanged (Figure 12, 𝑅𝐴 → 𝑅𝐷).

2. Lattice pitch of the whole core to adjust the input file for the increase in

outer radius of the assemblies (Figure 12, 𝑝𝐴 → 𝑝𝐷).

Figure 12: Core radial expansion model.

The pitch pD and radius RD (Figure 12) are perturbed as

( ) [ ]( ) 1 ( )

2

D A D ApD T pA T T TpDRD

α= + −

=

(16)

where DT and AT are the perturbed and reference inlet coolant temperatures

respectively.

pD

RA = pA/2

R0

Input A Input D

RD = pD/2

R0

pA

Coolant channel

Fuel Assembly Wrapper

Fuel Pin

25

Case E: Coolant Expansion

To calculate coolant temperature coefficient 𝛼𝐶𝑇𝐶 and expansion derivative [∂Σ/ ∂γ]𝛾0

we use simulation results of the reference case (Table 5, input A) and the perturbed

case (Table 5, input E). The only difference between the reference case and the

perturbed case is the value of coolant density.

Case F: Control Rod Worth

To estimate control system worth two calculations need to be performed, one without

CR-s (Table 5, input A) shown in Figure 13-b and one with all CR-s (Table 5, input F)

shown in Figure 13-c.

Figure 13: Control rod positioning in ESFR core.

PARCS requires only the delta XS-s, ΔΣ which was calculated as

ΔΣ = 𝑋𝑆𝐹𝑂𝐿 − 𝑋𝑆𝐶𝑅 = Σ𝐴 − Σ𝐹

where 𝑋𝑆𝐹𝑂𝐿 are the cross sections of the control rod follower and 𝑋𝑆𝐶𝑅 are the cross

sections of control rod (Figure 13).

a) b) c)

FOL AXS = Σ

Heig

ht

Radius

FCRXS Σ=

26

Table 5: Calculation methodology of safety parameters and XS derivatives.Ca

se le

tter

Case

Nam

e

Equations Perturbed parameters inside Serpent input

Serpent Safety coefficients

Cross sections and their derivatives

A Reference − − − Σ𝐴

B Doppler − 𝑇𝐵 Fuel temperature 𝐾𝐷 ≈

𝜌𝐴 − 𝜌𝐵𝑙𝑛𝑇𝐴 − 𝑙𝑛𝑇𝐵

𝜕Σ𝜕𝑙𝑛𝑇

≈ΔΣΔlnT

=ΣA − ΣB

lnTA − lnTB

C Axial fuel Expansion

𝐻𝐶 = 𝐻𝐴�1 + 𝛼�(𝑇𝐶 − 𝑇𝐴)�

𝛾𝐶 =𝛾𝐴

1 + 𝛼�(𝑇𝐶 − 𝑇𝐴) 𝐻𝐶 , 𝛾𝐶

Fuel height and fuel density 𝛼𝐴𝐹𝐸𝐶 ≈

𝜌𝐴 − 𝜌𝐶𝑇𝐴 − 𝑇𝑐

𝜕Σ∂H

≈ΔΣΔH

=ΣA − ΣC𝐻𝐴 − 𝐻𝐶

D Radial expansion

𝑝𝐷 = 𝑝𝐴�1 + 𝛼�(𝑇𝐷 − 𝑇𝐴)�

𝑟𝐷 =𝑝𝐷2

𝑝𝐷 , 𝑟𝐷

Diagrid pitch and assembly radius 𝛼𝐶𝑅𝐸𝐶 ≈

𝜌𝐴 − 𝜌𝐷𝑇𝐴 − 𝑇𝐷

𝜕Σ∂p

≈ΔΣΔp

=ΣA − ΣC𝑝𝐴 − 𝑝𝐶

E Coolant expansion − γE

Coolant density 𝛼𝐶𝑇𝐶 ≈𝜌𝐴 − 𝜌𝐸𝑇𝐴 − 𝑇𝐸

∂Σ∂γ

≈ΔΣΔγ

=ΣA − ΣE𝛾𝐴 − 𝛾𝐸

F Control –Rods Worth − 𝐻𝐹

Control Rod position Δ𝜌 = 𝜌𝐴 − 𝜌𝐹 ΔΣ = Σ𝐹 − Σ𝐴

27

3.5. S2P WRAPPER

To generate all the necessary cross sections for equation (2) we need to perform at least

one reference and five perturbed simulations (Table 5). S2P (Serpent to PARCS) is a

Matlab based wrapper for the Serpent MC code. S2P automates the generation and

simulation of different Serpent input cases, calculates XS derivatives, according to the

methodology described in Chapter 3, and converts calculated results into PARCS

compatible XSEC formatted cross section database [9]. The information flow inside S2P

wrapper is shown in Figure 14.

Figure 14: The flowchart inside S2P Wrapper.

S2P wrapper takes 2 input files to perform calculations

• caselist file (Appendix B)

• parameterized Serpent input file (Appendix C)

CREATE SERPENT INPUT J

RUN SSS WITH INPUT J

READ DATA FROM OUTPUT J

CASE J <= N

XSEC CONVERTERDATA

XSEC CARD

TRUE

J = J + 1

FALSE

S2P WRAPPER

CASE LIST DATA, INPUT PARAMETERS, INPUT FILES,

OUTPUT DATA. DATA FORMAT IS MATLAB

STRUCTURE ARRAY

XSEC CONVERTER CONVERTS DATA FROM

SIMULATION TO XSEC CARD FORMAT COMPATIBLE WITH

PARCS

PARAMETERIZED SERPENT INPUT FILE.

CASE LIST CONTAINS DIFFERENT SETS OF PARAMETER

FOR DIFFERENT SIMULATION CASES

START

END

PARAMETRICSERPENT

INPUT

CASE LIST

28

Parameterized Serpent input contains parameters instead of constants such as fuel

temperature, diagrid pitch, coolant density, etc. These parameters are specified inside

tags "<>", e.g <CD>, which stands for coolant density. The values of parameters are

listed in sets inside caselist file, which represent different cases of Table 5. An example

of parameterized Serpent input file is presented in Appendix C.

S2P reads all sets in caselist file, substitutes each set of parameter values into

parameterized input file and converts it into a Serpent input file. Subsequently the

procedure calls Serpent and performs simulation with the generated input. After

simulating all cases and accumulating necessary output data, the XSEC converter (Figure

14) converts XS data into XSEC database. The source code of S2P wrapper is provided in

Appendix A.

3.6. PARCS MODEL

Only one sixth of the ESFR core has been modeled in PARCS, considering the 60°

symmetry of the modified ESFR core (Figure 15). Axially, the mesh size is set to 10 cm,

while radially the size of the node is equal to the core pitch. One sixth of the core

contains 85 fuel assemblies, 60 reflector channels and 7 control and safety assemblies.

Figure 15: PARCS model, one sixth of the ESFR core.

29

3.7. TRACE MODEL

TRACE model was constructed for 1/12th of the ESFR core (Figure 16) for the coupled

calculation with PARCS. This was possible because the modified 60° ESFR core has a 30°

mirror symmetry. This model consists of 51 parallel channels, from which 45 are FA-s, 4

CA-s and 1 pipe to represent all bypasses, including inter-assembly gaps and reflector

assemblies [11]. Each pipe represents a fuel assembly which is linked to a heat structure

(HTSTR). The power distribution of the heat structure is calculated by PARCS during the

coupled simulation.

Figure 16: Schematic of the TRACE model.

PARCS/TRACE coupled model allows simulation of radial core expansion and fuel axial

expansions. Radial expansion is driven by the diagrid temperature. The corresponding

thermal expansions are calculated for the diagrid material (SS316) using the inlet

Diagrid

Hot pool

Coolant temperature and flowrate

Coolant pressure

PIP

E

In

ner c

ore

HTS

TR

PIP

E

O

uter

cor

e

HTS

TR

PIP

E

A

ll ot

hers

PIP

E

Con

trol R

ods

1 21 1 5

PIP

E

In

ner c

ore

HTS

TR

24

PIP

E

O

uter

cor

e

HTS

TR

1... ...

HTSTR

30

temperature change to provide the radial core thermal expansion. For modeling fuel

axial expansion core-average fuel temperature change is used.

TRACE was coupled with PARCS by means of appropriate mapping scheme which links

both the pipe component nodes and the heat-structure nodes to the corresponding

PARCS neutronic nodes.

3.8. CALCULATING SAFETY PARAMETERS WITH PARCS/TRACE

Safety parameters are simulated with PARCS/TRACE based on modification of XSEC

database file. XS parameterization is described by equation (2). Each of these XS

derivatives is specified inside XSEC block. By setting all these derivatives to zero, we can

run a steady state calculation.

( ) ( )0 0 0 0 0 0Σ , , , , Σ , , , ,f c f cT R H Z T R H Zρ ρ= ≡ Σ (17)

It is important to note the fact, that PARCS will automatically set all derivatives

to zero, if they are not specified inside the XSEC block. This trick was used to compare

reference CZP cores simulated both with Serpent and PARCS (using XS-s generated by

Serpent).

At the same time all the temperatures inside TRACE channels are set to 400°C,

which does not influence the simulation, because the XS parameterization in (17) is not

temperature dependent.

To simulate separate single effect reactivity feedback, we need to provide PARCS

with only one derivative and set all others to zero

( ) ( ) ( )0

0 0ΣΣ Σ

X

X XX XX∂ = + ∂

−

(18)

where X is one of the perturbed parameters { }ln , , , ,f CT R H Zρ .

31

For example, to simulate Doppler feedback we provide PARCS only with 0

Σ

ff T

lnT ∂ ∂

and

it will solve the following

( ) ( )0

00 lnΣΣ , , , , Σn

nl

lf

f cf

f

T

fT TT R H ZT

ρ ∂

= +∂

−

(19)

In this way we are able to separate and simulate only Doppler feedback. TRACE

calculates and provides PARCS with the increased fuel temperature. Afterwards, PARCS

re-adjusts the XS-s according to (19).

32

4. Results and Discussion

Six different input calculations were performed with the Serpent MC code (v. 1.1.18) to

calculate safety coefficients and generate cross section database file for PARCS. The

multi-group XS-s in Serpent calculations were generated in the ECCO 33 group energy

structure employing JEFF-3.1 based continuous energy cross section library. This energy

structure is optimized for fast reactor applications. The main parameters of the

reference and perturbed cases were set as follows:

1) The reference case calculations were performed with all temperatures such as

coolant temperature, fuel and material temperature set to 300K. The geometry of

the core has the dimensions corresponding to 300K. Reactor core is simulated

without control rods.

2) Fuel height was increased by 3.41% to simulate fuel axial expansion effect. This

value corresponds to the hypothetical temperature increase of 2700K. At the

same time fuel density was decreased to keep the fuel mass constant. Linear

expansion coefficient of 1.27x10–5 1/K was used for the MOX fuel.

3) Fuel temperature was increased by 1500K to simulate Doppler feedback.

4) Coolant density was decreased by 28% to simulate coolant expansion effect.

5) Core assembly pitch was increased by 6% to simulate core radial expansion effect.

The material of the diagrid was assumed to be SS316 with an expansion coefficient

of 2.03x10–5 1/K.

6) Control rod fully inserted configuration was simulated to calculate control rod

worth.

33

Abovementioned expansions can be argued to be excessive and not realistic.

Nonetheless simulated reactivity feedback mechanisms are assumed linear for fast

reactor cores, which makes these expansions plausible. On the other hand big geometric

and material expansions are justified in Monte Carlo codes. The small reactivity effects

and cross-section changes present themselves clearly within relatively short simulation

time. All six simulations of 3D ESFR full-core were performed with a total number of

7.5×107 neutron histories (150000×500) using 500 inactive cycles. The number of

inactive cycles was selected according to convergence behavior of the Shannon entropy

(Figure 17, Appendix I).

Figure 17: Convergence of Shannon entropy and k-eff in the ESFR 3D full-core calculation.

Firstly, calculations were performed with the six different Serpent input files

which provided us with all the necessary data to calculate ESFR reactivity feedback

coefficients and generate XSEC cross-section database for PARCS. Secondly, the XSEC

0 200 400 600 800 10001

1.01

1.02

1.03

1.04

1.05

Neutron cycle,#

k-ef

f

k-eff instantk-eff cum. average

0 200 400 600 800 10000.69

0.692

0.694

0.696

0.698

Neutron cycle,#

Entr

opy

entropy instantentropy cum. average

34

block was used in PARCS/TRACE coupled code and the single effect reactivity feedbacks

were simulated and safety coefficients were calculated. Calculation results of k-effective

for reference case are presented in Table 6. Table 7 compares the values of safety

parameters calculated from Serpent and PARCS/TRACE. A comparison of the power

peaking factor for both deterministic and stochastic codes is illustrated in Figure 18.

Table 6: k-effective of ESFR 3D core for reference case at 300K calculated by Serpent MC and PARCS/TRACE codes.

Serpent MC PARCS stand alone PARCS/TRACE

k-effective 1.03512±0.00007 1.03809 1.03809

Reactivity, pcm 3392±6 3669 3669

Core temperature, °C 27 20 20

Figure 18: Power peaking and relative error for CZP ESFR 3D core.

0

0.5

1

1.5

pow

er p

eaki

ng, [

-]

0 50 100 150 200 250-4

-2

0

2

4

6

rela

tive

erro

r, %

core radius, cm

serpentparcs

35

Table 7: Safety parameters and their relative deviations calculated with Serpent MC and PARCS/TRACE for ESFR 3D core.

Safety parameters Serpent MC PARCS/TRACE Δ, %

Axial Fuel expansion coefficient, pcm/K -0.158(±0.003) -0.184 16±2

Core Radial expansion coefficient, pcm/K -0.763(±0.003) -0.656 14±0.4

Doppler constant, pcm -1245(±5) -1327 6±0.4

Coolant expansion coefficient, pcm/K 0.159(±0.01) 0.197 24±6

Control Rod Worth, pcm 5069(±10) 5167 2±0.2

The results show reasonable agreement between k-effective values and safety

parameters. The k-effective values differ by only 277 pcm (Table 6). This is a good

agreement between fundamentally different codes. It can be reasoned that differences

between Serpent and PARCS are due to statistical noise in the Monte Carlo results.

Statistical errors in the flux values are shown in Figure 19. Different simulations with

increased number of neutron histories/cycles did not improve calculated results.

Figure 19: Statistical uncertainty of neutron flux of inner FA.

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 330

0.02

0.04

0.06

0.08

0.1

0.12

Nor

mal

ized

inte

gral

flux

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 3310-2

10-1

100

101

102

Rel

ativ

e st

anda

rd d

evia

tion,

%

Energy group

36

The difference between estimated safety parameters can be up to 24% (Table 7)

for coolant expansion coefficient which has the most statistical noise of about 6%. This

is a clear illustration that statistical effect of a MC code may mask the results when

evaluating small perturbation such as coolant expansion. At the same time, strong

agreement was observed for the control-rod worth, which differs by only 2%. The

comparison of the power profile shows maximum 4% deviation between the codes

(Figure 18).

37

5. Conclusions and Future Work

5.1. CONCLUSIONS

The main goal of this study is preparation of multi-group constants for fast

spectrum 3D full-core transient simulation with the PARCS simulator. In this study the

feasibility of using the Serpent Monte Carlo code for generating multi-group BOL

homogenized XS-s for a range of possible branch cases was investigated. To correctly

predict changes in operating conditions multiple branch cases must be simulated to

calculate necessary reactivity feedbacks. On the other hand Serpent code has no

method to perform these analyses. To fill in this gap, a branch case generating wrapper,

S2P, was coded to automate multiple branch simulations and organize generated multi-

group constants and kinetic parameters into a XSEC cross section database file which is

compatible with the PARCS code.

The first part of a three-step procedure was to simulate six different Serpent

inputs and generate XS-s and their derivatives with respect to 1) average fuel

temperature, 2) coolant density, 3)average core radius, 4) average fuel height and 5)

control rod position. The second step was to convert generated ECCO 33-group

homogenized XS-s and their derivatives into PARCS compatible XSEC database file. The

final step was to perform steady-state and single-effect zero-transient analyses with the

PARCS/TRACE coupled code using generated XSEC database and compare k-effective

values, safety parameters and power distribution between conceptually different

stochastic Serpent and deterministic PARCS codes.

Results point out that the differences between Serpent and PARCS are mainly

related to the statistical uncertainty of MC simulations.

38

The positive outcome of this study is that continuous energy Serpent MC code

can be a promising tool as a 3D reactor core design calculator and 3D detailed

homogenized group constant generator.

The downsize of the presented methodology is that only BOL XSEC cross section

database can be currently generated. The burnup module of the Serpent MC code has

prohibitively high memory requirements for performing 3D full core burnup calculations

because of unionized energy grid implementation [5]. Therefore the application of this

methodology is presently limited to BOL calculations.

5.2. FUTURE WORK

This work presents conceptually new approach to XS generation problem and

has quite good potential for fast-reactor system analyses. As a result there is a large

space for future work on improvement of the presented methodology and the S2P

wrapper. In this section suggestions for improvement of Serpent and S2P are given.

Serpent

From experience gained in this study, there are some improvements that could

be implemented in the Serpent code. One essential improvement will be lower memory

requirements for burn-up calculations. This will allow generation of XSEC database for

any point of the fuel-cycle. Another improvement will be to implement a module in

Serpent which will check the convergence of k-eff and statistical validity of the results.

The fission source convergence for full-core simulations is an important issue. A module

which will check the convergence of the fission source will be an essential update. Also,

Serpent should have a more detailed manual. Many questions related to units and

39

methodologies are not described at all. However this drawback is partly compensated

with the Serpent discussion forum.

S2P

S2P automates generation and simulation of multiple Serpent input files which

differ from each other in geometry or material properties. S2P implements a

methodology which is designed for full-core fast-spectrum systems. There are many

things which can be added into this wrapper code. The possible suggestions are listed

below

• S2P was written in Matlab using procedural programming. As a result there are

24 functions, which present themselves as 24 files. One upgrade is to implement

object oriented programming and put all these functions inside two objects

which will present themselves as two files and in a way will be more organized

and versatile code.

• S2P presently implements only ECCO 33 energy-group structure. Expanding the

wrapper for more freedom of choice for different energy-group structures will be

an important upgrade.

• S2P generates only BOL XSEC database. An upgrade to the full range of the cycle,

namely from BOL to EOL will be an essential upgrade. This is a long term plan and

is based on the assumption that memory requirements of Serpent-2 will be

essentially improved.

40

A. S2P Wrapper

function main_s2p() % S2P WRAPPER % AUTHOR: Levon Ghasabyan % Email: levong@kth.se % Date: 07/01/13 %----------- % SECTION 1 %----------- clear all;clc % specify paths to branch file and matlab source code SRCPATH = pwd; [branchfname BRANCHPATH] = uigetfile('*','Select the BRANCH file'); addpaths(BRANCHPATH,SRCPATH); % get execution parameters exeopt = get_args([BRANCHPATH branchfname], 'exeopt'); cpunum = get_args([BRANCHPATH branchfname],'cpu'); exepath = get_args([BRANCHPATH branchfname],'exepath'); geomfile = get_args([BRANCHPATH branchfname],'geomfile'); % generate caselist structure with all branch calculation data caselist = get_casenames([BRANCHPATH branchfname]); % create new folder for REF1 calculations ref_folder =[BRANCHPATH caselist.REF1.type ]; if ~isdir(ref_folder); mkdir(ref_folder); end % get equations, solve, subsitute and save in caselist equations = get_equations([ BRANCHPATH geomfile{:}]); values = solve_equations(caselist.REF1, equations); s_input_name = [ref_folder filesep caselist.REF1.name]; % check for existance else create an input file and save to caselist if ~exist(s_input_name, 'file') s_input = create_input(s_input_name,geomfile,equations,values); else s_input = fileread(s_input_name); end caselist.REF1.input = s_input; % run calculation if ~exist([s_input_name '_res.m'], 'file') STATUS = run_serpent(exepath,s_input_name,exeopt,cpunum); end %List of variables to retrieve from _res.m file VARNAMES = {... 'CHI';'CHID';'BETA_EFF';'P1_TRANSPXS';'RABSXS';'NSF';... 'FISSXS';'FISSE';... 'GPRODXS';'RECIPVEL';... 'ADFS';'ADFC';... 'PRECURSOR_GROUPS';'BETA_EFF';'BETA_ZERO';'DECAY_CONSTANT'... }; % read reference output data, get VARNAMES values and add to caselist ref_data = read_res_output(VARNAMES,[s_input_name '_res.m']); caselist.REF1.output = ref_data; %% get the case names and evaluate in a loop case_names = fieldnames(caselist); i = 1; while i <= length(case_names) if strcmp(case_names{i},'REF1') i = i + 1; continue end % get the case names from caselist structure case_data = eval(['caselist.' case_names{i}]); case_input_name = eval(['caselist.' case_names{i} '.name']); case_folder = eval(['caselist.' case_names{i} '.type']); % create folder for case calculations folder =[BRANCHPATH case_folder ]; if ~isdir(folder); mkdir(folder); end; % get equations, solve equations and subsitute in input file values = solve_equations(case_data, equations); s_input_name = [folder filesep case_input_name]; % check for existance or create an input file and save to caselist if ~exist(s_input_name, 'file') s_input = create_input(s_input_name,geomfile,equations,values); else s_input = fileread(s_input_name); end eval(['caselist.' case_names{i} '.input = s_input;']) % run calculation if ~exist([s_input_name '_res.m'], 'file') STATUS = run_serpent(exepath,s_input_name,exeopt,cpunum); end % read reference output data, get VARNAMES values and add to caselist data = read_res_output(VARNAMES,[s_input_name '_res.m']); eval(['caselist.' case_names{i} '.output = data;']) i = i+1;

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end save([BRANCHPATH 'caselist'], 'caselist') %----------- % SECTION 2 %----------- %% generate XSEC CARDS cases = {'SS','DOPPLER','AXEXP','RADEXP','COOLEXP','ALL'}; for i = 1:length(cases) XSEC = create_xsec(... caselist,... [98 99 100 101 104 198 199 200 201 204 50 61 71 81],... [[60 61] [70 71] [80 81]],... 33,... cases{i}); end end %----------------------------------------------------------------------------- % SECTION 1 FUNCTIONS %----------------------------------------------------------------------------- function addpaths(INPUTPATH,SRCPATH) % add INPUTPATH to linux path setenv('PATH', [ getenv('PATH') ';' INPUTPATH ]) % add SRC & INPUT paths to matlab path path(path,SRCPATH) path(path,INPUTPATH) end %----------------------------------------------------------------------------- function argval = get_args(inputfile,argstr) % initialize argval argval = ''; % read the data into cell array k = 1; fid = fopen(inputfile); while ~feof(fid) line{k} = fgetl(fid); k =k+1; end fclose(fid); % Loop through lines i = 1; while i < length(line) % split lines % sline = split(line(i)); try sline = textscan(line{i},'%s'); catch exception sline = {''}; end if length(sline{:})<1 i = i + 1; continue end % search for keyword argstr if strcmp(sline{:}(1),argstr) argval = sline{:}(2); end i = i+1; end end %----------------------------------------------------------------------------- function caselist = get_casenames(infile) % read the data into cell array k = 1; fid = fopen(infile); while ~feof(fid) line{k} = fgetl(fid); k = k+1; end fclose(fid); % initialise structure caselist = struct; for i = 1:length(line) % split lines try sline = textscan(line{i},'%s'); catch exception sline = {''}; end % sline = split(line(i)); if length(sline{:})<1 i = i + 1; continue

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end % search for keyword 'case' if strcmp(sline{:}(1),'case') casename = sline{:}(2); casetype = sline{:}(3); caseindex = sline{:}(4); caseid = strcat( casetype, caseindex ); % put into structure according to caseid eval(sprintf('caselist.%s.name = ''%s'';',caseid{:},casename{:})); eval(sprintf('caselist.%s.type = ''%s'';',caseid{:},casetype{:})); eval(sprintf('caselist.%s.ind = %s;',caseid{:},caseindex{:})); % create structure with case parameters while i < length(line) i = i + 1; % split lines try sline = textscan(line{i},'%s'); catch exception sline = {''}; end % end if line is empty if length(sline{:})<1 break end switch sline{:}{1} case 'FHE' %FHE - Fuel Height Expansion par.FHE = sline{:}{2}; case 'FDC' %FDC - Fuel Density Coefficient par.FDC = sline{:}{2}; case 'FT' %FT - Fuel Temperature par.FT = sline{:}{2}; case 'CD' %CD - Coolant Density par.CD = sline{:}{2}; case 'CT' %CT - Coolant Temperature par.CT = sline{:}{2}; case 'DGP' %DGP - Diagrid pitch par.DGP = sline{:}{2}; case 'CRP' %CRP - Control Rod Position par.CRP = sline{:}{2}; otherwise disp(['Not a default parameter: ' sline{:}{1}]) eval([ 'par.' sline{:}{1} ' = sline{:}{2};' ]) end end % add the parameters to the structure eval(sprintf('caselist.%s.par = par;',caseid{:})); end end end %----------------------------------------------------------------------------- function equations = get_equations(geomfile) % read the data into cell array k = 1; if ~iscell(geomfile) geomfile = {geomfile}; end fid = fopen(geomfile{1}); while ~feof(fid) line{k} = fgetl(fid); k = k+1; end fclose(fid); k = 1; i = 1; while i < length(line) exp = '(<[^>]+>)'; match = regexp(line{i},exp,'match'); if isempty(match)~=1 for l = 1:length(match) equations{k} = match(l); k = k + 1; end end i = i + 1; end end %----------------------------------------------------------------------------- function values = solve_equations(caseinfo, equations) % get parameter values from caseinfo varn = fieldnames(caseinfo.par); for i = 1:length(varn) eval(sprintf('%s = str2num(caseinfo.par.%s);',varn{i},varn{i})) end % get equations from equations for i = 1:length(equations)

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% convert equation to str eq = char(equations{i}); % strip < > signs stripeq{i} = eq(2:end-1); end % Loop through and evaluate the equations i = 1; while i <= length(stripeq) try values{i} = eval(stripeq{i}); catch exception if strcmp(stripeq{i},'FTL') if rem(FT,300)==0 FTL = sprintf('%02d', FT/100); elseif rem(FT,300)>0 libtemp = FT-rem(FT,300); FTL = sprintf('%02d',libtemp/100); else error('wrong input') end values{i} = FTL; elseif strcmp(stripeq{i}, 'CTL') if rem(CT,300)==0 CTL = sprintf('%02d', CT/100); elseif rem(CT,300)>0 libtemp = CT-rem(CT,300); CTL = sprintf('%02d',libtemp/100); else error('wrong input') end values{i} = CTL; elseif strcmp(stripeq{i}, 'TITLE') values{i} = caseinfo.name; elseif strcmp(stripeq{i}, 'HALFDGP') values{i} = sprintf('%s',char(vpa(DGP/2,7))); else exp = '(\w*\s\w*)'; match = regexp(stripeq{i},exp,'match'); if isempty(match)~=1 match = textscan(match{:},'%s'); v = eval(match{:}{2}); if rem(v,300)==0 v = ''; elseif rem(v,300)>0 v = sprintf('%s %i',match{1},v); else error('wrong input') end values{i} = v; else error('wrong input') end end end i = i + 1; end for i = 1:length(values) if ischar(values{i}) continue elseif isnumeric(values{i}) values{i} = num2str(values{i}); end end end %----------------------------------------------------------------------------- function text = create_input(INPUT_NAME,SERPENT_INPUT,EQUATIONS,SOLVED_EQUATIONS) % check if SERPENT_INPUT is cell if iscell(SERPENT_INPUT) SERPENT_INPUT = SERPENT_INPUT{:}; end % read the file text = fileread(SERPENT_INPUT); % subsitute equations with values in SERPENT_INPUT for i = 1:length(EQUATIONS) text = strrep(text, EQUATIONS{i}, SOLVED_EQUATIONS{i}); end % write ready input to file fid = fopen(INPUT_NAME, 'wb'); fwrite(fid, text{:}); fclose(fid); % get the text from the cell text = text{:};

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end %----------------------------------------------------------------------------- function STATUS = run_serpent(EXEPATH, SERPENT_INPUT_NAME, EXEOPT, CPU) if ~iscell(SERPENT_INPUT_NAME) SERPENT_INPUT_NAME = {SERPENT_INPUT_NAME}; end % get path directory and name [path, name, ~] = fileparts(SERPENT_INPUT_NAME{:}); % run SERPENT and write terminal output to .serpentout file if strcmp(EXEOPT{:},'serial') disp(['Calculation started on ' datestr(now)]) disp(['Executing ' name ' case'] ) command = [EXEPATH{:} ' ' SERPENT_INPUT_NAME{:}... ' >' SERPENT_INPUT_NAME{:} '.serpentout;']; fid = fopen([path filesep 'run.sh'], 'wb'); fprintf(fid,'%s', command); fclose(fid); STATUS = system(command); elseif strcmp(EXEOPT{:},'parallel') disp(['Calculation started on ' datestr(now)]) disp(['Executing ' name ' case on ' CPU{:} ' cores in parallel'] ) command{1}='module available mpi/openmpi-1.4.3-gcc-4.5.1'; command{2}='module add mpi/openmpi-1.4.3-gcc-4.5.1'; command{3} = [EXEPATH{:} ' -mpi ' CPU{:} ' ' SERPENT_INPUT_NAME{:}... ' >' SERPENT_INPUT_NAME{:} '.serpentout;']; command = [command{1} ';' command{2} ';' command{3}]; fid = fopen([path filesep 'run.sh'], 'wb'); fprintf(fid,'%s', command); fclose(fid); STATUS = system(command); else error(['Wrong EXEOPT parameter:' EXEOPT{:}]) end if STATUS == 0 disp([name ' case complete']) else error([name ' case calculation failed']) end end %----------------------------------------------------------------------------- function OUTDATA = read_res_output(VARNAMES,SERPENT_OUTPUT) % define structure OUTDATA = struct; try [path, name, ~] = fileparts(SERPENT_OUTPUT); % load _res.m data into matlab run([path filesep name]) % organise data in structure OUTDATA.GC_UNI = GC_UNI; OUTDATA.SEED = int64(SEED(1,1)); OUTDATA.ANA_KEFF = ANA_KEFF(1,:); OUTDATA.IMP_KEFF = IMP_KEFF(1,:); for K = 1 : length(GC_UNI) for M = 1 : length(VARNAMES) eval(sprintf('OUTDATA.%s.UNI_%d = %s(%d,:);',... VARNAMES{M},GC_UNI(K,1),VARNAMES{M},K)); end end if any(strcmp('FISSXS', VARNAMES)) && any(strcmp('FISSE', VARNAMES)) % create KFISS variable, KFISS = FISSE*FISSXS*1.60219E-13, 1MeV = 1.60219E-13 J for K = 1:length(GC_UNI) eval(sprintf('KFISS = %s(%d,:).*%s(%d,:)*1.60219E-13;',... 'FISSE',K,'FISSXS',K )); eval(sprintf('OUTDATA.%s.UNI_%d = %s;',... 'KFISS',GC_UNI(K,1),'KFISS')); end end catch exception disp([SERPENT_OUTPUT ' does not exist']) rethrow(exception); end end %----------------------------------------------------------------------------- % SECTION 2 FUNCTIONS %----------------------------------------------------------------------------- function XSEC = create_xsec(CASELIST, SA_UNI_NUM, CA_UNI_NUM, NGROUPS,STATE) % composition = create_xsec(CASELIST, SA_UNI_NUM, CA_UNI_NUM, NGROUPS,STATE) % input parameters

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% CASELIST structure - type: structure, contains all the necessary data % SA_UNI_NUM - type: integer, Sub Assembly universe number, e.g. 100, 1000 % CA_UNI_NUM - type: integer, Control Assembly universe number, e.g. 60, 70 % NGROUPS - type: integer, number of energy groups, e.g. 33 % output parameter % STATE - type: cell str, compositions for parcs XSEC block if nargin == 4 STATE = 'ALL'; end title = ['XSEC !SA_UNI: ' num2str(SA_UNI_NUM,' %d')... ' !CA_UNI: ' num2str(CA_UNI_NUM) '!STATE: ' STATE ]; switch STATE case {'SS','DOPPLER','AXEXP','RADEXP','COOLEXP','ALL'} % create composition card for i = 1:length(SA_UNI_NUM) COMP_NUM{i} = create_comp_num(CASELIST, SA_UNI_NUM(i), NGROUPS, STATE); end % create control assembly delcr_comp card for j = 1:2:length(CA_UNI_NUM) DELCR_COMP{j} = create_delcr_comp(CASELIST, [CA_UNI_NUM(j),CA_UNI_NUM(j+1)], NGROUPS); end % create sub_assembly kin_comp card % for k = 1:length(SA_UNI_NUM) % % KIN_COMP{k} = create_kin_comp(CASELIST, SA_UNI_NUM(k), NGROUPS); % % end otherwise error(['Wrong STATE value ' STATE]) end %% write data to file % XSEC = sprintf('%s\n%s%s',title, COMP_NUM{:},DELCR_COMP{:},KIN_COMP{:}); XSEC = sprintf('%s\n%s%s',title, COMP_NUM{:},DELCR_COMP{:}); XSEC_NAME = ['XSEC_' STATE '_' datestr(now, 'mmddyy_HH')]; fid = fopen(XSEC_NAME, 'wb'); fprintf(fid,'%s', XSEC); fclose(fid); end %----------------------------------------------------------------------------- function COMP_NUM = create_comp_num(CASELIST, UNI_NUM, NGROUPS, STATE) % COMP_NUM = create_comp_num(CASELIST, UNI_NUM, NGROUPS) % input parameters: % CASELIST structure - type: structure, contains all the necessary data % UNI_NUM - type: integer, universe number, e.g. 100, 1000 % NGROUPS - type: integer, number of energy groups, e.g. 33 % output parameter % COMP_NUM - type: string, parcs comp_num card if nargin == 3 STATE = 'TR'; end switch STATE case 'ALL' BASE_MACRO = create_base_macro( CASELIST, UNI_NUM, NGROUPS ); DXS_DTF = create_dxs_dtf(CASELIST, UNI_NUM, NGROUPS); DXS_AXEXP = create_dxs_axexp(CASELIST, UNI_NUM, NGROUPS); DXS_RADEXP = create_dxs_radexp(CASELIST, UNI_NUM, NGROUPS); DXS_DDM = create_dxs_ddm(CASELIST, UNI_NUM, NGROUPS); a{1} = sprintf(' comp_num %d !UNIVERSE %d\n',UNI_NUM*ones(1,2)); a{2} = sprintf('%s%s%s%s%s',BASE_MACRO,DXS_DTF,DXS_AXEXP,DXS_RADEXP,DXS_DDM); case 'SS' BASE_MACRO = create_base_macro( CASELIST, UNI_NUM, NGROUPS ); a{1} = sprintf(' comp_num %d !UNIVERSE %d\n',UNI_NUM*ones(1,2)); a{2} = sprintf('%s',BASE_MACRO); case 'DOPPLER' BASE_MACRO = create_base_macro( CASELIST, UNI_NUM, NGROUPS ); DXS_DTF = create_dxs_dtf(CASELIST, UNI_NUM, NGROUPS); a{1} = sprintf(' comp_num %d !UNIVERSE %d\n',UNI_NUM*ones(1,2)); a{2} = sprintf('%s%s',BASE_MACRO,DXS_DTF); case 'AXEXP' BASE_MACRO = create_base_macro( CASELIST, UNI_NUM, NGROUPS ); DXS_AXEXP = create_dxs_axexp(CASELIST, UNI_NUM, NGROUPS); a{1} = sprintf(' comp_num %d !UNIVERSE %d\n',UNI_NUM*ones(1,2)); a{2} = sprintf('%s%s',BASE_MACRO,DXS_AXEXP); case 'RADEXP' BASE_MACRO = create_base_macro( CASELIST, UNI_NUM, NGROUPS ); DXS_RADEXP = create_dxs_radexp(CASELIST, UNI_NUM, NGROUPS); a{1} = sprintf(' comp_num %d !UNIVERSE %d\n',UNI_NUM*ones(1,2)); a{2} = sprintf('%s%s',BASE_MACRO,DXS_RADEXP);

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case 'COOLEXP' BASE_MACRO = create_base_macro( CASELIST, UNI_NUM, NGROUPS ); DXS_DDM = create_dxs_ddm(CASELIST, UNI_NUM, NGROUPS); a{1} = sprintf(' comp_num %d !UNIVERSE %d\n',UNI_NUM*ones(1,2)); a{2} = sprintf('%s%s',BASE_MACRO,DXS_DDM); otherwise error(['Wrong STATE value ' STATE]) end COMP_NUM = sprintf('%s',a{:}); end %----------------------------------------------------------------------------- function [DELCR_COMP delcr_base dscat_mat_delcr] = create_delcr_comp(CASELIST, UNI_NUM, NGROUPS) % DELCR_COMP = create_delcr_base(CASELIST, UNI_NUM, NGROUPS) % input parameters: % CASELIST structure - type: structure, contains all the necessary data % UNI_NUM - type: integer, universe number, e.g. 100, 1000 % NGROUPS - type: integer, number of energy groups, e.g. 33 % output parameter % DELCR_COMP - type: string, parcs delcr_comp input card % delcr_base - type: array, parcs delcr_base input card values % dscat_mat_delcr - type: square matrix, parcs delcr_base scattering matrix % caselist eval('caselist = CASELIST;') % variables to be written into string A = {'P1_TRANSPXS','RABSXS','NSF','KFISS'}; B = {'GPRODXS'}; % delcr_comp a = sprintf(' delcr_comp !%d %d -%d !UNIVERSE %d %d\n',... UNI_NUM(2)*ones(1,3),UNI_NUM(1),UNI_NUM(2)); %% create delcr_base card for i = 1:length(A) [value, abs_std] = get_derivatives_cr_new(CASELIST,'CRP',A{i},UNI_NUM,NGROUPS); delcr_base(:,i) = value'; end [row, col] = size(delcr_base); b{1} = sprintf([' delcr_base ' repmat('%16.6E',1,length(A)) '\n'],delcr_base(1,:)); for j = 2:row b{j} = sprintf([' ' repmat('%16.6E',1,length(A)) '\n'],delcr_base(j,:)); end b = sprintf('%s',b{:}); %% create scattering matrix using GPRODXS [value, abs_std] = get_derivatives_cr_new(CASELIST,'CRP',B{1},UNI_NUM,NGROUPS); dscat_mat_delcr = value; for m = 1:length(dscat_mat_delcr) c{m} = sprintf([ repmat('%16.6E',1,m) '\n'],dscat_mat_delcr(m,1:m)); end c = sprintf('%s',c{:}); %% write all into one string DELCR_COMP = sprintf('%s%s%s',a,b,c); end %----------------------------------------------------------------------------- function KIN_COMP = create_kin_comp(CASELIST, UNI_NUM, NGROUPS) % KIN_COMP = create_kin_comp(CASELIST, UNI_NUM, NGROUPS) % input parameters: % CASELIST structure - type: structure, contains all the necessary data % UNI_NUM - type: integer, universe number, e.g. 100, 1000 % NGROUPS - type: integer, number of energy groups, e.g. 33 % output parameter % KIN_COMP - type: string, parcs kin_comp card % caselist eval('caselist = CASELIST;') % serpent output data names A = {'PRECURSOR_GROUPS','BETA_EFF','DECAY_CONSTANT','RECIPVEL'}; % universe name UNI_NAME = ['UNI_' num2str(UNI_NUM)]; %% create dnp_ngrp sdir{1} = [ 'caselist.REF1.output.' A{1} '.' UNI_NAME]; dnp_ngrp = eval(sdir{1}); a = sprintf(' ! dnp_ngrp %d\n',dnp_ngrp); %% create kin_comp b = sprintf(' ! kin_comp !%d %d -%d !UNIVERSE %d\n',UNI_NUM*ones(1,4));

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%% create dnp_beta sdir{2} = [ 'caselist.REF1.output.' A{2} '.' UNI_NAME]; [value, abs_std] = optimize_data(caselist,sdir{2},A{2},NGROUPS); dnp_beta = value; c = sprintf([' ! dnp_beta ' repmat('%16.6E',1,length(dnp_beta)) '\n'],dnp_beta); %% create dnp_lambda sdir{3} = [ 'caselist.REF1.output.' A{3} '.' UNI_NAME]; [value, abs_std] = optimize_data(caselist,sdir{3},A{3},NGROUPS); dnp_lambda = value; d = sprintf([' ! dnp_lambda ' repmat('%16.6E',1,length(dnp_lambda)) '\n'],dnp_lambda); %% create neut_velo sdir{4} = [ 'caselist.REF1.output.' A{4} '.' UNI_NAME]; [value, abs_std] = optimize_data(caselist,sdir{4},A{4},NGROUPS); neut_velo = value; e = sprintf([' ! neut_velo ' repmat('%16.6E',1,length(neut_velo)) '\n'],neut_velo); %% write all into one string KIN_COMP = sprintf('%s%s%s%s%s',a,b,c,d,e); end %----------------------------------------------------------------------------- function [BASE_MACRO base_macro scat_mat fiss_spec] = create_base_macro(CASELIST, UNI_NUM, NGROUPS) % [ BASE_MACRO base_macro scat_mat fiss_spec ] = create_base_macro(CASELIST, UNI_NUM, NGROUPS) % input parameters: % CASELIST structure - type: structure, contains all the necessary data % UNI_NUM - type: integer, universe number, e.g. 100, 1000 % NGROUPS - type: integer, number of energy groups, e.g. 33 % output parameter % BASE_MACRO - type: string, parcs base_macro input card % base_macro - type: array, parcs base_macro input card % scat_mat - type: square matrix, parcs base_macro scattering matrix % fiss_spec - type: array, parcs normalised fission spectrum % caselist eval('caselist = CASELIST;') % variables to be written into string A = {'P1_TRANSPXS','RABSXS','NSF','KFISS'}; B = {'GPRODXS'}; C = {'CHI'}; % universe name UNI_NAME = ['UNI_' num2str(UNI_NUM)]; %% create base_macro for i = 1:length(A) sdir{i} = [ 'caselist.REF1.output.' A{i} '.' UNI_NAME]; [value, abs_std] = optimize_data(caselist,sdir{i},A{i},NGROUPS); base_macro(:,i) = value'; end [row, col] = size(base_macro); a{1} = sprintf([' base_macro ' repmat('%16.6E',1,length(A)) '\n'],base_macro(1,:)); for j = 2:row a{j} = sprintf([' ' repmat('%16.6E',1,length(A)) '\n'],base_macro(j,:)); end a = sprintf('%s',a{:}); %% create scattering matrix using GPRODXS sdir{1} = [ 'caselist.REF1.output.' B{1} '.' UNI_NAME]; [value, abs_std] = optimize_data(caselist,sdir{1},B{1},NGROUPS); scat_mat = value; for m = 1:length(scat_mat) b{m} = sprintf([ repmat('%16.6E',1,m) '\n'],scat_mat(m,1:m)); end b = sprintf('%s',b{:}); %% create fiss_spec using CHI sdir{1} = [ 'caselist.REF1.output.' C{1} '.' UNI_NAME]; [value, abs_std] = optimize_data(caselist,sdir{1},C{1},NGROUPS); fiss_spec = value; c = sprintf([' fiss_spec ' repmat('%16.6E',1,length(fiss_spec)) '\n'],fiss_spec); %% write all into one string BASE_MACRO = sprintf('%s%s%s%s',a,b,c); end %----------------------------------------------------------------------------- function [DXS_DTF dxs_dtf dscat_mat_dtf] = create_dxs_dtf(CASELIST, UNI_NUM, NGROUPS) % DXS_DTF = create_dxs_dtf(CASELIST, UNI_NUM, NGROUPS) % input parameters: % CASELIST structure - type: structure, contains all the necessary data % UNI_NUM - type: integer, universe number, e.g. 100, 1000 % NGROUPS - type: integer, number of energy groups, e.g. 33 % output parameter % DXS_DTF - type: string, parcs dxs_dtf input card % dxs_dtf - type: array, parcs dxs_dtf input card

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% dscat_mat_dtf - type: square matrix, parcs dxs_dtf scattering matrix % caselist eval('caselist = CASELIST;') % variables to be written into string A = {'P1_TRANSPXS','RABSXS','NSF','KFISS'}; B = {'GPRODXS'}; %% create dxs_dtf card for i = 1:length(A) [value, abs_std] = get_derivatives_new(CASELIST,'FT',A{i},UNI_NUM,NGROUPS); dxs_dtf(:,i) = value'; end [row, col] = size(dxs_dtf); a{1} = sprintf([' dxs_dtf ' repmat('%16.6E',1,length(A)) '\n'],dxs_dtf(1,:)); for j = 2:row a{j} = sprintf([' ' repmat('%16.6E',1,length(A)) '\n'],dxs_dtf(j,:)); end a = sprintf('%s',a{:}); %% create scattering matrix using GPRODXS [value, abs_std] = get_derivatives_new(CASELIST,'FT',B{1},UNI_NUM,NGROUPS); dscat_mat_dtf = value; for m = 1:length(dscat_mat_dtf) b{m} = sprintf([ repmat('%16.6E',1,m) '\n'],dscat_mat_dtf(m,1:m)); end b = sprintf('%s',b{:}); %% write all into one string DXS_DTF = sprintf('%s%s',a,b); end %----------------------------------------------------------------------------- function [DXS_AXEXP dxs_axexp dscat_mat_axexp] = create_dxs_axexp(CASELIST, UNI_NUM, NGROUPS) % [ DXS_AXEXP dxs_axexp dscat_mat_axexp ] = create_dxs_axexp(CASELIST, UNI_NUM, NGROUPS) % input parameters: % CASELIST structure - type: structure, contains all the necessary data % UNI_NUM - type: integer, universe number, e.g. 100, 1000 % NGROUPS - type: integer, number of energy groups, e.g. 33 % output parameter % DXS_AXEXP - type: string, parcs dxs_axexp input card % dxs_axexp - type: array, parcs dxs_axexp input card % dscat_mat_axexp - type: square matrix, parcs dxs_axexp scattering matrix % caselist eval('caselist = CASELIST;') % variables to be written into string A = {'P1_TRANSPXS','RABSXS','NSF','KFISS'}; B = {'GPRODXS'}; %% create dxs_axexp card for i = 1:length(A) [value, abs_std] = get_derivatives_new(CASELIST,'FHE',A{i},UNI_NUM,NGROUPS); dxs_axexp(:,i) = value'; end [row, col] = size(dxs_axexp); a{1} = sprintf([' dxs_axexp ' repmat('%16.6E',1,length(A)) '\n'],dxs_axexp(1,:)); for j = 2:row a{j} = sprintf([' ' repmat('%16.6E',1,length(A)) '\n'],dxs_axexp(j,:)); end a = sprintf('%s',a{:}); %% create scattering matrix using GPRODXS [value, abs_std] = get_derivatives_new(CASELIST,'FHE',B{1},UNI_NUM,NGROUPS); dscat_mat_axexp = value; for m = 1:length(dscat_mat_axexp) b{m} = sprintf([ repmat('%16.6E',1,m) '\n'],dscat_mat_axexp(m,1:m)); end b = sprintf('%s',b{:}); %% write all into one string DXS_AXEXP = sprintf('%s%s',a,b); end %----------------------------------------------------------------------------- function [DXS_RADEXP dxs_radexp dscat_mat_radexp] = create_dxs_radexp(CASELIST, UNI_NUM, NGROUPS) % [ DXS_RADEXP dxs_radexp dscat_mat_radexp ] = create_dxs_radexp(CASELIST, UNI_NUM, NGROUPS)

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% input parameters: % CASELIST structure - type: structure, contains all the necessary data % UNI_NUM - type: integer, universe number, e.g. 100, 1000 % NGROUPS - type: integer, number of energy groups, e.g. 33 % output parameter % DXS_RADEXP - type: string, parcs dxs_radexp input card % dxs_radexp - type: array, parcs dxs_radexp input card % dscat_mat_radexp - type: square matrix, parcs dxs_radexp scattering matrix % caselist eval('caselist = CASELIST;') % variables to be written into string A = {'P1_TRANSPXS','RABSXS','NSF','KFISS'}; B = {'GPRODXS'}; %% create dxs_radexp card for i = 1:length(A) [value, abs_std] = get_derivatives_new(CASELIST,'DGP',A{i},UNI_NUM,NGROUPS); dxs_radexp(:,i) = value'; end [row, col] = size(dxs_radexp); a{1} = sprintf([' dxs_radexp ' repmat('%16.6E',1,length(A)) '\n'],dxs_radexp(1,:)); for j = 2:row a{j} = sprintf([' ' repmat('%16.6E',1,length(A)) '\n'],dxs_radexp(j,:)); end a = sprintf('%s',a{:}); %% create scattering matrix using GPRODXS [value, abs_std] = get_derivatives_new(CASELIST,'DGP',B{1},UNI_NUM,NGROUPS); dscat_mat_radexp = value; for m = 1:length(dscat_mat_radexp) b{m} = sprintf([ repmat('%16.6E',1,m) '\n'],dscat_mat_radexp(m,1:m)); end b = sprintf('%s',b{:}); %% write all into one string DXS_RADEXP = sprintf('%s%s',a,b); end %----------------------------------------------------------------------------- function [DXS_DDM dxs_ddm dscat_mat_ddm] = create_dxs_ddm(CASELIST, UNI_NUM, NGROUPS) % [ DXS_DDM dxs_ddm dscat_mat_ddm ] = create_dxs_ddm(CASELIST, UNI_NUM, NGROUPS) % input parameters: % CASELIST structure - type: structure, contains all the necessary data % UNI_NUM - type: integer, universe number, e.g. 100, 1000 % NGROUPS - type: integer, number of energy groups, e.g. 33 % output parameter % DXS_DDM - type: string, parcs dxs_ddm input card % dxs_ddm - type: array, parcs dxs_ddm input card % dscat_mat_ddm - type: square matrix, parcs dxs_ddm scattering matrix % caselist eval('caselist = CASELIST;') % variables to be written into string A = {'P1_TRANSPXS','RABSXS','NSF','KFISS'}; B = {'GPRODXS'}; %% create dxs_ddm card for i = 1:length(A) [value, abs_std] = get_derivatives_new(CASELIST,'CD',A{i},UNI_NUM,NGROUPS); dxs_ddm(:,i) = value'; end [row, col] = size(dxs_ddm); a{1} = sprintf([' dxs_ddm ' repmat('%16.6E',1,length(A)) '\n'],dxs_ddm(1,:)); for j = 2:row a{j} = sprintf([' ' repmat('%16.6E',1,length(A)) '\n'],dxs_ddm(j,:)); end a = sprintf('%s',a{:}); %% create scattering matrix using GPRODXS [value, abs_std] = get_derivatives_new(CASELIST,'CD',B{1},UNI_NUM,NGROUPS); dscat_mat_ddm = value; for m = 1:length(dscat_mat_ddm) b{m} = sprintf([ repmat('%16.6E',1,m) '\n'],dscat_mat_ddm(m,1:m)); end b = sprintf('%s',b{:}); %% write all into one string DXS_DDM = sprintf('%s%s',a,b);

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end %----------------------------------------------------------------------------- % not active function [ADF_CDF adf cdf] = create_adf_cdf(CASELIST, UNI_NUM, NGROUPS) % [ADF_CDF adf cdf] = create_adf_cdf(CASELIST, UNI_NUM, NGROUPS) % input parameters: % CASELIST structure - type: structure, contains all the necessary data % UNI_NUM - type: integer, universe number, e.g. 100, 1000 % NGROUPS - type: integer, number of energy groups, e.g. 33 % output parameter % ADF_CDF - type: string, parcs adf and cdf input cards % adf - type: array, parcs adf input card values % cdf - type: array, parcs cdf input card values % caselist eval('caselist = CASELIST;') % variables to be written into string A = {'ADFS','ADFC'}; % universe name UNI_NAME = ['UNI_' num2str(UNI_NUM)]; %% create adf sdir{1} = [ 'caselist.REF1.output.' A{1} '.' UNI_NAME]; [value, abs_std] = optimize_data(caselist,sdir{1},A{1},NGROUPS); adf = value; [row, col] = size(adf); a{1} = sprintf([' !adf ' repmat('%16.6E',1,col) '\n'],adf(1,:)); for j = 2:row a{j} = sprintf(['! ' repmat('%16.6E',1,col) '\n'],adf(j,:)); end ADF = sprintf('%s',a{:}); %% create cdf sdir{2} = [ 'caselist.REF1.output.' A{2} '.' UNI_NAME]; [value, abs_std] = optimize_data(caselist,sdir{2},A{2},NGROUPS); cdf = value; [row, col] = size(cdf); b{1} = sprintf([' !cdf ' repmat('%16.6E',1,col) '\n'],cdf(1,:)); for j = 2:row b{j} = sprintf(['! ' repmat('%16.6E',1,col) '\n'],cdf(j,:)); end CDF = sprintf('%s',b{:}); %% write all into one string ADF_CDF = sprintf('%s%s',ADF,CDF); end %----------------------------------------------------------------------------- function [DERIVATIVE, ABSSTD] = get_derivatives_new(CASELIST,CASE_NAME,SERP_ID,UNI_NUM,NGROUPS) % [DERIVATIVE, ABSSTD] = get_derivatives_new(CASELIST,CASE_NAME,SERP_ID,UNI_NUM,NGROUPS) % input parameters: % CASELIST structure - type: structure, contains all the necessary data % CASE_NAME - type: string, e.g. CD, FT, FHE, DGP % SERP_ID - type: string, name of the variable from serp % output file e.g. P1_TRANSPXS,RABSXS, NSF % UNI_NUM - type: number, universe number, e.g. 100, 1000 % NGROUPS - type: number, number of energy groups, default value 33 % output parameters % DERIVATIVE - type: number/array, calculated derivative for the % given CASE_NAME % ABSSTD - type: number/array, absolute standard deviation % energy groups, default 33 if nargin == 4 NGROUPS = 33; end % caselist eval('caselist = CASELIST;') % universe name UNI_NAME = ['UNI_' num2str(UNI_NUM)]; % get the structure of the caselist sc = get_structure(CASELIST); if strcmp(CASE_NAME,'REF') error(['Wrong input parameter ' CASE_NAME]) end try name = eval(['sc.' CASE_NAME '.name']); catch exception disp ('Enter one of the following strings for CASE_NAME') disp (sc.utype) error([ 'Wrong input parameter ' CASE_NAME ])

51

end if length(name)==2 sdir{1} = ['caselist.' name{1} '.output.' SERP_ID '.' UNI_NAME ]; sdir{2} = ['caselist.' name{2} '.output.' SERP_ID '.' UNI_NAME ]; elseif length(name)==1 sdir{1} = ['caselist.' name{1} '.output.' SERP_ID '.' UNI_NAME ]; name{2} = 'REF1'; sdir{2} = ['caselist.' name{2} '.output.' SERP_ID '.' UNI_NAME ]; end % get values [value_1, abs_std_1] = optimize_data(caselist,sdir{1},SERP_ID,NGROUPS); [value_2, abs_std_2] = optimize_data(caselist,sdir{2},SERP_ID,NGROUPS); % calculate difference dval = value_1-value_2; disp([sdir{1} '-' sdir{2}]) dstd = abs_std_1 + abs_std_2; % standard deviation % get parameter values p{1} = eval(['caselist.' name{1} '.par.' CASE_NAME]); p{2} = eval(['caselist.' name{2} '.par.' CASE_NAME]); par_1 = str2double(p{1}); par_2 = str2double(p{2}); % calculate parameter difference if strcmp(CASE_NAME,'FT') dpar = log(par_1)-log(par_2); disp(['log' p{1} ' log' p{2}]) elseif strcmp(CASE_NAME,'CRP') dpar = 1; disp([p{1} ' ' p{2}]) disp('dpar = 1') else dpar = par_1-par_2; disp([p{1} ' ' p{2}]) end % calculate derivatives DERIVATIVE = dval/dpar; ABSSTD = dstd/dpar; end %----------------------------------------------------------------------------- function [DERIVATIVE, ABSSTD] = get_derivatives_cr_new(CASELIST,CASE_NAME,SERP_ID,UNI_NUM,NGROUPS) % [DERIVATIVE, ABSSTD] = get_derivatives_cr_new(CASELIST,CASE_NAME,SERP_ID,UNI_NUM,NGROUPS) % input parameters: % CASELIST structure - type: structure, contains all the necessary data % CASE_NAME - type: string, e.g. CD, FT, FHE, DGP % SERP_ID - type: string, name of the variable from serp % output file e.g. P1_TRANSPXS,RABSXS, NSF % UNI_NUM - type: number, universe number, e.g. 100, 1000 % NGROUPS - type: number, number of energy groups, default value 33 % output parameters % DERIVATIVE - type: number/array, calculated derivative for the % given CASE_NAME % ABSSTD - type: number/array, absolute standard deviation % energy groups, default 33 if nargin == 4 NGROUPS = 33; end % caselist eval('caselist = CASELIST;') % universe name UNI_NAME{1} = ['UNI_' num2str(UNI_NUM(1))]; UNI_NAME{2} = ['UNI_' num2str(UNI_NUM(2))]; % get the structure of the caselist sc = get_structure(CASELIST); if strcmp(CASE_NAME,'REF') error(['Wrong input parameter ' CASE_NAME]) end try name = eval(['sc.' CASE_NAME '.name']); catch exception disp ('Enter one of the following strings for CASE_NAME') disp (sc.utype) error([ 'Wrong input parameter ' CASE_NAME ]) end if length(name)==2 sdir{1} = ['caselist.' name{1} '.output.' SERP_ID '.' UNI_NAME{1} ]; sdir{2} = ['caselist.' name{2} '.output.' SERP_ID '.' UNI_NAME{2} ]; elseif length(name)==1 sdir{1} = ['caselist.' name{1} '.output.' SERP_ID '.' UNI_NAME{1} ]; name{2} = 'REF1'; sdir{2} = ['caselist.' name{2} '.output.' SERP_ID '.' UNI_NAME{2} ]; end

52

% get values [value_1, abs_std_1] = optimize_data(caselist,sdir{1},SERP_ID,NGROUPS); [value_2, abs_std_2] = optimize_data(caselist,sdir{2},SERP_ID,NGROUPS); % calculate difference dval = value_1-value_2; disp([sdir{1} '-' sdir{2}]) dstd = abs_std_1 + abs_std_2; % standard deviation % get parameter values p{1} = eval(['caselist.' name{1} '.par.' CASE_NAME]); p{2} = eval(['caselist.' name{2} '.par.' CASE_NAME]); par_1 = str2double(p{1}); par_2 = str2double(p{2}); % calculate parameter difference if strcmp(CASE_NAME,'FT') dpar = log(par_1)-log(par_2); disp(['log' p{1} ' log' p{2}]) elseif strcmp(CASE_NAME,'CRP') dpar = 1; disp([p{1} ' ' p{2}]) disp('dpar = 1') else dpar = par_1-par_2; disp([p{1} ' ' p{2}]) end % calculate derivatives DERIVATIVE = dval/dpar; ABSSTD = dstd/dpar; end %----------------------------------------------------------------------------- function [value, abs_std] = optimize_data(CASELIST,STRUCT_DIR,SERP_NAME,NGROUPS) % [value, abs_std] = optimize_data(DATA_NAME,NGROUPS,SERP_NAME) % executes DATA_NAME and modifies array % DICT - struct type data % NGROUPS - number of cross section groups % STRUCT_DIR - location of the data in struct field % SERP_NAMES - e.g. 'RECIPVEL','PRECURSOR_GROUPS','CHI'... % NGROUPS - number of energy groups, default value 33 % caselist eval('caselist = CASELIST;') try DATA = eval(STRUCT_DIR); catch exception disp([STRUCT_DIR ' does not exist']) if strcmp(SERP_NAME,'KFISS') disp('KFISS substituted with zeros') DATA = zeros(1,2*NGROUPS); end end % check number of input arguments, substite missing ones if nargin == 3 NGROUPS = 33; elseif nargin == 2 NGROUPS = 33; SERP_NAME = ''; end switch SERP_NAME case {'ANA_KEFF','IMP_KEFF'} value = DATA(1); abs_std = DATA(2); case 'RECIPVEL' value = 1./DATA(3:2:end); if nargout == 2 abs_std = value.* DATA(4:2:end); end case 'PRECURSOR_GROUPS' value = DATA; if nargout == 2 abs_std = []; end case {'BETA_EFF','DECAY_CONSTANT'} value = DATA(3:2:end); if nargout == 2 abs_std = DATA(3:2:end).* DATA(4:2:end); end case {'ADFS','ADFC'} MATRIX = zeros(NGROUPS,6); for row = 1:NGROUPS for col = 1:6 MATRIX(row,col) = DATA( 2*(col-1)*NGROUPS+2*row-1 ); end end value = MATRIX; if nargout == 2 STD_MAT = zeros(NGROUPS,6); for row = 1:NGROUPS for col = 1:6

53

STD_MAT(row,col) =... DATA( 2*(col-1)*NGROUPS+2*row-1 )*... DATA( 2*(col-1)*NGROUPS+2*row ); end end abs_std = STD_MAT; end otherwise switch length(DATA); case NGROUPS*2 % data without total values, e.g. CHI value = DATA(1:2:end); if nargout == 2 abs_std = DATA(1:2:end).* DATA(2:2:end); end case NGROUPS*2+2 % data with total value, e.g. NSF,RABSXS value = DATA(3:2:end); if nargout == 2 abs_std = DATA(3:2:end).* DATA(4:2:end); end case (NGROUPS.^2)*2 % square matrix, e.g. GPRODXS MATRIX = zeros(NGROUPS); for row = 1:NGROUPS for col = 1:NGROUPS MATRIX(row,col) =DATA( 2*(row-1)*NGROUPS+2*col-1 ); end end % get elements below diagonal and delete first raw and last column value = tril(MATRIX,-1); value(1,:) = []; value(:,end)=[]; if nargout == 2 STD_MAT = zeros(NGROUPS); for row = 1:NGROUPS for col = 1:NGROUPS STD_MAT(row,col) = ... DATA( 2*(row-1)*NGROUPS+2*col-1 )*DATA( 2*(row-1)*NGROUPS+2*col ); end end abs_std = tril(STD_MAT,-1); abs_std(1,:) = []; abs_std(:,end)=[]; end otherwise disp([SERP_NAME 'cannot be handled']) error('ERROR: Length of input parameter is out of range') end end end %----------------------------------------------------------------------------- function scene = get_structure(caselist) % scene = get_structure(caselist) % finds unique types in the caselist caseid = fieldnames(caselist); casetype = regexprep(caseid,'\d',''); id = regexprep(caseid,'[A-Z]+',''); UNIQ = regexprep(caseid,'\d','');%remove last digit from the cell array [UNIQ{end+1}] = deal('');% add one empty cell at the end of the cell array ind = ~all(strcmp(UNIQ(1:end-1), UNIQ(2:end)),2);% get indexes of unique elements UNIQ = UNIQ(ind);% make unique cell array scene = struct; scene.caseid = caseid; scene.casetype = casetype; scene.casenum = id; scene.utype = UNIQ; for uq = 1:length(UNIQ) i = 1; for ct = 1:length(casetype) if all(strcmp(UNIQ{uq},casetype{ct})) eval(['scene.' UNIQ{uq} '.name{i}=''' caseid{ct} ''';']) eval(['scene.' UNIQ{uq} '.index(i)=' num2str(ct) ';']) i = i + 1; end end end end

54

B. S2P case-list

01 %%%Serpent input template 02 03 geomfile ESFR_SERPENT_TEMPLATE_COLD_DET_60S_HALFDGP 04 05 %%%Execution options 06 07 exeopt serial 08 exepath sss 09 10 %%% branches 11 12 case reference REF 1 13 FHE 0 %fuel height expansion ,[cm] 14 FDC 1 %fuel density coefficient, FDC and FHE reflect each other 15 FT 300 %Fuel temperature, [K] 16 CD 0.95 %Coolant density at 743K, [g/cm3] 17 CT 300 %Coolant temperature, [K] 18 DGP 21.08 %diagrid pitch, [cm] 19 CRP 50 %control rod position, [cm] 20 21 case fhhi FHE 1 22 FHE 3.4174 23 FDC 0.9670 24 FT 300 25 CT 300 26 CD 0.95 27 DGP 21.08 28 CRP 50 29 30 case fthi FT 1 31 FHE 0 32 FDC 1 33 FT 1800 34 CT 300 35 CD 0.95 36 DGP 21.08 37 CRP 50 38 39 case cdlow CD 1 40 FHE 0 41 FDC 1 42 FT 300 43 CT 300 44 CD 0.681 45 DGP 21.08 46 CRP 50 47 48 case dgphi DGP 1 49 FHE 0 50 FDC 1 51 FT 300 52 CT 300 53 CD 0.95 54 DGP 22.2345 55 CRP 50 56 57 case crin CRP 1 58 FHE 0 59 FDC 1 60 FT 300 61 CT 300 62 CD 0.95 63 DGP 21.08 64 CRP -50

55

C. SFR Parameterized Serpent Input

0001 % --- ESFRMU Core ------------------------- 0002 0003 set title "<TITLE>" 0004 0005 % --- Cross section library file path: 0006 0007 set acelib "/afs/psi.ch/project/.../Libraries/jeff31/sss_jeff31u.xsdata" 0008 set declib "/afs/psi.ch/project/.../Libraries/endfb7/sss_endfb7.dec" 0009 set nfylib "/afs/psi.ch/project/.../Libraries/endfb7/sss_endfb7.nfy" 0010 0011 % --- Use of unresolved resonance data : 0012 0013 set ures 1 0014 set seed 1329841260 0015 set bc 1 0016 0017 % --- Group constant generation 0018 0019 set gcu 0 0020 98 99 100 101 104 %universes of inner fuel assembly 0021 198 199 200 201 204 %universes of outer fuel assembly 0022 60 61 %universes of inner CSD assembly 0023 70 71 %universes of central DSD assembly 0024 80 81 %universes of outer CSD assembly 0025 50 %universe of Reflector assembly 0026 0027 set sym 12 0028 0029 set nfg 33 1.000000E-07 5.400000E-07 4.000000E-06 8.315290E-06 1.370960E-05 2.260330E-05 0030 4.016900E-05 6.790400E-05 9.166090E-05 1.486250E-04 3.043250E-04 4.539990E-04 7.485180E-04 0031 1.234100E-03 2.034680E-03 3.354630E-03 5.530840E-03 9.118820E-03 1.503440E-02 2.478750E-02 0032 4.086770E-02 6.737950E-02 1.110900E-01 1.831560E-01 3.019740E-01 4.978710E-01 8.208500E-01 0033 1.353353E+00 2.231302E+00 3.678794E+00 6.065307E+00 1.000000E+01 0034 0035 0036 % --- Neutron population and criticality cycles: 0037 0038 set pop 150000 500 500 0039 set power 3.60E+09 0040 0041 % ----------------------------------------------------------- 0042 0043 % --- Universe for fuel1 ------------------------------------ 0044 0045 % ----------------------------------------------------------- 0046 0047 % --- Empty lattice position: 0048 0049 pin 3 0050 0051 naf 0052 0053 % --- Fuel pin : 0054 0055 pin 10 0056 0057 %void 0.1200 0058 fuel1 0.4700 0059 heg 0.4850 0060 ods 0.5380 0061 naf 0062 0063 % ---Fission gas pin 0064 0065 pin 11 0066 0067 heg 0.4850 0068 ods 0.5380 0069 naf 0070 0071 % ---Lower Axial Reflector Pin 0072 0073 pin 12 0074 0075 f17 0.4850 0076 ods 0.5380 0077 naf 0078 0079 % ---Upper Axial Reflector Pin 0080 0081 pin 14 0082 0083 f17 0.49175 0084 naf 0085 0086 0087 % ---Fuel Pin Lattice : 0088 0089 lat 110 2 0.0 0.0 21 21 1.174 0090 0091 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0092 3 3 3 3 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 10 3 0093 3 3 3 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 10 10 3 0094 3 3 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 10 10 10 3 0095 3 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 10 10 10 10 3 0096 3 3 3 3 3 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 3 0097 3 3 3 3 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 3 0098 3 3 3 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 3 0099 3 3 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 3 0100 3 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 3 0101 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 3 0102 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 3 3 0103 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 3 3 3 0104 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 3 3 3 3 0105 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 3 3 3 3 3 0106 3 10 10 10 10 10 10 10 10 10 10 10 10 10 10 3 3 3 3 3 3 0107 3 10 10 10 10 10 10 10 10 10 10 10 10 10 3 3 3 3 3 3 3

56

0108 3 10 10 10 10 10 10 10 10 10 10 10 10 3 3 3 3 3 3 3 3 0109 3 10 10 10 10 10 10 10 10 10 10 10 3 3 3 3 3 3 3 3 3 0110 3 10 10 10 10 10 10 10 10 10 10 3 3 3 3 3 3 3 3 3 3 0111 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0112 0113 % ---FGP pin lattice 0114 0115 lat 111 2 0.0 0.0 21 21 1.174 0116 0117 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0118 3 3 3 3 3 3 3 3 3 3 11 11 11 11 11 11 11 11 11 11 3 0119 3 3 3 3 3 3 3 3 3 11 11 11 11 11 11 11 11 11 11 11 3 0120 3 3 3 3 3 3 3 3 11 11 11 11 11 11 11 11 11 11 11 11 3 0121 3 3 3 3 3 3 3 11 11 11 11 11 11 11 11 11 11 11 11 11 3 0122 3 3 3 3 3 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 0123 3 3 3 3 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 0124 3 3 3 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 0125 3 3 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 0126 3 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 0127 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 0128 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 3 0129 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 3 3 0130 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 3 3 3 0131 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 3 3 3 3 0132 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 3 3 3 3 3 0133 3 11 11 11 11 11 11 11 11 11 11 11 11 11 3 3 3 3 3 3 3 0134 3 11 11 11 11 11 11 11 11 11 11 11 11 3 3 3 3 3 3 3 3 0135 3 11 11 11 11 11 11 11 11 11 11 11 3 3 3 3 3 3 3 3 3 0136 3 11 11 11 11 11 11 11 11 11 11 3 3 3 3 3 3 3 3 3 3 0137 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0138 0139 % ---Lower Axial Reflector lattice 0140 0141 lat 112 2 0.0 0.0 21 21 1.174 0142 0143 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0144 3 3 3 3 3 3 3 3 3 3 12 12 12 12 12 12 12 12 12 12 3 0145 3 3 3 3 3 3 3 3 3 12 12 12 12 12 12 12 12 12 12 12 3 0146 3 3 3 3 3 3 3 3 12 12 12 12 12 12 12 12 12 12 12 12 3 0147 3 3 3 3 3 3 3 12 12 12 12 12 12 12 12 12 12 12 12 12 3 0148 3 3 3 3 3 3 12 12 12 12 12 12 12 12 12 12 12 12 12 12 3 0149 3 3 3 3 3 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 3 0150 3 3 3 3 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 3 0151 3 3 3 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 3 0152 3 3 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 3 0153 3 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 3 0154 3 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 3 3 0155 3 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 3 3 3 0156 3 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 3 3 3 3 0157 3 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 3 3 3 3 3 0158 3 12 12 12 12 12 12 12 12 12 12 12 12 12 12 3 3 3 3 3 3 0159 3 12 12 12 12 12 12 12 12 12 12 12 12 12 3 3 3 3 3 3 3 0160 3 12 12 12 12 12 12 12 12 12 12 12 12 3 3 3 3 3 3 3 3 0161 3 12 12 12 12 12 12 12 12 12 12 12 3 3 3 3 3 3 3 3 3 0162 3 12 12 12 12 12 12 12 12 12 12 3 3 3 3 3 3 3 3 3 3 0163 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0164 0165 % ---Upper Axial Reflector lattice 0166 0167 lat 114 2 0.0 0.0 21 21 1.174 0168 0169 0170 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0171 3 3 3 3 3 3 3 3 3 3 14 14 14 14 14 14 14 14 14 14 3 0172 3 3 3 3 3 3 3 3 3 14 14 14 14 14 14 14 14 14 14 14 3 0173 3 3 3 3 3 3 3 3 14 14 14 14 14 14 14 14 14 14 14 14 3 0174 3 3 3 3 3 3 3 14 14 14 14 14 14 14 14 14 14 14 14 14 3 0175 3 3 3 3 3 3 14 14 14 14 14 14 14 14 14 14 14 14 14 14 3 0176 3 3 3 3 3 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 3 0177 3 3 3 3 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 3 0178 3 3 3 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 3 0179 3 3 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 3 0180 3 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 3 0181 3 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 3 3 0182 3 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 3 3 3 0183 3 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 3 3 3 3 0184 3 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 3 3 3 3 3 0185 3 14 14 14 14 14 14 14 14 14 14 14 14 14 14 3 3 3 3 3 3 0186 3 14 14 14 14 14 14 14 14 14 14 14 14 14 3 3 3 3 3 3 3 0187 3 14 14 14 14 14 14 14 14 14 14 14 14 3 3 3 3 3 3 3 3 0188 3 14 14 14 14 14 14 14 14 14 14 14 3 3 3 3 3 3 3 3 3 0189 3 14 14 14 14 14 14 14 14 14 14 3 3 3 3 3 3 3 3 3 3 0190 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0191 0192 0193 0194 % --- --- Universe 100 --- --- Inner Fuel Region 0195 0196 surf 100A00 hexyc 0.0 0.0 9.86500 0197 surf 100A01 hexyc 0.0 0.0 10.31500 0198 surf 100A02 hexyc 0.0 0.0 <HALFDGP> 0199 surf 100A03 pz -50.00 0200 surf 100A04 pz <50.00+FHE> 0201 0202 cell 100A901 100 outside 100A04 0203 0204 cell 100A002 100 fill 110 -100A00 100A03 -100A04 0205 cell 100A003 100 em10 100A00 -100A01 100A03 -100A04 0206 cell 100A004 100 naf 100A01 -100A02 100A03 -100A04 0207 cell 100A905 100 naf 100A02 100A03 -100A04 0208 0209 cell 100A906 100 outside -100A03 0210 0211 % --- --- Universe 99 --- --- Lower Reflector 0212 0213 surf 99A00 hexyc 0.0 0.0 9.84650 0214 surf 99A01 hexyc 0.0 0.0 10.31500 0215 surf 99A02 hexyc 0.0 0.0 <HALFDGP> 0216 surf 99A03 pz -80.00000 0217 surf 99A04 pz -50.00000 0218 0219 cell 99A901 99 outside 99A04 0220 0221 cell 99A002 99 fill 112 -99A00 99A03 -99A04 0222 cell 99A003 99 em10 99A00 -99A01 99A03 -99A04

57

0223 cell 99A004 99 naf 99A01 -99A02 99A03 -99A04 0224 cell 99A905 99 naf 99A02 99A03 -99A04 0225 0226 cell 99A906 99 outside -99A03 0227 0228 % --- --- Universe 98 --- --- Lower FGP 0229 0230 surf 98A00 hexyc 0.0 0.0 9.84650 0231 surf 98A01 hexyc 0.0 0.0 10.31500 0232 surf 98A02 hexyc 0.0 0.0 <HALFDGP> 0233 surf 98A03 pz -171.00000 0234 surf 98A04 pz -80.00000 0235 0236 cell 98A901 98 outside 98A04 0237 0238 cell 98A002 98 fill 111 -98A00 98A03 -98A04 0239 cell 98A003 98 em10 98A00 -98A01 98A03 -98A04 0240 cell 98A004 98 naf 98A01 -98A02 98A03 -98A04 0241 cell 98A905 98 naf 98A02 98A03 -98A04 0242 0243 cell 98A906 98 outside -98A03 0244 0245 % --- --- Universe 101 --- --- Upper FGP 0246 0247 surf 101A00 hexyc 0.0 0.0 9.84650 0248 surf 101A01 hexyc 0.0 0.0 10.31500 0249 surf 101A02 hexyc 0.0 0.0 <HALFDGP> 0250 surf 101A03 pz <50.00+FHE> 0251 surf 101A04 pz 61.00000 0252 0253 cell 101A901 101 outside 101A04 0254 0255 cell 101A002 101 fill 111 -101A00 101A03 -101A04 0256 cell 101A003 101 em10 101A00 -101A01 101A03 -101A04 0257 cell 101A004 101 naf 101A01 -101A02 101A03 -101A04 0258 cell 101A905 101 naf 101A02 101A03 -101A04 0259 0260 cell 101A906 101 outside -101A03 0261 0262 % --- --- Universe 104 --- --- Upper Axial Reflector 0263 0264 surf 104A00 hexyc 0.0 0.0 9.44350 0265 surf 104A01 hexyc 0.0 0.0 10.31500 0266 surf 104A02 hexyc 0.0 0.0 <HALFDGP> 0267 surf 104A03 pz 61.00000 0268 surf 104A04 pz 131.00000 0269 0270 cell 104A901 104 outside 104A04 0271 0272 cell 104A002 104 fill 114 -104A00 104A03 -104A04 0273 cell 104A003 104 em10 104A00 -104A01 104A03 -104A04 0274 cell 104A004 104 naf 104A01 -104A02 104A03 -104A04 0275 cell 104A905 104 naf 104A02 104A03 -104A04 0276 0277 cell 104A906 104 outside -104A03 0278 0279 % --- --- Universe 1000 --- --- 0280 0281 surf A00 hexyc 0.0 0.0 <HALFDGP> 0282 surf A01 pz -171.00000 0283 surf A02 pz -80.00000 0284 surf A03 pz -50.00000 0285 surf A04 pz <50.00000+FHE> 0286 surf A05 pz 61.00000 0287 surf A06 pz 131.00000 0288 0289 cell A901 1000 outside A06 0290 cell A002 1000 fill 104 -A00 A05 -A06 0291 cell A003 1000 naf A00 A05 -A06 0292 cell A004 1000 fill 101 -A00 A04 -A05 0293 cell A005 1000 naf A00 A04 -A05 0294 cell A006 1000 fill 100 -A00 A03 -A04 0295 cell A007 1000 naf A00 A03 -A04 0296 cell A008 1000 fill 99 -A00 A02 -A03 0297 cell A009 1000 naf A00 A02 -A03 0298 cell A010 1000 fill 98 -A00 A01 -A02 0299 cell A011 1000 naf A00 A01 -A02 0300 cell A909 1000 outside -A01 0301 0302 0303 % ----------------------------------------------------------- 0304 0305 % --- Universe for fuel2 ------------------------------------ 0306 0307 % ----------------------------------------------------------- 0308 0309 % --- Empty lattice position: 0310 0311 %pin 3 0312 0313 %naf 0314 0315 % --- Fuel pin : 0316 0317 pin 20 0318 0319 %void 0.1200 0320 fuel2 0.4700 0321 heg 0.4850 0322 ods 0.5380 0323 naf 0324 0325 % ---Fission gas pin 0326 0327 pin 21 0328 0329 heg 0.4850 0330 ods 0.5380 0331 naf 0332 0333 % ---Lower Axial Reflector Pin 0334 0335 pin 22 0336 0337 f17 0.4850

58

0338 ods 0.5380 0339 naf 0340 0341 % ---Upper Axial Reflector Pin 0342 0343 pin 24 0344 0345 f17 0.49175 0346 naf 0347 0348 0349 0350 0351 % ---Fuel Pin Lattice: 0352 0353 lat 220 2 0.0 0.0 21 21 1.174 0354 0355 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0356 3 3 3 3 3 3 3 3 3 3 20 20 20 20 20 20 20 20 20 20 3 0357 3 3 3 3 3 3 3 3 3 20 20 20 20 20 20 20 20 20 20 20 3 0358 3 3 3 3 3 3 3 3 20 20 20 20 20 20 20 20 20 20 20 20 3 0359 3 3 3 3 3 3 3 20 20 20 20 20 20 20 20 20 20 20 20 20 3 0360 3 3 3 3 3 3 20 20 20 20 20 20 20 20 20 20 20 20 20 20 3 0361 3 3 3 3 3 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 3 0362 3 3 3 3 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 3 0363 3 3 3 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 3 0364 3 3 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 3 0365 3 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 3 0366 3 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 3 3 0367 3 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 3 3 3 0368 3 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 3 3 3 3 0369 3 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 3 3 3 3 3 0370 3 20 20 20 20 20 20 20 20 20 20 20 20 20 20 3 3 3 3 3 3 0371 3 20 20 20 20 20 20 20 20 20 20 20 20 20 3 3 3 3 3 3 3 0372 3 20 20 20 20 20 20 20 20 20 20 20 20 3 3 3 3 3 3 3 3 0373 3 20 20 20 20 20 20 20 20 20 20 20 3 3 3 3 3 3 3 3 3 0374 3 20 20 20 20 20 20 20 20 20 20 3 3 3 3 3 3 3 3 3 3 0375 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0376 0377 % ---FGP pin lattice 0378 0379 lat 221 2 0.0 0.0 21 21 1.174 0380 0381 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0382 3 3 3 3 3 3 3 3 3 3 21 21 21 21 21 21 21 21 21 21 3 0383 3 3 3 3 3 3 3 3 3 21 21 21 21 21 21 21 21 21 21 21 3 0384 3 3 3 3 3 3 3 3 21 21 21 21 21 21 21 21 21 21 21 21 3 0385 3 3 3 3 3 3 3 21 21 21 21 21 21 21 21 21 21 21 21 21 3 0386 3 3 3 3 3 3 21 21 21 21 21 21 21 21 21 21 21 21 21 21 3 0387 3 3 3 3 3 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 3 0388 3 3 3 3 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 3 0389 3 3 3 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 3 0390 3 3 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 3 0391 3 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 3 0392 3 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 3 3 0393 3 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 3 3 3 0394 3 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 3 3 3 3 0395 3 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 3 3 3 3 3 0396 3 21 21 21 21 21 21 21 21 21 21 21 21 21 21 3 3 3 3 3 3 0397 3 21 21 21 21 21 21 21 21 21 21 21 21 21 3 3 3 3 3 3 3 0398 3 21 21 21 21 21 21 21 21 21 21 21 21 3 3 3 3 3 3 3 3 0399 3 21 21 21 21 21 21 21 21 21 21 21 3 3 3 3 3 3 3 3 3 0400 3 21 21 21 21 21 21 21 21 21 21 3 3 3 3 3 3 3 3 3 3 0401 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0402 0403 % ---Lower Axial Reflector lattice 0404 0405 lat 222 2 0.0 0.0 21 21 1.174 0406 0407 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0408 3 3 3 3 3 3 3 3 3 3 22 22 22 22 22 22 22 22 22 22 3 0409 3 3 3 3 3 3 3 3 3 22 22 22 22 22 22 22 22 22 22 22 3 0410 3 3 3 3 3 3 3 3 22 22 22 22 22 22 22 22 22 22 22 22 3 0411 3 3 3 3 3 3 3 22 22 22 22 22 22 22 22 22 22 22 22 22 3 0412 3 3 3 3 3 3 22 22 22 22 22 22 22 22 22 22 22 22 22 22 3 0413 3 3 3 3 3 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 3 0414 3 3 3 3 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 3 0415 3 3 3 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 3 0416 3 3 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 3 0417 3 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 3 0418 3 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 3 3 0419 3 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 3 3 3 0420 3 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 3 3 3 3 0421 3 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 3 3 3 3 3 0422 3 22 22 22 22 22 22 22 22 22 22 22 22 22 22 3 3 3 3 3 3 0423 3 22 22 22 22 22 22 22 22 22 22 22 22 22 3 3 3 3 3 3 3 0424 3 22 22 22 22 22 22 22 22 22 22 22 22 3 3 3 3 3 3 3 3 0425 3 22 22 22 22 22 22 22 22 22 22 22 3 3 3 3 3 3 3 3 3 0426 3 22 22 22 22 22 22 22 22 22 22 3 3 3 3 3 3 3 3 3 3 0427 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0428 0429 % ---Upper Axial Reflector lattice 0430 0431 lat 224 2 0.0 0.0 21 21 1.174 0432 0433 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0434 3 3 3 3 3 3 3 3 3 3 24 24 24 24 24 24 24 24 24 24 3 0435 3 3 3 3 3 3 3 3 3 24 24 24 24 24 24 24 24 24 24 24 3 0436 3 3 3 3 3 3 3 3 24 24 24 24 24 24 24 24 24 24 24 24 3 0437 3 3 3 3 3 3 3 24 24 24 24 24 24 24 24 24 24 24 24 24 3 0438 3 3 3 3 3 3 24 24 24 24 24 24 24 24 24 24 24 24 24 24 3 0439 3 3 3 3 3 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 3 0440 3 3 3 3 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 3 0441 3 3 3 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 3 0442 3 3 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 3 0443 3 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 3 0444 3 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 3 3 0445 3 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 3 3 3 0446 3 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 3 3 3 3 0447 3 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 3 3 3 3 3 0448 3 24 24 24 24 24 24 24 24 24 24 24 24 24 24 3 3 3 3 3 3 0449 3 24 24 24 24 24 24 24 24 24 24 24 24 24 3 3 3 3 3 3 3 0450 3 24 24 24 24 24 24 24 24 24 24 24 24 3 3 3 3 3 3 3 3 0451 3 24 24 24 24 24 24 24 24 24 24 24 3 3 3 3 3 3 3 3 3 0452 3 24 24 24 24 24 24 24 24 24 24 3 3 3 3 3 3 3 3 3 3

59

0453 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0454 0455 0456 0457 % --- --- Universe 200 --- --- Outer Fuel 0458 0459 surf 200B00 hexyc 0.0 0.0 9.86500 0460 surf 200B01 hexyc 0.0 0.0 10.31500 0461 surf 200B02 hexyc 0.0 0.0 <HALFDGP> 0462 surf 200B03 pz -50.00000 0463 surf 200B04 pz <50.00000+FHE> 0464 0465 cell 200B901 200 outside 200B04 0466 0467 cell 200B002 200 fill 220 -200B00 200B03 -200B04 0468 cell 200B003 200 em10 200B00 -200B01 200B03 -200B04 0469 cell 200B004 200 naf 200B01 -200B02 200B03 -200B04 0470 cell 200B905 200 naf 200B02 200B03 -200B04 0471 0472 cell 200B906 200 outside -200B03 0473 0474 % --- --- Universe 199 --- --- Lower Axial Reflector 0475 0476 surf 199B00 hexyc 0.0 0.0 9.84650 0477 surf 199B01 hexyc 0.0 0.0 10.31500 0478 surf 199B02 hexyc 0.0 0.0 <HALFDGP> 0479 surf 199B03 pz -80.00000 0480 surf 199B04 pz -50.00000 0481 0482 cell 199B901 199 outside 199B04 0483 0484 cell 199B002 199 fill 222 -199B00 199B03 -199B04 0485 cell 199B003 199 em10 199B00 -199B01 199B03 -199B04 0486 cell 199B004 199 naf 199B01 -199B02 199B03 -199B04 0487 cell 199B905 199 naf 199B02 199B03 -199B04 0488 0489 cell 199B906 199 outside -199B03 0490 0491 % --- --- Universe 198 --- --- Lower FGP 0492 0493 surf 198B00 hexyc 0.0 0.0 9.84650 0494 surf 198B01 hexyc 0.0 0.0 10.31500 0495 surf 198B02 hexyc 0.0 0.0 <HALFDGP> 0496 surf 198B03 pz -171.00000 0497 surf 198B04 pz -80.00000 0498 0499 cell 198B901 198 outside 198B04 0500 0501 cell 198B002 198 fill 221 -198B00 198B03 -198B04 0502 cell 198B003 198 em10 198B00 -198B01 198B03 -198B04 0503 cell 198B004 198 naf 198B01 -198B02 198B03 -198B04 0504 cell 198B905 198 naf 198B02 198B03 -198B04 0505 0506 cell 198B906 198 outside -198B03 0507 0508 % --- --- Universe 201 --- --- Upper FGP 0509 0510 surf 201B00 hexyc 0.0 0.0 9.84650 0511 surf 201B01 hexyc 0.0 0.0 10.31500 0512 surf 201B02 hexyc 0.0 0.0 <HALFDGP> 0513 surf 201B03 pz <50.00000+FHE> 0514 surf 201B04 pz 61.00000 0515 0516 cell 201B901 201 outside 201B04 0517 0518 cell 201B002 201 fill 221 -201B00 201B03 -201B04 0519 cell 201B003 201 em10 201B00 -201B01 201B03 -201B04 0520 cell 201B004 201 naf 201B01 -201B02 201B03 -201B04 0521 cell 201B905 201 naf 201B02 201B03 -201B04 0522 0523 cell 201B906 201 outside -201B03 0524 0525 % --- --- Universe 204 --- --- Upper Reflector 0526 0527 surf 204B00 hexyc 0.0 0.0 9.44350 0528 surf 204B01 hexyc 0.0 0.0 10.31500 0529 surf 204B02 hexyc 0.0 0.0 <HALFDGP> 0530 surf 204B03 pz 61.00000 0531 surf 204B04 pz 131.00000 0532 0533 cell 204B901 204 outside 204B04 0534 0535 cell 204B002 204 fill 224 -204B00 204B03 -204B04 0536 cell 204B003 204 em10 204B00 -204B01 204B03 -204B04 0537 cell 204B004 204 naf 204B01 -204B02 204B03 -204B04 0538 cell 204B905 204 naf 204B02 204B03 -204B04 0539 0540 cell 204B906 204 outside -204B03 0541 0542 % --- --- Universe 2000 --- --- 0543 0544 surf B00 hexyc 0.0 0.0 <HALFDGP> 0545 surf B01 pz -171.00000 0546 surf B02 pz -80.00000 0547 surf B03 pz -50.00000 0548 surf B04 pz <50.00000+FHE> 0549 surf B05 pz 61.00000 0550 surf B06 pz 131.00000 0551 0552 0553 cell B901 2000 outside B06 0554 cell B006 2000 fill 204 -B00 B05 -B06 0555 cell B007 2000 naf B00 B05 -B06 0556 cell B008 2000 fill 201 -B00 B04 -B05 0557 cell B009 2000 naf B00 B04 -B05 0558 cell B010 2000 fill 200 -B00 B03 -B04 0559 cell B011 2000 naf B00 B03 -B04 0560 cell B012 2000 fill 199 -B00 B02 -B03 0561 cell B013 2000 naf B00 B02 -B03 0562 cell B014 2000 fill 198 -B00 B01 -B02 0563 cell B015 2000 naf B00 B01 -B02 0564 cell B909 2000 outside -B01 0565 0566 % ----------------------------------------------------------- 0567

60

0568 % --- Universe for INNER CSD -------------------------------- 0569 0570 % ----------------------------------------------------------- 0571 0572 % --- Empty lattice position: 0573 0574 %pin 3 0575 0576 %naf 0577 0578 % --- CSD pins 0579 0580 pin 30 0581 0582 b4c1 0.9050 0583 heg 1.0415 0584 ods 1.1400 0585 naf 0586 0587 0588 % ---CSD Pin Lattice : 0589 0590 lat 330 2 0.0 0.0 9 9 2.432 0591 0592 3 3 3 3 3 3 3 3 3 0593 3 3 3 3 30 30 30 30 3 0594 3 3 3 30 30 30 30 30 3 0595 3 3 30 30 30 30 30 30 3 0596 3 30 30 30 30 30 30 30 3 0597 3 30 30 30 30 30 30 3 3 0598 3 30 30 30 30 30 3 3 3 0599 3 30 30 30 30 3 3 3 3 0600 3 3 3 3 3 3 3 3 3 0601 0602 0603 0604 % --- --- Universe 60 --- ---Control Assembly CSD 0605 0606 surf 60C00 hexyc 0.0 0.0 7.60000 0607 surf 60C01 hexyc 0.0 0.0 7.80000 0608 surf 60C02 hexyc 0.0 0.0 9.86500 0609 surf 60C03 hexyc 0.0 0.0 10.31500 0610 surf 60C04 hexyc 0.0 0.0 <HALFDGP> 0611 surf 60C05 pz <CRP> 0612 surf 60C06 pz 131.00000 0613 0614 cell 60C901 60 outside 60C06 0615 0616 cell 60C002 60 fill 330 -60C00 60C05 -60C06 0617 cell 60C003 60 em10 60C00 -60C01 60C05 -60C06 0618 cell 60C004 60 naf 60C01 -60C02 60C05 -60C06 0619 cell 60C005 60 em10 60C02 -60C03 60C05 -60C06 0620 cell 60C006 60 naf 60C03 -60C04 60C05 -60C06 0621 cell 60C907 60 naf 60C04 60C05 -60C06 0622 0623 cell 60C908 60 outside -60C05 0624 0625 % --- --- Universe 61 --- ---Follower 0626 0627 surf 61C00 hexyc 0.0 0.0 9.86500 0628 surf 61C01 hexyc 0.0 0.0 10.31500 0629 surf 61C02 hexyc 0.0 0.0 <HALFDGP> 0630 surf 61C03 pz -171.00000 0631 surf 61C04 pz <CRP> 0632 0633 cell 61C901 61 outside 61C04 0634 0635 cell 61C002 61 naf -61C00 61C03 -61C04 0636 cell 61C003 61 em10 61C00 -61C01 61C03 -61C04 0637 cell 61C004 61 naf 61C01 -61C02 61C03 -61C04 0638 cell 61C905 61 naf 61C02 61C03 -61C04 0639 0640 cell 61C906 61 outside -61C03 0641 0642 % --- --- Universe 600 --- --- 0643 0644 surf C00 hexyc 0.0 0.0 <HALFDGP> 0645 surf C01 pz -171.00000 0646 surf C02 pz <CRP> 0647 surf C03 pz 131.00000 0648 0649 cell C901 600 outside C03 0650 0651 cell C002 600 fill 60 -C00 C02 -C03 0652 cell C003 600 naf C00 C02 -C03 0653 cell C004 600 fill 61 -C00 C01 -C02 0654 cell C005 600 naf C00 C01 -C02 0655 0656 cell C906 600 outside -C01 0657 0658 0659 % ----------------------------------------------------------- 0660 0661 % --- Universe for DSD -------------------------------------- 0662 0663 % ----------------------------------------------------------- 0664 0665 % --- Empty lattice position: 0666 0667 %pin 3 0668 0669 %naf 0670 0671 % --- DSD pins 0672 0673 pin 40 0674 0675 b4c2 0.6900 0676 heg 0.7565 0677 ods 0.8175 0678 naf 0679 0680 0681 % ---DSD Pin Lattice (type = 2, pin pitch = 1.742 cm): 0682

61

0683 lat 440 2 0.0 0.0 11 11 1.742 0684 0685 3 3 3 3 3 3 3 3 3 3 3 0686 3 3 3 3 3 3 40 40 40 3 3 0687 3 3 3 3 40 40 40 40 40 40 3 0688 3 3 3 40 40 40 40 40 40 40 3 0689 3 3 40 40 40 40 40 40 40 40 3 0690 3 3 40 40 40 40 40 40 40 3 3 0691 3 40 40 40 40 40 40 40 40 3 3 0692 3 40 40 40 40 40 40 40 3 3 3 0693 3 40 40 40 40 40 40 3 3 3 3 0694 3 3 40 40 40 3 3 3 3 3 3 0695 3 3 3 3 3 3 3 3 3 3 3 0696 0697 0698 % --- --- Universe 70 --- ---Control Assembly DSD 0699 0700 surf 70D00 cyl 0.0 0.0 7.20000 0701 surf 70D01 cyl 0.0 0.0 7.40000 0702 surf 70D02 hexyc 0.0 0.0 9.86500 0703 surf 70D03 hexyc 0.0 0.0 10.31500 0704 surf 70D04 hexyc 0.0 0.0 <HALFDGP> 0705 surf 70D05 pz <CRP> 0706 surf 70D06 pz 131.00000 0707 0708 cell 70D901 70 outside 70D06 0709 0710 cell 70D002 70 fill 440 -70D00 70D05 -70D06 0711 cell 70D003 70 em10 70D00 -70D01 70D05 -70D06 0712 cell 70D004 70 naf 70D01 -70D02 70D05 -70D06 0713 cell 70D005 70 em10 70D02 -70D03 70D05 -70D06 0714 cell 70D006 70 naf 70D03 -70D04 70D05 -70D06 0715 cell 70D907 70 naf 70D04 70D05 -70D06 0716 0717 cell 70D908 70 outside -70D05 0718 0719 % --- --- Universe 71 --- ---Follower 0720 0721 surf 71D00 hexyc 0.0 0.0 9.86500 0722 surf 71D01 hexyc 0.0 0.0 10.31500 0723 surf 71D02 hexyc 0.0 0.0 <HALFDGP> 0724 surf 71D03 pz -171.00000 0725 surf 71D04 pz <CRP> 0726 0727 cell 71D901 71 outside 71D04 0728 0729 cell 71D002 71 naf -71D00 71D03 -71D04 0730 cell 71D003 71 em10 71D00 -71D01 71D03 -71D04 0731 cell 71D004 71 naf 71D01 -71D02 71D03 -71D04 0732 cell 71D905 71 naf 71D02 71D03 -71D04 0733 0734 cell 71D906 71 outside -71D03 0735 0736 % --- --- Universe 700 --- --- 0737 0738 surf D00 hexyc 0.0 0.0 <HALFDGP> 0739 surf D01 pz -171.00000 0740 surf D02 pz <CRP> 0741 surf D03 pz 131.00000 0742 0743 cell D901 700 outside D03 0744 0745 cell D002 700 fill 70 -D00 D02 -D03 0746 cell D003 700 naf D00 D02 -D03 0747 cell D004 700 fill 71 -D00 D01 -D02 0748 cell D005 700 naf D00 D01 -D02 0749 0750 cell D906 700 outside -D01 0751 0752 0753 % ----------------------------------------------------------- 0754 0755 % --- Universe for OUTER CSD -------------------------------- 0756 0757 % ----------------------------------------------------------- 0758 0759 % --- Empty lattice position: 0760 0761 %pin 3 0762 0763 %naf 0764 0765 % --- CSD pins 0766 0767 pin 31 0768 0769 b4c1 0.9050 % b4c for CSD 0770 heg 1.0315 % he gap 0771 ods 1.1390 % cladding 0772 naf %fills the rest of the universe 0773 0774 0775 % ---CSD Pin Lattice : 0776 0777 lat 331 2 0.0 0.0 9 9 2.432 0778 0779 3 3 3 3 3 3 3 3 3 0780 3 3 3 3 31 31 31 31 3 0781 3 3 3 31 31 31 31 31 3 0782 3 3 31 31 31 31 31 31 3 0783 3 31 31 31 31 31 31 31 3 0784 3 31 31 31 31 31 31 3 3 0785 3 31 31 31 31 31 3 3 3 0786 3 31 31 31 31 3 3 3 3 0787 3 3 3 3 3 3 3 3 3 0788 0789 0790 0791 % --- --- Universe 80 --- ---Outer Control Assembly CSD 0792 0793 surf 80E00 hexyc 0.0 0.0 7.60000 0794 surf 80E01 hexyc 0.0 0.0 7.80000 0795 surf 80E02 hexyc 0.0 0.0 9.86500 0796 surf 80E03 hexyc 0.0 0.0 10.31500 0797 surf 80E04 hexyc 0.0 0.0 <HALFDGP>

62

0798 surf 80E05 pz <CRP> 0799 surf 80E06 pz 131.00000 0800 0801 cell 80E901 80 outside 80E06 0802 0803 cell 80E002 80 fill 331 -80E00 80E05 -80E06 0804 cell 80E003 80 em10 80E00 -80E01 80E05 -80E06 0805 cell 80E004 80 naf 80E01 -80E02 80E05 -80E06 0806 cell 80E005 80 em10 80E02 -80E03 80E05 -80E06 0807 cell 80E006 80 naf 80E03 -80E04 80E05 -80E06 0808 cell 80E907 80 naf 80E04 80E05 -80E06 0809 0810 cell 80E908 80 outside -80E05 0811 0812 % --- --- Universe 81 --- ---Follower 0813 0814 surf 81E00 hexyc 0.0 0.0 9.86500 0815 surf 81E01 hexyc 0.0 0.0 10.31500 0816 surf 81E02 hexyc 0.0 0.0 <HALFDGP> 0817 surf 81E03 pz -171.00000 0818 surf 81E04 pz <CRP> 0819 0820 cell 81E901 81 outside 81E04 0821 0822 cell 81E002 81 naf -81E00 81E03 -81E04 0823 cell 81E003 81 em10 81E00 -81E01 81E03 -81E04 0824 cell 81E004 81 naf 81E01 -81E02 81E03 -81E04 0825 cell 81E905 81 naf 81E02 81E03 -81E04 0826 0827 cell 81E906 81 outside -81E03 0828 0829 % --- --- Universe 800 --- --- 0830 0831 surf E00 hexyc 0.0 0.0 <HALFDGP> 0832 surf E01 pz -171.00000 0833 surf E02 pz <CRP> 0834 surf E03 pz 131.00000 0835 0836 cell E901 800 outside E03 0837 0838 cell E002 800 fill 80 -E00 E02 -E03 0839 cell E003 800 naf E00 E02 -E03 0840 cell E004 800 fill 81 -E00 E01 -E02 0841 cell E005 800 naf E00 E01 -E02 0842 0843 cell E906 800 outside -E01 0844 0845 0846 % ----------------------------------------------------------- 0847 0848 % --- Universe for Radial Reflector ------------------------- 0849 0850 % ----------------------------------------------------------- 0851 0852 % --- Surfaces: 0853 0854 surf R00 hexyc 0.0 0.0 9.8650 % Shroud tube inner radius 0855 surf R01 hexyc 0.0 0.0 10.3150 % Shroud tube outer radius 0856 surf R02 hexyc 0.0 0.0 <HALFDGP> % Outer boundary 0857 0858 surf R03 pz -171 0859 surf R04 pz 131 0860 0861 % --- Cells: 0862 0863 cell R901 50 outside R04 0864 0865 cell R001 50 rrf -R00 R03 -R04 0866 cell R002 50 em10 R00 -R01 R03 -R04 0867 cell R003 50 naf R01 -R02 R03 -R04 0868 cell R902 50 naf R02 R03 -R04 0869 0870 cell R903 50 outside -R03 0871 0872 % ----------------------------------------------------------- 0873 0874 % --- Universe for Empty Assembly --------------------------- 0875 0876 % ----------------------------------------------------------- 0877 0878 % --- Surfaces: 0879 0880 surf F00 hexyc 0.0 0.0 <HALFDGP> % Outer boundary 0881 0882 surf F01 pz -171 0883 surf F02 pz 131 0884 0885 % --- Cells: 0886 0887 cell F901 7 outside F02 0888 0889 cell F001 7 naf -F00 F01 -F02 0890 cell F902 7 naf F00 F01 -F02 0891 0892 cell F903 7 outside -F01 0893 0894 0895 % ----------------------------------------------------------- 0896 0897 % --- Universe for ESFR Core -------------------------------- 0898 0899 % ----------------------------------------------------------- 0900 0901 % --- Core lattice 0902 0903 lat 660 3 0.0 0.0 35 35 <DGP> %21.08 0904 0905 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 0906 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 0907 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 0908 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 0909 7 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 50 50 50 2000 2000 2000 2000 50 50 50 50 50 50 50 50 7 0910 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 50 50 50 50 50 7 0911 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 50 50 50 50 7 0912 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 2000 2000 2000 2000 2000 2000 2000 800 2000 2000 2000 2000 2000 2000 2000 50 50 50 50 7 0913 7 7 7 7 7 7 7 7 7 7 50 50 50 50 2000 2000 2000 2000 2000 800 1000 1000 1000 1000 800 2000 2000 2000 2000 2000 50 50 50 50 7 0914 7 7 7 7 7 7 7 7 7 50 50 50 2000 2000 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 2000 2000 2000 50 50 50 7 0915 7 7 7 7 7 7 7 7 50 50 50 2000 2000 2000 2000 800 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 800 2000 2000 2000 2000 50 50 50 7 0916 7 7 7 7 7 7 7 50 50 50 2000 2000 2000 2000 1000 1000 1000 1000 700 1000 1000 1000 700 1000 1000 1000 1000 2000 2000 2000 2000 50 50 50 7

63

0917 7 7 7 7 7 7 50 50 50 2000 2000 2000 800 1000 1000 1000 700 1000 1000 1000 1000 1000 1000 700 1000 1000 1000 800 2000 2000 2000 50 50 50 7 0918 7 7 7 7 7 50 50 50 50 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 2000 50 50 50 50 7 0919 7 7 7 7 50 50 50 50 2000 2000 2000 1000 1000 1000 1000 1000 1000 600 1000 1000 600 1000 1000 1000 1000 1000 1000 2000 2000 2000 50 50 50 50 7 0920 7 7 7 50 50 50 50 2000 2000 2000 800 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 800 2000 2000 2000 50 50 50 50 7 0921 7 7 50 50 50 50 2000 2000 2000 2000 1000 1000 700 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 700 1000 1000 2000 2000 2000 2000 50 50 50 50 7 0922 7 50 50 50 50 50 2000 2000 2000 1000 1000 1000 1000 1000 600 1000 1000 50 1000 1000 600 1000 1000 1000 1000 1000 2000 2000 2000 50 50 50 50 50 7 0923 7 50 50 50 50 2000 2000 2000 2000 1000 1000 700 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 700 1000 1000 2000 2000 2000 2000 50 50 50 50 7 7 0924 7 50 50 50 50 2000 2000 2000 800 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 800 2000 2000 2000 50 50 50 50 7 7 7 0925 7 50 50 50 50 2000 2000 2000 1000 1000 1000 1000 1000 1000 600 1000 1000 600 1000 1000 1000 1000 1000 1000 2000 2000 2000 50 50 50 50 7 7 7 7 0926 7 50 50 50 50 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 2000 50 50 50 50 7 7 7 7 7 0927 7 50 50 50 2000 2000 2000 800 1000 1000 1000 700 1000 1000 1000 1000 1000 1000 700 1000 1000 1000 800 2000 2000 2000 50 50 50 7 7 7 7 7 7 0928 7 50 50 50 2000 2000 2000 2000 1000 1000 1000 1000 700 1000 1000 1000 700 1000 1000 1000 1000 2000 2000 2000 2000 50 50 50 7 7 7 7 7 7 7 0929 7 50 50 50 2000 2000 2000 2000 800 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 800 2000 2000 2000 2000 50 50 50 7 7 7 7 7 7 7 7 0930 7 50 50 50 2000 2000 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 2000 2000 2000 50 50 50 7 7 7 7 7 7 7 7 7 0931 7 50 50 50 50 2000 2000 2000 2000 2000 800 1000 1000 1000 1000 800 2000 2000 2000 2000 2000 50 50 50 50 7 7 7 7 7 7 7 7 7 7 0932 7 50 50 50 50 2000 2000 2000 2000 2000 2000 2000 800 2000 2000 2000 2000 2000 2000 2000 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 0933 7 50 50 50 50 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 0934 7 50 50 50 50 50 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 0935 7 50 50 50 50 50 50 50 50 2000 2000 2000 2000 50 50 50 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 7 0936 7 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 0937 7 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 0938 7 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 0939 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

0940 0941 0942 0943 % --- Surfaces: REACTOR CORE 0944 0945 surf G01 hexxc 0.0 0.0 306 % core boundary 0946 0947 surf G02 pz -171 % bottom 0948 surf G03 pz 131 % top 0949 0950 % --- Cells: 0951 0952 cell G901 0 outside G03 0953 cell G001 0 fill 660 -G01 G02 -G03 0954 cell G902 0 outside G01 G02 -G03 0955 cell G903 0 outside -G02 0956 0957 0958 %% ---Materials for ESFR--- %% 0959 0960 mat fuel1 -<9.78972*FDC> <tmp FT> 0961 0962 92235.<FTL>c -0.0018843 %U-235 0963 92238.<FTL>c -0.7518450 %U-238 0964 94238.<FTL>c -0.0046034 %Pu-238 0965 94239.<FTL>c -0.0611083 %Pu-239 0966 94240.<FTL>c -0.0382461 %Pu-240 0967 94241.<FTL>c -0.0106124 %Pu-241 0968 94242.<FTL>c -0.0133849 %Pu-242 0969 95241.<FTL>c -0.0010058 %Am-241 0970 8016.<FTL>c -0.1173097 %O-16 0971 0972 mat fuel2 -<9.80059*FDC> <tmp FT> 0973 0974 92235.<FTL>c -0.0018319 %U-235 0975 92238.<FTL>c -0.7309608 %U-238 0976 94238.<FTL>c -0.0053514 %Pu-238 0977 94239.<FTL>c -0.0710378 %Pu-239 0978 94240.<FTL>c -0.0444604 %Pu-240 0979 94241.<FTL>c -0.0123368 %Pu-241 0980 94242.<FTL>c -0.0155597 %Pu-242 0981 95241.<FTL>c -0.0011692 %Am-241 0982 8016.<FTL>c -0.1172919 %O-16 0983 0984 mat ods -7.25 0985 0986 26054.03c -4.06463E-02 %Fe-54 0987 26056.03c -6.42772E-01 %Fe-56 0988 26057.03c -1.54176E-02 %Fe-57 0989 26058.03c -1.96223E-03 %Fe-58 0990 24050.03c -9.33098E-03 %Cr-50 0991 24052.03c -1.80189E-01 %Cr-52 0992 24053.03c -2.04035E-02 %Cr-53 0993 24054.03c -5.07403E-03 %Cr-54 0994 39089.03c -5.51239E-03 %Y-89 0995 8016.03c -1.48759E-03 %O-16 0996 13027.03c -5.74999E-02 %Al-27 0997 22000.03c -6.00324E-03 %Ti-nat 0998 28000.03c -5.00206E-03 %Ni-nat 0999 25055.03c -2.99999E-03 %Mn-55 1000 27059.03c -2.99999E-03 %Co-59 1001 29000.03c -1.50031E-03 %Cu-nat 1002 6000.03c -9.99172E-04 %C-nat 1003 15031.03c -1.99999E-04 %P-31 1004 1005 mat em10 -7.76 1006 1007 26054.03c -5.16197E-02 %Fe-54 1008 26056.03c -8.16303E-01 %Fe-56 1009 26057.03c -1.95799E-02 %Fe-57 1010 26058.03c -2.49198E-03 %Fe-58 1011 24050.03c -3.68898E-03 %Cr-50 1012 24052.03c -7.12374E-02 %Cr-52 1013 24053.03c -8.06646E-03 %Cr-53 1014 24054.03c -2.00600E-03 %Cr-54 1015 28058.03c -3.41350E-03 %Ni-58 1016 28060.03c -1.30499E-03 %Ni-60 1017 28061.03c -5.65000E-05 %Ni-61 1018 28062.03c -1.79498E-04 %Ni-62 1019 28064.03c -4.54998E-05 %Ni-64 1020 42000.03c -1.00069E-02 %Mo-nat 1021 25055.03c -4.99997E-03 %Mn-55 1022 6000.03c -9.99169E-04 %C-nat 1023 22000.03c -2.00107E-04 %Ti-nat 1024 14000.03c -3.00057E-03 %Si-nat 1025 2004.03c -7.99992E-04 %He-4 1026 1027 mat f17 -7.7 1028 1029 26054.03c -0.04610 %Fe-54 1030 26056.03c -0.75598 %Fe-56 1031 26057.03c -0.01846 %Fe-57 1032 26058.03c -0.00239 %Fe-58 1033 24050.03c -0.00672 %Cr-50 1034 24052.03c -0.13496 %Cr-52 1035 24053.03c -0.01558 %Cr-53 1036 24054.03c -0.00395 %Cr-54 1037 25055.03c -0.01002 %Mn-55 1038 6000.03c -0.00018 %C-nat 1039 14000.03c -0.00512 %Si-nat

64

1040 15031.03c -0.00023 %P-31 1041 16000.03c -0.00023 %S-nat 1042 7014.03c -0.00010 %N-14 1043 1044 mat rrf -6.01559 1045 1046 26054.03c -0.04449 %Fe-54 1047 26056.03c -0.72951 %Fe-56 1048 26057.03c -0.01780 %Fe-57 1049 26058.03c -0.00231 %Fe-58 1050 24050.03c -0.00648 %Cr-50 1051 24052.03c -0.13024 %Cr-52 1052 24053.03c -0.01503 %Cr-53 1053 24054.03c -0.00381 %Cr-54 1054 25055.03c -0.00967 %Mn-55 1055 6000.03c -0.00017 %C-nat 1056 14000.03c -0.00494 %Si-nat 1057 15031.03c -0.00022 %P-31 1058 16000.03c -0.00022 %S-nat 1059 7014.03c -0.00010 %N-14 1060 11023.03c -0.03501 %Na23 1061 1062 mat b4c1 -2.418 1063 1064 5010.03c -0.14419 %B-10 1065 5011.03c -0.63843 %B-11 1066 6000.03c -0.21738 %C-nat 1067 1068 mat b4c2 -2.296 1069 1070 5010.03c -0.68702 %B-10 1071 5011.03c -0.08397 %B-11 1072 6000.03c -0.22901 %C-nat 1073 1074 mat naf -<CD> <tmp CT> 1075 1076 11023.<CTL>c -1.0 %Na-23 1077 1078 mat heg sum 1079 1080 2004.03c 1.50455E-11 %He4

65

D. SFR Parcs Input 001 !------------------------------------------------------------------------------------------------------- 002 CASEID LOF 003 !------------------------------------------------------------------------------------------------------- 004 CNTL 005 !------------------------------------------------------------------------------------------------------- 006 ! core_type pwr 007 core_power 100.0 ! % 008 ! ppm 0.0 009 ! 010 ! step size 1 cm 011 ! 012 bank_pos 3*221 013 ! 014 th_fdbk F 1 015 ! ext_th T 60.map_detailed TRAC 3 016 ! transient T 017 ! 018 ! xe_sm 0 019 ! decay_heat F 020 ! 021 ! search keff 022 ! pin_power F 023 ! 024 !------------------------------------------------------------------------------------------------------- 025 ! 026 ! 1input 2iteration 3planar 4 5 adj 027 ! edit table power pin reac 028 print_opt F T F F T 029 ! 6 fdbk 7 flux 8 planar 030 ! rho precurs flux 9 Xe 10 T/H 031 print_opt T F F F F 032 ! 11 1D c. 12 0D 13 rad. 14 rad 033 ! group data power shape flux sh 034 print_opt F F F F 035 036 !------------------------------------------------------------------------------------------------------- 037 PARAM 038 !------------------------------------------------------------------------------------------------------- 039 ! 040 ! epseig epsl2 epslinf epstf 041 conv_ss 1.0e-10 1.0e-10 1.0e-10 0.001 042 n_iters 10 200 043 ! 044 !------------------------------------------------------------------------------------------------------- 045 XSEC 046 !------------------------------------------------------------------------------------------------------- 047 ! 048 group_spec 33 15 049 ! 050 ! 051 !------------------------------------------------------------------------------------------------------- 052 ! boron T °C mod dens g.cm-3 fuel T °C 053 ref_cond 0.0 20.0 0.95 20.0 054 !------------------------------------------------------------------------------------------------------- 055 comp_num 98 !UNIVERSE 98 056 !------------------------------------------------------------------------------------------------------- 057 ! 1 2 3 4 058 base_macro 7.230610E-002 4.663070E-005 0.000000E+000 0.000000E+000 !1 059 7.878660E-002 6.125370E-004 0.000000E+000 0.000000E+000 !2 060 8.133730E-002 8.615290E-004 0.000000E+000 0.000000E+000 !3 061 ... ... ... ... 062 1.953910E-001 1.363060E-002 0.000000E+000 0.000000E+000 !32 063 3.862620E-001 2.264690E-002 0.000000E+000 0.000000E+000 !33 064 065 ! 1 2 3 ... 31 32 066 2.346520E-003 !1 067 1.705180E-002 1.577980E-002 !2 068 1.485690E-002 1.413020E-002 2.239020E-002 !3 069 ... ... ... ... 070 0.000000E+000 0.000000E+000 0.000000E+000 ... 1.405900E-003 !31 071 0.000000E+000 0.000000E+000 0.000000E+000 ... 0.000000E+000 7.471740E-004 !32 072 073 ! 1 2 3 ... 32 33 074 fiss_spec 0.000000E+000 0.000000E+000 0.000000E+000 ... 0.000000E+000 0.000000E+000 075 !------------------------------------------------------------------------------------------------------- 076 ! 1 2 3 4 077 dxs_dtf -3.606678E-003 7.565597E-005 0.000000E+000 0.000000E+000 !1 078 -2.501173E-003 2.140354E-005 0.000000E+000 0.000000E+000 !2 079 -2.395188E-003 -3.232800E-005 0.000000E+000 0.000000E+000 !3 080 ... ... ... ... 081 8.220970E-004 6.998707E-005 0.000000E+000 0.000000E+000 !32 082 4.390098E-003 2.237856E-003 0.000000E+000 0.000000E+000 !33 083 084 ! 1 2 3 ... 31 32 085 2.733280E-003 !1 086 -4.816779E-003 -4.923094E-004 !2 087 -5.213110E-003 9.139620E-004 -6.815647E-004 !3 088 ... ... ... ... 089 0.000000E+000 0.000000E+000 0.000000E+000 ... -2.059428E-006 !31 090 0.000000E+000 0.000000E+000 0.000000E+000 ... 0.000000E+000 1.271041E-005 !32 091 !------------------------------------------------------------------------------------------------------- 092 ! 1 2 3 4 093 dxs_axexp -4.109498E-003 1.210862E-006 0.000000E+000 0.000000E+000 !1 094 -2.487183E-003 2.680400E-005 0.000000E+000 0.000000E+000 !2 095 -1.856089E-004 -7.359601E-005 0.000000E+000 0.000000E+000 !3 096 ... ... ... ... 097 1.653304E-004 1.410429E-005 0.000000E+000 0.000000E+000 !32 098 9.452215E-003 6.327325E-004 0.000000E+000 0.000000E+000 !33 099 100 ! 1 2 3 ... 31 32 101 -5.495371E-004 !1 102 -8.850881E-004 -9.890560E-004 !2 103 -1.012114E-003 1.084128E-003 2.260490E-004 !3 104 ... ... ... ... 105 0.000000E+000 0.000000E+000 0.000000E+000 ... 3.804062E-008 !31 106 0.000000E+000 0.000000E+000 0.000000E+000 ... 0.000000E+000 1.492363E-008 !32 107 !------------------------------------------------------------------------------------------------------- 108 ! 1 2 3 4 109 dxs_radexp -1.498415E-002 -9.138337E-005 0.000000E+000 0.000000E+000 !1 110 2.045474E-003 4.076336E-004 0.000000E+000 0.000000E+000 !2

66

111 -3.034647E-003 -6.984495E-005 0.000000E+000 0.000000E+000 !3 112 ... ... ... ... 113 -2.559550E-003 -2.038978E-004 0.000000E+000 0.000000E+000 !32 114 4.381117E-003 1.167276E-002 0.000000E+000 0.000000E+000 !33 115 116 ! 1 2 3 ... 31 32 117 5.873019E-004 !1 118 -5.974621E-003 9.774794E-004 !2 119 -5.803179E-003 2.263231E-003 -1.155738E-003 !3 120 ... ... ... ... 121 0.000000E+000 0.000000E+000 0.000000E+000 ... 7.612819E-005 !31 122 0.000000E+000 0.000000E+000 0.000000E+000 ... 0.000000E+000 1.821187E-004 !32 123 !------------------------------------------------------------------------------------------------------- 124 ! 1 2 3 4 125 dxs_ddm -4.091450E-003 -1.282413E-004 -0.000000E+000 -0.000000E+000 !1 126 -7.616729E-003 -2.040558E-004 -0.000000E+000 -0.000000E+000 !2 127 3.349740E-002 4.989888E-004 -0.000000E+000 -0.000000E+000 !3 128 ... ... ... ... 129 9.981413E-003 -4.572491E-004 -0.000000E+000 -0.000000E+000 !32 130 1.496283E-002 2.276766E-002 -0.000000E+000 -0.000000E+000 !33 131 132 ! 1 2 3 ... 31 32 133 -2.993599E-002 !1 134 4.304517E-002 -6.042007E-003 !2 135 2.580182E-002 -5.539405E-003 5.978810E-003 !3 136 ... ... ... ... 137 -0.000000E+000 -0.000000E+000 -0.000000E+000 ... 6.896283E-004 !31 138 -0.000000E+000 -0.000000E+000 -0.000000E+000 ... -0.000000E+000 2.829814E-004 !32 139 !------------------------------------------------------------------------------------------------------- 140 comp_num 99 !UNIVERSE 99 141 ... 142 comp_num 100 !UNIVERSE 100 143 ... 144 comp_num 101 !UNIVERSE 101 145 ... 146 comp_num 104 !UNIVERSE 104 147 ... 148 149 comp_num 198 !UNIVERSE 198 150 ... 151 comp_num 199 !UNIVERSE 199 152 ... 153 comp_num 200 !UNIVERSE 200 154 ... 155 comp_num 201 !UNIVERSE 201 156 ... 157 comp_num 204 !UNIVERSE 204 158 ... 159 160 comp_num 50 !UNIVERSE 50 161 ... 162 163 comp_num 61 !UNIVERSE 61 164 ... 165 comp_num 71 !UNIVERSE 71 166 ... 167 comp_num 81 !UNIVERSE 81 168 ... 169 170 !------------------------------------------------------------------------------------------------------- 171 delcr_comp 1 61 -61 !UNIVERSE 60 61 172 ! 1 2 3 4 173 delcr_base 3.140260E-002 -2.614750E-003 0.000000E+000 0.000000E+000 !1 174 5.493210E-002 7.678600E-004 0.000000E+000 0.000000E+000 !2 175 4.926930E-002 2.771505E-003 0.000000E+000 0.000000E+000 !3 176 ... ... ... ... 177 4.720262E+000 1.035146E-001 0.000000E+000 0.000000E+000 !32 178 -8.579900E-002 -1.223190E-003 0.000000E+000 0.000000E+000 !33 179 180 ! 1 2 3 ... 31 32 181 1.378110E-002 !1 182 4.560600E-003 2.063260E-002 !2 183 7.248500E-003 7.081940E-003 1.999800E-002 !3 184 185 0.000000E+000 0.000000E+000 0.000000E+000 ... 4.628940E-003 !31 186 0.000000E+000 0.000000E+000 0.000000E+000 ... 0.000000E+000 1.043901E-002 !32 187 !------------------------------------------------------------------------------------------------------- 188 delcr_comp 2 71 -71 !UNIVERSE 70 71 189 ... 190 delcr_comp 3 81 -81 !UNIVERSE 80 81 191 ... 192 193 !------------------------------------------------------------------------------------------------------- 194 !Delayed Neutron Precursor Data 195 196 dnp_ngrp 6 197 ! 198 kin_comp 1 1 -1 199 dnp_lambda 1.330406E-02 3.049546E-02 1.193959E-01 3.186770E-01 9.563087E-01 3.014438E+00 200 dnp_beta 1.02930819E-04 9.12120624E-04 7.93283689E-04 1.79625954E-03 9.61881364E-04 3.28008930E-04 201 neut_velo 5.33541E+09 3.92799E+09 3.05912E+09 ... 202 ! 203 kin_comp 2 2 -2 204 dnp_lambda 1.330406E-02 3.049546E-02 1.193959E-01 3.186770E-01 9.563087E-01 3.014438E+00 205 dnp_beta 1.04605693E-04 9.24194232E-04 8.10332946E-04 1.84854749E-03 9.95675218E-04 3.41750216E-04 206 neut_velo 5.33541E+09 3.92799E+09 3.05912E+09 ... 207 ! 208 !------------------------------------------------------------------------------------------------------- 209 GEOMHEX 210 !------------------------------------------------------------------------------------------------------- 211 ! ESFR Oxide core 212 ! 213 geo_dim 17 30 ! nring, nz TRACE mesh 214 ! 215 rad_conf 60 !60 degree symmetry 216 217 3 1 1 4 1 1 1 1 1 2 2 2 3 3 3 3 3 218 1 1 1 1 1 5 1 1 2 2 2 2 3 3 3 3 219 1 1 1 1 1 1 1 6 2 2 2 3 3 3 3 220 4 1 1 1 1 1 1 2 2 2 3 3 3 3 221 1 1 1 1 1 1 2 2 2 3 3 3 3 222 1 5 1 1 1 6 2 2 2 3 3 3 223 1 1 1 1 2 2 2 2 3 3 3 224 1 1 6 2 2 2 2 3 3 3 225 1 2 2 2 2 2 3 3 3

67

226 2 2 2 2 3 3 3 3 227 2 2 2 3 3 3 3 228 2 2 3 3 3 3 229 3 3 3 3 3 230 3 3 3 3 231 3 3 3 232 3 3 233 3 234 235 236 ! 237 grid_hex 21.08 ! Oxide Core - pitch cm 238 ! 239 ! TRACE mesh 240 grid_z 9*10.11 3*10. 10*10. 1*11. 7*10. 241 ! 242 assy_type 1 9*98 3*99 10*100 1*101 7*104 ! 243 assy_type 2 9*198 3*199 10*200 1*201 7*204 ! 244 assy_type 3 9*50 3*50 10*50 1*50 7*50 ! RREFL = 30*REFLECTOR 245 assy_type 4 9*61 3*61 10*61 1*61 7*61 ! CSD = 13*FLLOWER + 6*CSD CR first ring 246 assy_type 5 9*71 3*71 10*71 1*71 7*71 ! DSD = 13*FLLOWER + 6*DSD CR second ring 247 assy_type 6 9*81 3*81 10*81 1*81 7*81 ! CSD = 13*FLLOWER + 6*CSD CR third ring 248 ! 249 albedo_r 33*0.0 ! radial 250 albedo_zb 33*0.0 ! bottom 251 albedo_zt 33*0.0 ! top 252 ! 253 ! CR position, cm, from bottom 254 ! 255 cr_axinfo 0.0 1.0 256 257 258 bank_conf 259 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 260 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 261 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 262 1 0 0 0 0 0 0 0 0 0 0 0 0 0 263 0 0 0 0 0 0 0 0 0 0 0 0 0 264 0 2 0 0 0 3 0 0 0 0 0 0 265 0 0 0 0 0 0 0 0 0 0 0 266 0 0 3 0 0 0 0 0 0 0 267 0 0 0 0 0 0 0 0 0 268 0 0 0 0 0 0 0 0 269 0 0 0 0 0 0 0 270 0 0 0 0 0 0 271 0 0 0 0 0 272 0 0 0 0 273 0 0 0 274 0 0 275 0 276 277 TH 278 fa_powpit 8.0 21.08 !assembly power(MW) and pitch (cm) 279 280 TRAN 281 time_step 600.0 0.20 282 rst_freq 50 283 theta 1.0 1.0 0.5 284 conv_tr 0.001 1.E-5 1.E-4 0.001 285 .

68

E. GFR Serpent Input 001 % --- GFRMU Core ------------------------- 002 % modified version of reference GFR core reported in Reference 16. 003 set title "GFRMU-Hot Full Power" 004 005 % --- Cross section library file path: 006 007 %set acelib "/afs/psi.ch/project/.../Libraries/jeff31/sss_jeff31u.xsdata" 008 %set declib "/afs/psi.ch/project/.../Libraries/endfb7/sss_endfb7.dec" 009 %set nfylib "/afs/psi.ch/project/.../Libraries/endfb7/sss_endfb7.nfy" 010 011 % --- Use of unresolved resonance data : 012 013 set ures 1 014 set seed 1329841260 015 set bc 1 016 017 % --- Group constant generation: 018 019 set gcu 0 020 98 99 100 101 102 %universes of inner fuel assembly 021 198 199 200 201 202 %universes of outer fuel assembly 022 60 61 600 %universes of CSD assembly 023 70 71 700 %universes of DSD assembly 024 50 %universe of Reflector assembly 025 026 set sym 12 027 028 set nfg 33 1.000000E-07 5.400000E-07 4.000000E-06 8.315290E-06 1.370960E-05 2.260330E-05 029 4.016900E-05 6.790400E-05 9.166090E-05 1.486250E-04 3.043250E-04 4.539990E-04 7.485180E-04 030 1.234100E-03 2.034680E-03 3.354630E-03 5.530840E-03 9.118820E-03 1.503440E-02 2.478750E-02 031 4.086770E-02 6.737950E-02 1.110900E-01 1.831560E-01 3.019740E-01 4.978710E-01 8.208500E-01 032 1.353353E+00 2.231302E+00 3.678794E+00 6.065307E+00 1.000000E+01 033 034 % --- Neutron population and criticality cycles: 035 036 set pop 150000 500 500 037 set power 2.40E+09 % 2400MW 038 039 % --- Empty lattice position: 040 041 pin 3 042 043 hec 044 045 % --- Fuel pin :1 046 047 pin 1 048 049 fuel1 0.34000 050 heg 0.35000 051 wre 0.35400 052 re 0.35600 053 sic 0.45900 054 hec 055 056 % ---Fuel pin :2 057 058 pin 2 059 060 fuel2 0.34000 061 heg 0.35000 062 wre 0.35400 063 re 0.35600 064 sic 0.45900 065 hec 066 067 % --- Empty pin:11 068 069 pin 11 070 071 heg 0.35000 072 wre 0.35400 073 re 0.35600 074 sic 0.45900 075 hec 076 077 % --- Lattice 110 filled with inner fuel pins 078 079 lat 110 2 0.0 0.0 19 19 1.159 080 081 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 082 3 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 3 083 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 3 084 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 3 085 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 3 086 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 087 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 088 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 089 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 090 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 091 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 092 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 093 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 094 3 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 095 3 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 096 3 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 097 3 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 098 3 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 099 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 100 101 102 % --- Lattice 210 filled with outer fuel pins 103 104 lat 210 2 0.0 0.0 19 19 1.159 105 106 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 107 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 3 108 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 3

69

109 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 3 110 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 3 111 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 3 112 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 113 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 114 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 115 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 116 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 117 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 118 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 119 3 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 120 3 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 121 3 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 122 3 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 123 3 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 124 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 125 126 % --- Lattice 310 filled with fission gas plenum 127 128 lat 310 2 0.0 0.0 19 19 1.159 129 130 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 131 3 3 3 3 3 3 3 3 3 11 11 11 11 11 11 11 11 11 3 132 3 3 3 3 3 3 3 3 11 11 11 11 11 11 11 11 11 11 3 133 3 3 3 3 3 3 3 11 11 11 11 11 11 11 11 11 11 11 3 134 3 3 3 3 3 3 11 11 11 11 11 11 11 11 11 11 11 11 3 135 3 3 3 3 3 11 11 11 11 11 11 11 11 11 11 11 11 11 3 136 3 3 3 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 137 3 3 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 138 3 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 139 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 140 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 3 141 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 3 3 142 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 3 3 3 143 3 11 11 11 11 11 11 11 11 11 11 11 11 11 3 3 3 3 3 144 3 11 11 11 11 11 11 11 11 11 11 11 11 3 3 3 3 3 3 145 3 11 11 11 11 11 11 11 11 11 11 11 3 3 3 3 3 3 3 146 3 11 11 11 11 11 11 11 11 11 11 3 3 3 3 3 3 3 3 147 3 11 11 11 11 11 11 11 11 11 3 3 3 3 3 3 3 3 3 148 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 149 150 % ----------------------------------------------------------- 151 152 % --- Universes for fuel1 ----------------------------------- 153 154 % ----------------------------------------------------------- 155 156 % --- --- Universe 100 --- --- 157 158 surf 100A00 hexyc 0.0 0.0 8.54600 159 surf 100A01 hexyc 0.0 0.0 8.78300 160 surf 100A02 hexyc 0.0 0.0 8.91450 161 surf 100A03 pz -82.50000 162 surf 100A04 pz 82.50000 163 164 cell 100A901 100 outside 100A04 165 166 cell 100A002 100 fill 110 -100A00 100A03 -100A04 167 cell 100A003 100 sic 100A00 -100A01 100A03 -100A04 168 cell 100A004 100 hec 100A01 -100A02 100A03 -100A04 169 cell 100A905 100 outside 100A02 100A03 -100A04 170 171 cell 100A906 100 outside -100A03 172 173 % --- --- Universe 99 --- --- 174 175 surf 99A00 hexyc 0.0 0.0 8.54600 176 surf 99A01 hexyc 0.0 0.0 8.78300 177 surf 99A02 hexyc 0.0 0.0 8.91450 178 surf 99A03 pz -132.50000 179 surf 99A04 pz -82.50000 180 181 cell 99A901 99 outside 99A04 182 183 cell 99A002 99 fill 310 -99A00 99A03 -99A04 184 cell 99A003 99 sic 99A00 -99A01 99A03 -99A04 185 cell 99A004 99 hec 99A01 -99A02 99A03 -99A04 186 cell 99A905 99 outside 99A02 99A03 -99A04 187 188 cell 99A906 99 outside -99A03 189 190 % --- --- Universe 98 --- --- 191 192 surf 98A00 hexyc 0.0 0.0 8.91450 193 surf 98A01 pz -232.50000 194 surf 98A02 pz -132.50000 195 196 cell 98A901 98 outside 98A02 197 cell 98A002 98 lur -98A00 98A01 -98A02 198 cell 98A003 98 outside 98A00 98A01 -98A02 199 cell 98A904 98 outside -98A01 200 201 % --- --- Universe 101 --- --- 202 203 surf 101A00 hexyc 0.0 0.0 8.54600 204 surf 101A01 hexyc 0.0 0.0 8.78300 205 surf 101A02 hexyc 0.0 0.0 8.91450 206 surf 101A03 pz 82.50000 207 surf 101A04 pz 167.50000 208 209 cell 101A901 101 outside 101A04 210 211 cell 101A002 101 fill 310 -101A00 101A03 -101A04 212 cell 101A003 101 sic 101A00 -101A01 101A03 -101A04 213 cell 101A004 101 hec 101A01 -101A02 101A03 -101A04 214 cell 101A905 101 outside 101A02 101A03 -101A04 215 216 cell 101A906 101 outside -101A03 217 218 % --- --- Universe 102 --- --- 219 220 surf 102A00 hexyc 0.0 0.0 8.91450 221 surf 102A01 pz 167.50000 222 surf 102A02 pz 267.50000 223

70

224 cell 102A901 102 outside 102A02 225 cell 102A002 102 lur -102A00 102A01 -102A02 226 cell 102A003 102 outside 102A00 102A01 -102A02 227 cell 102A904 102 outside -102A01 228 229 % --- --- Universe 1000 --- --- 230 231 surf A00 hexyc 0.0 0.0 8.91450 232 surf A01 pz -232.50000 233 surf A02 pz -132.50000 234 surf A03 pz -82.50000 235 surf A04 pz 82.50000 236 surf A05 pz 167.50000 237 surf A06 pz 267.50000 238 239 cell A901 1000 outside A06 240 cell A002 1000 fill 102 -A00 A05 -A06 241 cell A003 1000 outside A00 A05 -A06 242 cell A004 1000 fill 101 -A00 A04 -A05 243 cell A005 1000 outside A00 A04 -A05 244 cell A006 1000 fill 100 -A00 A03 -A04 245 cell A007 1000 outside A00 A03 -A04 246 cell A008 1000 fill 99 -A00 A02 -A03 247 cell A009 1000 outside A00 A02 -A03 248 cell A010 1000 fill 98 -A00 A01 -A02 249 cell A011 1000 outside A00 A01 -A02 250 cell A912 1000 outside -A01 251 252 253 % ----------------------------------------------------------- 254 255 % --- Universes for fuel2 ----------------------------------- 256 257 % ----------------------------------------------------------- 258 259 260 % --- --- Universe 200 --- --- 261 262 surf 200B00 hexyc 0.0 0.0 8.54600 263 surf 200B01 hexyc 0.0 0.0 8.78300 264 surf 200B02 hexyc 0.0 0.0 8.91450 265 surf 200B03 pz -82.50000 266 surf 200B04 pz 82.50000 267 268 cell 200B901 200 outside 200B04 269 270 cell 200B002 200 fill 210 -200B00 200B03 -200B04 271 cell 200B003 200 sic 200B00 -200B01 200B03 -200B04 272 cell 200B004 200 hec 200B01 -200B02 200B03 -200B04 273 cell 200B905 200 outside 200B02 200B03 -200B04 274 275 cell 200B906 200 outside -200B03 276 277 % --- --- Universe 199 --- --- 278 279 surf 199B00 hexyc 0.0 0.0 8.54600 280 surf 199B01 hexyc 0.0 0.0 8.78300 281 surf 199B02 hexyc 0.0 0.0 8.91450 282 surf 199B03 pz -132.50000 283 surf 199B04 pz -82.50000 284 285 cell 199B901 199 outside 199B04 286 287 cell 199B002 199 fill 310 -199B00 199B03 -199B04 288 cell 199B003 199 sic 199B00 -199B01 199B03 -199B04 289 cell 199B004 199 hec 199B01 -199B02 199B03 -199B04 290 cell 199B905 199 outside 199B02 199B03 -199B04 291 292 cell 199B906 199 outside -199B03 293 294 % --- --- Universe 198 --- --- 295 296 surf 198B00 hexyc 0.0 0.0 8.91450 297 surf 198B01 pz -232.50000 298 surf 198B02 pz -132.50000 299 300 cell 198B901 198 outside 198B02 301 cell 198B002 198 lur -198B00 198B01 -198B02 302 cell 198B003 198 outside 198B00 198B01 -198B02 303 cell 198B904 198 outside -198B01 304 305 % --- --- Universe 201 --- --- 306 307 surf 201B00 hexyc 0.0 0.0 8.54600 308 surf 201B01 hexyc 0.0 0.0 8.78300 309 surf 201B02 hexyc 0.0 0.0 8.91450 310 surf 201B03 pz 82.50000 311 surf 201B04 pz 167.50000 312 313 cell 201B901 201 outside 201B04 314 315 cell 201B002 201 fill 310 -201B00 201B03 -201B04 316 cell 201B003 201 sic 201B00 -201B01 201B03 -201B04 317 cell 201B004 201 hec 201B01 -201B02 201B03 -201B04 318 cell 201B905 201 outside 201B02 201B03 -201B04 319 320 cell 201B906 201 outside -201B03 321 322 % --- --- Universe 202 --- --- 323 324 surf 202B00 hexyc 0.0 0.0 8.91450 325 surf 202B01 pz 167.50000 326 surf 202B02 pz 267.50000 327 328 cell 202B901 202 outside 202B02 329 cell 202B002 202 lur -202B00 202B01 -202B02 330 cell 202B003 202 outside 202B00 202B01 -202B02 331 cell 202B904 202 outside -202B01 332 333 % --- --- Universe 2000 --- --- 334 335 surf B00 hexyc 0.0 0.0 8.91450 336 surf B01 pz -232.50000 337 surf B02 pz -132.50000 338 surf B03 pz -82.50000

71

339 surf B04 pz 82.50000 340 surf B05 pz 167.50000 341 surf B06 pz 267.50000 342 343 cell B901 2000 outside B06 344 cell B002 2000 fill 202 -B00 B05 -B06 345 cell B003 2000 outside B00 B05 -B06 346 cell B004 2000 fill 201 -B00 B04 -B05 347 cell B005 2000 outside B00 B04 -B05 348 cell B006 2000 fill 200 -B00 B03 -B04 349 cell B007 2000 outside B00 B03 -B04 350 cell B008 2000 fill 199 -B00 B02 -B03 351 cell B009 2000 outside B00 B02 -B03 352 cell B010 2000 fill 198 -B00 B01 -B02 353 cell B011 2000 outside B00 B01 -B02 354 cell B912 2000 outside -B01 355 356 357 358 % ----------------------------------------------------------- 359 360 % --- Universes for CSD and DSD ---------------------------- 361 362 % ----------------------------------------------------------- 363 364 % --- CSD pins 365 366 pin 30 367 368 b4c 0.750 %0.900 % b4c Nat 369 heg 0.832 %1.000 % heg 370 aim1 0.915 %1.100 % cladding 371 hec %fills the rest of the universe 372 373 % ---CSD Pin Lattice (type = 2, pin pitch = 2.03831 cm): 374 375 lat 330 2 0.0 0.0 11 11 2.03831 376 377 3 3 3 3 3 3 3 3 3 3 3 378 3 3 3 3 3 30 30 30 30 30 3 379 3 3 3 3 30 30 30 30 30 30 3 380 3 3 3 30 30 30 30 30 30 30 3 381 3 3 30 30 30 3 3 30 30 30 3 382 3 30 30 30 3 3 3 30 30 30 3 383 3 30 30 30 3 3 30 30 30 3 3 384 3 30 30 30 30 30 30 30 3 3 3 385 3 30 30 30 30 30 30 3 3 3 3 386 3 30 30 30 30 30 3 3 3 3 3 387 3 3 3 3 3 3 3 3 3 3 3 388 389 390 % --- --- Universe 60 --- --- 391 392 surf 60C00 hexyc 0.0 0.0 2.32000 393 surf 60C01 hexyc 0.0 0.0 2.50000 394 surf 60C02 hexyc 0.0 0.0 8.07000 395 surf 60C03 hexyc 0.0 0.0 8.82000 396 surf 60C04 hexyc 0.0 0.0 8.91450 397 surf 60C05 pz 82.50000 398 surf 60C06 pz 267.50000 399 400 cell 60C901 60 outside 60C06 401 402 cell 60C002 60 hec -60C00 60C05 -60C06 403 cell 60C003 60 aim1 60C00 -60C01 60C05 -60C06 404 cell 60C004 60 fill 330 60C01 -60C02 60C05 -60C06 405 cell 60C005 60 sic 60C02 -60C03 60C05 -60C06 406 cell 60C006 60 hec 60C03 -60C04 60C05 -60C06 407 cell 60C907 60 outside 60C04 60C05 -60C06 408 409 cell 60C908 60 outside -60C05 410 411 % --- --- Universe 61 --- --- 412 413 surf 61C00 cyl 0.0 0.0 2.61400 414 surf 61C01 hexyc 0.0 0.0 8.07000 415 surf 61C02 hexyc 0.0 0.0 8.82000 416 surf 61C03 hexyc 0.0 0.0 8.91450 417 surf 61C04 pz -232.50000 418 surf 61C05 pz 82.50000 419 420 cell 61C901 61 outside 61C05 421 422 cell 61C002 61 hec -61C00 61C04 -61C05 423 cell 61C003 61 hec 61C00 -61C01 61C04 -61C05 424 cell 61C004 61 sic 61C01 -61C02 61C04 -61C05 425 cell 61C005 61 hec 61C02 -61C03 61C04 -61C05 426 cell 61C906 61 outside 61C03 61C04 -61C05 427 428 cell 61C907 61 outside -61C04 429 430 % --- --- Universe 600 --- --- 431 432 surf C00 hexyc 0.0 0.0 8.91450 433 surf C01 pz -232.50000 434 surf C02 pz 82.50000 435 surf C03 pz 267.50000 436 437 cell C901 600 outside C03 438 cell C002 600 fill 60 -C00 C02 -C03 439 cell C003 600 outside C00 C02 -C03 440 cell C004 600 fill 61 -C00 C01 -C02 441 cell C005 600 outside C00 C01 -C02 442 cell C906 600 outside -C01 443 444 445 % --- --- Universe70 --- --- 446 447 surf 70D00 hexyc 0.0 0.0 2.32000 448 surf 70D01 hexyc 0.0 0.0 2.50000 449 surf 70D02 hexyc 0.0 0.0 8.0700 450 surf 70D03 hexyc 0.0 0.0 8.82000 451 surf 70D04 hexyc 0.0 0.0 8.91450 452 surf 70D05 pz 82.50000 453 surf 70D06 pz 267.50000

72

454 455 cell 70D901 70 outside 70D06 456 457 cell 70D002 70 hec -70D00 70D05 -70D06 458 cell 70D003 70 aim1 70D00 -70D01 70D05 -70D06 459 cell 70D004 70 fill 330 70D01 -70D02 70D05 -70D06 460 cell 70D005 70 sic 70D02 -70D03 70D05 -70D06 461 cell 70D006 70 hec 70D03 -70D04 70D05 -70D06 462 cell 70D907 70 outside 70D04 70D05 -70D06 463 464 cell 70D908 70 outside -70D05 465 466 % --- --- Universe 71 --- --- 467 468 surf 71D00 cyl 0.0 0.0 2.61400 469 surf 71D01 hexyc 0.0 0.0 8.0700 470 surf 71D02 hexyc 0.0 0.0 8.82000 471 surf 71D03 hexyc 0.0 0.0 8.91450 472 surf 71D04 pz -232.50000 473 surf 71D05 pz 82.50000 474 475 cell 71D901 71 outside 71D05 476 477 cell 71D002 71 hec -71D00 71D04 -71D05 478 cell 71D003 71 hec 71D00 -71D01 71D04 -71D05 479 cell 71D004 71 sic 71D01 -71D02 71D04 -71D05 480 cell 71D005 71 hec 71D02 -71D03 71D04 -71D05 481 cell 71D906 71 outside 71D03 71D04 -71D05 482 483 cell 71D907 71 outside -71D04 484 485 % --- --- Universe700 --- --- 486 487 surf D00 hexyc 0.0 0.0 8.91450 488 surf D01 pz -232.50000 489 surf D02 pz 82.50000 490 surf D03 pz 267.50000 491 492 cell D901 700 outside D03 493 cell D002 700 fill 70 -D00 D02 -D03 494 cell D003 700 outside D00 D02 -D03 495 cell D004 700 fill 71 -D00 D01 -D02 496 cell D005 700 outside D00 D01 -D02 497 cell D906 700 outside -D01 498 499 % ----------------------------------------------------------- 500 501 % --- Universe for Radial Reflector ------------------------- 502 503 % ----------------------------------------------------------- 504 505 506 surf R00 hexyc 0.0 0.0 8.91450 507 surf R01 pz -232.50000 508 surf R02 pz 267.50000 509 510 cell R901 50 outside R02 511 cell R002 50 rra -R00 R01 -R02 512 cell R003 50 outside R00 R01 -R02 513 cell R904 50 outside -R01 514 515 516 % ----------------------------------------------------------- 517 518 % --- Universe 7 for Empty Assembly ------------------------- 519 520 % ----------------------------------------------------------- 521 522 523 surf E00 hexyc 0.0 0.0 8.91450 524 surf E01 pz -232.50000 525 surf E02 pz 267.50000 526 527 cell E901 7 outside E02 528 cell E002 7 hec -E00 E01 -E02 529 cell E003 7 outside E00 E01 -E02 530 cell E904 7 outside -E01 531 532 % ----------------------------------------------------------- 533 534 % --- Universe for GFR Core --------------------------------- 535 536 % ----------------------------------------------------------- 537 538 % --- Core lattice 539 540 lat 610 3 0.0 0.0 39 39 17.829 541 542 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 543 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 544 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 545 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 546 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 547 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 50 50 50 50 2000 2000 2000 2000 2000 50 50 50 50 50 50 50 50 50 7 548 7 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 50 50 50 2000 2000 2000 2000 2000 2000 2000 2000 50 50 50 50 50 50 50 50 7 549 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 50 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 50 50 50 50 50 50 7 550 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 50 2000 2000 2000 2000 2000 600 2000 2000 2000 2000 2000 2000 2000 2000 50 50 50 50 50 50 7 551 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 2000 2000 2000 2000 2000 2000 2000 1000 1000 1000 2000 2000 600 2000 2000 2000 2000 50 50 50 50 50 7 552 7 7 7 7 7 7 7 7 7 7 50 50 50 50 2000 2000 2000 2000 600 2000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 2000 2000 2000 2000 50 50 50 50 7 553 7 7 7 7 7 7 7 7 7 50 50 50 50 2000 2000 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 2000 2000 2000 50 50 50 50 7 554 7 7 7 7 7 7 7 7 50 50 50 50 2000 2000 2000 2000 2000 1000 1000 700 1000 1000 1000 700 1000 1000 700 1000 1000 2000 600 2000 2000 2000 50 50 50 50 7 555 7 7 7 7 7 7 7 50 50 50 50 2000 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 2000 2000 50 50 50 50 7 556 7 7 7 7 7 7 50 50 50 50 2000 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 2000 2000 50 50 50 50 7 557 7 7 7 7 7 50 50 50 50 50 2000 2000 600 1000 1000 1000 700 1000 1000 1000 1000 1000 600 1000 1000 1000 1000 1000 1000 1000 2000 2000 2000 50 50 50 50 50 7 558 7 7 7 7 50 50 50 50 50 2000 2000 2000 2000 1000 1000 1000 1000 1000 600 1000 1000 1000 1000 1000 1000 1000 700 1000 1000 2000 2000 2000 2000 50 50 50 50 50 7 559 7 7 7 50 50 50 50 50 50 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 2000 50 50 50 50 50 50 7 560 7 7 50 50 50 50 50 50 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 600 1000 1000 1000 1000 1000 600 2000 2000 50 50 50 50 50 50 7 561 7 50 50 50 50 50 50 2000 2000 2000 2000 1000 700 1000 1000 1000 1000 1000 1000 600 1000 1000 1000 1000 1000 1000 700 1000 2000 2000 2000 2000 50 50 50 50 50 50 7 562 7 50 50 50 50 50 50 2000 2000 600 1000 1000 1000 1000 1000 600 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 2000 50 50 50 50 50 50 7 7 563 7 50 50 50 50 50 50 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 2000 50 50 50 50 50 50 7 7 7 564 7 50 50 50 50 50 2000 2000 2000 2000 1000 1000 700 1000 1000 1000 1000 1000 1000 1000 600 1000 1000 1000 1000 1000 2000 2000 2000 2000 50 50 50 50 50 7 7 7 7 565 7 50 50 50 50 50 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000 600 1000 1000 1000 1000 1000 700 1000 1000 1000 600 2000 2000 50 50 50 50 50 7 7 7 7 7 566 7 50 50 50 50 2000 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 2000 2000 50 50 50 50 7 7 7 7 7 7 567 7 50 50 50 50 2000 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 2000 2000 50 50 50 50 7 7 7 7 7 7 7 568 7 50 50 50 50 2000 2000 2000 600 2000 1000 1000 700 1000 1000 700 1000 1000 1000 700 1000 1000 2000 2000 2000 2000 2000 50 50 50 50 7 7 7 7 7 7 7 7 569 7 50 50 50 50 2000 2000 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 2000 2000 2000 50 50 50 50 7 7 7 7 7 7 7 7 7 570 7 50 50 50 50 2000 2000 2000 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 2000 600 2000 2000 2000 2000 50 50 50 50 7 7 7 7 7 7 7 7 7 7 571 7 50 50 50 50 50 2000 2000 2000 2000 600 2000 2000 1000 1000 1000 2000 2000 2000 2000 2000 2000 2000 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 572 7 50 50 50 50 50 50 2000 2000 2000 2000 2000 2000 2000 2000 600 2000 2000 2000 2000 2000 50 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 573 7 50 50 50 50 50 50 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 50 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 574 7 50 50 50 50 50 50 50 50 2000 2000 2000 2000 2000 2000 2000 2000 50 50 50 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 7 575 7 50 50 50 50 50 50 50 50 50 2000 2000 2000 2000 2000 50 50 50 50 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 576 7 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 577 7 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 578 7 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 579 7 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 580 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

581

582 583 584 % --- Surfaces: REACTOR CORE

73

585 586 surf F01 hexxc 0.0 0.0 291.7 % core boundary 587 588 surf F02 pz -232.5 % bottom 589 surf F03 pz 267.5 % top 590 591 % --- Cells: 592 593 cell F901 0 outside F03 % outside world 594 cell F001 0 fill 610 -F01 F02 -F03 % fill with sa lattice 595 cell F902 0 outside F01 F02 -F03 % outside world 596 cell F903 0 outside -F02 % outside world 597 598 % ----------------------------------------------------------- 599 600 %% ---Materials for GFR--- %% 601 602 % --- Inner core (U,Pu)C fuel: fuel1 603 604 mat fuel1 -10.89718 605 606 92235.12c -0.005807 % U-235.12c 607 92238.12c -0.811021 % U-238.12c 608 94238.12c -0.003651 % Pu-238.12c 609 94239.12c -0.075724 % Pu-239.12c 610 94240.12c -0.035022 % Pu-240.12c 611 94241.12c -0.010006 % Pu-241.12c 612 94242.12c -0.009871 % Pu-242.12c 613 95241.12c -0.000947 % Am-241.12c 614 6000.12c -0.047950 % C-nat.12c 615 616 % --- Outer core(U,Pu)C fuel: fuel2 617 618 mat fuel2 -10.89638 619 620 92235.12c -0.005567 % U-235.12c 621 92238.12c -0.777506 % U-238.12c 622 94238.12c -0.004563 % Pu-238.12c 623 94239.12c -0.094633 % Pu-239.12c 624 94240.12c -0.043768 % Pu-240.12c 625 94241.12c -0.012505 % Pu-241.12c 626 94242.12c -0.012336 % Pu-242.12c 627 95241.12c -0.001183 % Am-241.12c 628 6000.12c -0.047939 % C-nat.12c 629 630 % --- Tungsten-Rhenium liner: wre 631 632 mat wre -19.48 633 634 74182.09c -0.223798 % W-182.09c 635 74183.09c -0.121682 % W-183.09c 636 74184.09c -0.263341 % W-184.09c 637 74186.09c -0.249642 % W-186.09c 638 75185.09c -0.052578 % Re-185.09c 639 75187.09c -0.088958 % Re-187.09c 640 641 % --- Rhenium liner:re 642 643 mat re -21.02 644 645 75185.09c -0.371482 % Re-185.09c 646 75187.09c -0.628518 % Re-187.09c 647 648 % --- SiC clad: sic 649 650 mat sic -2.6 651 652 14028.09c -0.643527 % Si-28.09c 653 14029.09c -0.033821 % Si-29.09c 654 14030.09c -0.023099 % Si-30.09c 655 6000.09c -0.299553 % C-nat.09c 656 657 % --- Lower and Upper Axial Reflector: lur 658 659 mat lur -3.52948452 660 661 40090.09c -0.420534 % Zr-90.09c 662 40091.09c -0.092729 % Zr-91.09c 663 40092.09c -0.143297 % Zr-92.09c 664 40094.09c -0.148381 % Zr-94.09c 665 40096.09c -0.024414 % Zr-96.09c 666 14028.09c -0.156392 % Si-28.09c 667 14029.09c -0.008219 % Si-29.09c 668 14030.09c -0.005614 % Si-30.09c 669 2004.09c -0.000421 % He-04.09c 670 671 % --- Radial Reflector Assembly 672 673 mat rra -4.70474226 674 675 40090.09c -0.420644 % Zr-90.09c 676 40091.09c -0.092754 % Zr-91.09c 677 40092.09c -0.143334 % Zr-92.09c 678 40094.09c -0.148420 % Zr-94.09c 679 40096.09c -0.024421 % Zr-96.09c 680 14028.09c -0.156433 % Si-28.09c 681 14029.09c -0.008221 % Si-29.09c 682 14030.09c -0.005615 % Si-30.09c 683 2004.09c -0.000158 % He-04.09c 684 685 % ---AIM1 686 687 mat aim1 -7.95 688 689 26054.09c -0.036833 % Fe-54.09c 690 26056.09c -0.604011 % Fe-56.09c 691 26057.09c -0.014747 % Fe-57.09c 692 26058.09c -0.001910 % Fe-58.09c 693 24050.09c -0.006045 % Cr-50.09c 694 24052.09c -0.121395 % Cr-52.09c 695 24053.09c -0.014010 % Cr-53.09c 696 24054.09c -0.003550 % Cr-54.09c 697 28058.09c -0.104462 % Ni-58.09c 698 28060.09c -0.041312 % Ni-60.09c 699 28061.09c -0.001818 % Ni-61.09c

74

700 28062.09c -0.005872 % Ni-62.09c 701 28064.09c -0.001536 % Ni-64.09c 702 42092.09c -0.001204 % Mo-92.09c 703 42094.09c -0.000751 % Mo-94.09c 704 42095.09c -0.001292 % Mo-95.09c 705 42096.09c -0.001354 % Mo-96.09c 706 42097.09c -0.000776 % Mo-97.09c 707 42098.09c -0.001960 % Mo-98.09c 708 42100.09c -0.007663 % Mo-100.09c 709 22000.09c -0.004000 % Ti-Nat.09c 710 %22046.09c -0.000317 % Ti-46.09c 711 %22047.09c -0.000292 % Ti-47.09c 712 %22048.09c -0.002954 % Ti-48.09c 713 %22049.09c -0.000221 % Ti-49.09c 714 %22050.09c -0.000216 % Ti-50.09c 715 14028.09c -0.007809 % Si-28.09c 716 14029.09c -0.000410 % Si-29.09c 717 14030.09c -0.000280 % Si-30.09c 718 25055.09c -0.015000 % Mn-55.09c 719 720 % ---DSD Enriched B4C: 721 722 mat b4c -2.296 723 724 5010.09c -0.68702 % B-10 725 5011.09c -0.08397 % B-11 726 6000.09c -0.22901 % C-nat 727 728 % --- Helium gap: heg 729 730 mat heg -0.000442 731 732 2004.09c -1.0 % He-04.09c 733 734 % --- Helium coolant: hec 735 736 mat hec -0.0037113 737 738 2004.09c -1.0 % He-04.09c

75

F. LFR Serpent Input 0001 % --- LFRMU Core ------------------------- 0002 % modified version of reference ELSY core reported in Reference 17. 0003 set title "LFRMU-Hot Full Power" 0004 0005 % --- Cross section library file path: 0006 0007 %set acelib "/afs/psi.ch/project/.../Libraries/jeff31/sss_jeff31u.xsdata" 0008 %set declib "/afs/psi.ch/project/.../Libraries/endfb7/sss_endfb7.dec" 0009 %set nfylib "/afs/psi.ch/project/.../Libraries/endfb7/sss_endfb7.nfy" 0010 0011 % --- Use of unresolved resonance data : 0012 0013 set ures 1 0014 set seed 1329841260 0015 set bc 1 0016 0017 % --- Group constant generation: 0018 0019 set gcu 0 0020 96 97 98 99 100 101 102 103 104 %universes of inner fuel assembly 0021 196 197 198 199 200 201 202 203 204 %universes of central FA 0022 296 297 298 299 300 301 302 303 304 %universes of outer fuel assembly 0023 59 60 61 600 %universes of CSD assembly 0024 50 %universe of Reflector assembly 0025 0026 set sym 12 0027 0028 set nfg 33 1.000000E-07 5.400000E-07 4.000000E-06 8.315290E-06 1.370960E-05 2.260330E-05 0029 4.016900E-05 6.790400E-05 9.166090E-05 1.486250E-04 3.043250E-04 4.539990E-04 7.485180E-04 0030 1.234100E-03 2.034680E-03 3.354630E-03 5.530840E-03 9.118820E-03 1.503440E-02 2.478750E-02 0031 4.086770E-02 6.737950E-02 1.110900E-01 1.831560E-01 3.019740E-01 4.978710E-01 8.208500E-01 0032 1.353353E+00 2.231302E+00 3.678794E+00 6.065307E+00 1.000000E+01 0033 0034 % --- Neutron population and criticality cycles: 0035 0036 set pop 150000 500 500 0037 set power 1.50E+09 % 1500MW 0038 0039 % --- Empty lattice position: 0040 0041 pin 3 0042 0043 lead 0044 0045 % --- Fuel pin :1 0046 0047 pin 11 0048 0049 heg 0.0800 0050 fuel1 0.4600 0051 heg 0.4700 0052 t91 0.5400 0053 lead 0054 0055 % ---Fuel pin :2 0056 0057 pin 12 0058 0059 heg 0.0800 0060 fuel2 0.4600 0061 heg 0.4700 0062 t91 0.5400 0063 lead 0064 0065 % ---Fuel pin :3 0066 0067 pin 13 0068 0069 heg 0.0800 0070 fuel3 0.4600 0071 heg 0.4700 0072 t91 0.5400 0073 lead 0074 0075 % --- Empty pin:4 for upper & lower FGP 0076 0077 pin 14 0078 0079 heg 0.4700 0080 t91 0.5400 0081 lead 0082 0083 % --- Bottom & top plug pin:5 0084 0085 pin 15 0086 0087 t91 0.5400 0088 lead 0089 0090 0091 0092 0093 0094 %-------------------------------------------------------- 0095 0096 % --- Lattice 111: inner fuel1 pins 0097 0098 lat 111 2 0.0 0.0 17 17 1.56 0099 0100 0101 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0102 3 3 3 3 3 3 3 3 11 11 11 11 11 11 11 11 3 0103 3 3 3 3 3 3 3 11 11 11 11 11 11 11 11 11 3 0104 3 3 3 3 3 3 11 11 11 11 11 11 11 11 11 11 3 0105 3 3 3 3 3 11 11 11 11 11 11 11 11 11 11 11 3 0106 3 3 3 3 11 11 11 11 11 11 11 11 11 11 11 11 3 0107 3 3 3 11 11 11 11 11 11 11 11 11 11 11 11 11 3 0108 3 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3

76

0109 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 0110 3 11 11 11 11 11 11 11 11 11 11 11 11 11 11 3 3 0111 3 11 11 11 11 11 11 11 11 11 11 11 11 11 3 3 3 0112 3 11 11 11 11 11 11 11 11 11 11 11 11 3 3 3 3 0113 3 11 11 11 11 11 11 11 11 11 11 11 3 3 3 3 3 0114 3 11 11 11 11 11 11 11 11 11 11 3 3 3 3 3 3 0115 3 11 11 11 11 11 11 11 11 11 3 3 3 3 3 3 3 0116 3 11 11 11 11 11 11 11 11 3 3 3 3 3 3 3 3 0117 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0118 0119 % --- Lattice 112: central fuel2 pins 0120 0121 lat 112 2 0.0 0.0 17 17 1.56 0122 0123 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0124 3 3 3 3 3 3 3 3 12 12 12 12 12 12 12 12 3 0125 3 3 3 3 3 3 3 12 12 12 12 12 12 12 12 12 3 0126 3 3 3 3 3 3 12 12 12 12 12 12 12 12 12 12 3 0127 3 3 3 3 3 12 12 12 12 12 12 12 12 12 12 12 3 0128 3 3 3 3 12 12 12 12 12 12 12 12 12 12 12 12 3 0129 3 3 3 12 12 12 12 12 12 12 12 12 12 12 12 12 3 0130 3 3 12 12 12 12 12 12 12 12 12 12 12 12 12 12 3 0131 3 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 3 0132 3 12 12 12 12 12 12 12 12 12 12 12 12 12 12 3 3 0133 3 12 12 12 12 12 12 12 12 12 12 12 12 12 3 3 3 0134 3 12 12 12 12 12 12 12 12 12 12 12 12 3 3 3 3 0135 3 12 12 12 12 12 12 12 12 12 12 12 3 3 3 3 3 0136 3 12 12 12 12 12 12 12 12 12 12 3 3 3 3 3 3 0137 3 12 12 12 12 12 12 12 12 12 3 3 3 3 3 3 3 0138 3 12 12 12 12 12 12 12 12 3 3 3 3 3 3 3 3 0139 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0140 0141 % --- Lattice 113: outer fuel3 pins 0142 0143 lat 113 2 0.0 0.0 17 17 1.56 0144 0145 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0146 3 3 3 3 3 3 3 3 13 13 13 13 13 13 13 13 3 0147 3 3 3 3 3 3 3 13 13 13 13 13 13 13 13 13 3 0148 3 3 3 3 3 3 13 13 13 13 13 13 13 13 13 13 3 0149 3 3 3 3 3 13 13 13 13 13 13 13 13 13 13 13 3 0150 3 3 3 3 13 13 13 13 13 13 13 13 13 13 13 13 3 0151 3 3 3 13 13 13 13 13 13 13 13 13 13 13 13 13 3 0152 3 3 13 13 13 13 13 13 13 13 13 13 13 13 13 13 3 0153 3 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 3 0154 3 13 13 13 13 13 13 13 13 13 13 13 13 13 13 3 3 0155 3 13 13 13 13 13 13 13 13 13 13 13 13 13 3 3 3 0156 3 13 13 13 13 13 13 13 13 13 13 13 13 3 3 3 3 0157 3 13 13 13 13 13 13 13 13 13 13 13 3 3 3 3 3 0158 3 13 13 13 13 13 13 13 13 13 13 3 3 3 3 3 3 0159 3 13 13 13 13 13 13 13 13 13 3 3 3 3 3 3 3 0160 3 13 13 13 13 13 13 13 13 3 3 3 3 3 3 3 3 0161 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0162 0163 % --- Lattice 114: fission gas plenum pins 0164 0165 lat 114 2 0.0 0.0 17 17 1.56 0166 0167 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0168 3 3 3 3 3 3 3 3 14 14 14 14 14 14 14 14 3 0169 3 3 3 3 3 3 3 14 14 14 14 14 14 14 14 14 3 0170 3 3 3 3 3 3 14 14 14 14 14 14 14 14 14 14 3 0171 3 3 3 3 3 14 14 14 14 14 14 14 14 14 14 14 3 0172 3 3 3 3 14 14 14 14 14 14 14 14 14 14 14 14 3 0173 3 3 3 14 14 14 14 14 14 14 14 14 14 14 14 14 3 0174 3 3 14 14 14 14 14 14 14 14 14 14 14 14 14 14 3 0175 3 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 3 0176 3 14 14 14 14 14 14 14 14 14 14 14 14 14 14 3 3 0177 3 14 14 14 14 14 14 14 14 14 14 14 14 14 3 3 3 0178 3 14 14 14 14 14 14 14 14 14 14 14 14 3 3 3 3 0179 3 14 14 14 14 14 14 14 14 14 14 14 3 3 3 3 3 0180 3 14 14 14 14 14 14 14 14 14 14 3 3 3 3 3 3 0181 3 14 14 14 14 14 14 14 14 14 3 3 3 3 3 3 3 0182 3 14 14 14 14 14 14 14 14 3 3 3 3 3 3 3 3 0183 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0184 0185 % --- Lattice 115: top and bottom plug pins 0186 0187 lat 115 2 0.0 0.0 17 17 1.56 0188 0189 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0190 3 3 3 3 3 3 3 3 15 15 15 15 15 15 15 15 3 0191 3 3 3 3 3 3 3 15 15 15 15 15 15 15 15 15 3 0192 3 3 3 3 3 3 15 15 15 15 15 15 15 15 15 15 3 0193 3 3 3 3 3 15 15 15 15 15 15 15 15 15 15 15 3 0194 3 3 3 3 15 15 15 15 15 15 15 15 15 15 15 15 3 0195 3 3 3 15 15 15 15 15 15 15 15 15 15 15 15 15 3 0196 3 3 15 15 15 15 15 15 15 15 15 15 15 15 15 15 3 0197 3 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 3 0198 3 15 15 15 15 15 15 15 15 15 15 15 15 15 15 3 3 0199 3 15 15 15 15 15 15 15 15 15 15 15 15 15 3 3 3 0200 3 15 15 15 15 15 15 15 15 15 15 15 15 3 3 3 3 0201 3 15 15 15 15 15 15 15 15 15 15 15 3 3 3 3 3 0202 3 15 15 15 15 15 15 15 15 15 15 3 3 3 3 3 3 0203 3 15 15 15 15 15 15 15 15 15 3 3 3 3 3 3 3 0204 3 15 15 15 15 15 15 15 15 3 3 3 3 3 3 3 3 0205 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0206 0207 % ----------------------------------------------------------- 0208 0209 % --- Universes for fuel1 ----------------------------------- 0210 0211 % ----------------------------------------------------------- 0212 0213 % --- --- Universe 104 --- ---Upper Lead 0214 0215 surf 104A00 hexyc 0.0 0.0 10.15000 0216 surf 104A01 hexyc 0.0 0.0 10.55000 0217 surf 104A02 hexyc 0.0 0.0 10.80000 0218 surf 104A03 pz 130.00000 0219 surf 104A04 pz 280.00000 0220 0221 cell 104A901 104 outside 104A04 0222 0223 cell 104A002 104 lead -104A00 104A03 -104A04

77

0224 cell 104A003 104 lead 104A00 -104A01 104A03 -104A04 0225 cell 104A004 104 lead 104A01 -104A02 104A03 -104A04 0226 cell 104A905 104 outside 104A02 104A03 -104A04 0227 0228 cell 104A906 104 outside -104A03 0229 0230 % --- --- Universe 103 --- --- Upper Axial Reflector 0231 0232 surf 103A00 hexyc 0.0 0.0 10.15000 0233 surf 103A01 hexyc 0.0 0.0 10.55000 0234 surf 103A02 hexyc 0.0 0.0 10.80000 0235 surf 103A03 pz 90.00000 0236 surf 103A04 pz 130.00000 0237 0238 cell 103A901 103 outside 103A04 0239 0240 cell 103A002 103 lead -103A00 103A03 -103A04 0241 cell 103A003 103 t91 103A00 -103A01 103A03 -103A04 0242 cell 103A004 103 lead 103A01 -103A02 103A03 -103A04 0243 cell 103A905 103 outside 103A02 103A03 -103A04 0244 0245 cell 103A906 103 outside -103A03 0246 0247 % --- --- Universe 102 --- --- Top Plug 0248 0249 surf 102A00 hexyc 0.0 0.0 10.15000 0250 surf 102A01 hexyc 0.0 0.0 10.55000 0251 surf 102A02 hexyc 0.0 0.0 10.80000 0252 surf 102A03 pz 84.00000 0253 surf 102A04 pz 90.00000 0254 0255 cell 102A901 102 outside 102A04 0256 0257 cell 102A002 102 fill 115 -102A00 102A03 -102A04 0258 cell 102A003 102 t91 102A00 -102A01 102A03 -102A04 0259 cell 102A004 102 lead 102A01 -102A02 102A03 -102A04 0260 cell 102A905 102 outside 102A02 102A03 -102A04 0261 0262 cell 102A906 102 outside -102A03 0263 0264 % --- --- Universe 101 --- --- Upper FGP 0265 0266 surf 101A00 hexyc 0.0 0.0 10.15000 0267 surf 101A01 hexyc 0.0 0.0 10.55000 0268 surf 101A02 hexyc 0.0 0.0 10.80000 0269 surf 101A03 pz 60.00000 0270 surf 101A04 pz 84.00000 0271 0272 cell 101A901 101 outside 101A04 0273 0274 cell 101A002 101 fill 114 -101A00 101A03 -101A04 0275 cell 101A003 101 t91 101A00 -101A01 101A03 -101A04 0276 cell 101A004 101 lead 101A01 -101A02 101A03 -101A04 0277 cell 101A905 101 outside 101A02 101A03 -101A04 0278 0279 cell 101A906 101 outside -101A03 0280 0281 % --- --- Universe 100 --- --- Inner Fuel Region 0282 0283 surf 100A00 hexyc 0.0 0.0 10.15000 0284 surf 100A01 hexyc 0.0 0.0 10.55000 0285 surf 100A02 hexyc 0.0 0.0 10.80000 0286 surf 100A03 pz -60.00000 0287 surf 100A04 pz 60.00000 0288 0289 cell 100A901 100 outside 100A04 0290 0291 cell 100A002 100 fill 111 -100A00 100A03 -100A04 0292 cell 100A003 100 t91 100A00 -100A01 100A03 -100A04 0293 cell 100A004 100 lead 100A01 -100A02 100A03 -100A04 0294 cell 100A905 100 outside 100A02 100A03 -100A04 0295 0296 cell 100A906 100 outside -100A03 0297 0298 % --- --- Universe 99 --- --- Lower FGP 0299 0300 surf 99A00 hexyc 0.0 0.0 10.15000 0301 surf 99A01 hexyc 0.0 0.0 10.55000 0302 surf 99A02 hexyc 0.0 0.0 10.80000 0303 surf 99A03 pz -156.00000 0304 surf 99A04 pz -60.00000 0305 0306 cell 99A901 99 outside 99A04 0307 0308 cell 99A002 99 fill 114 -99A00 99A03 -99A04 0309 cell 99A003 99 t91 99A00 -99A01 99A03 -99A04 0310 cell 99A004 99 lead 99A01 -99A02 99A03 -99A04 0311 cell 99A905 99 outside 99A02 99A03 -99A04 0312 0313 cell 99A906 99 outside -99A03 0314 0315 % --- --- Universe 98 --- --- Bottom Plug 0316 0317 surf 98A00 hexyc 0.0 0.0 10.15000 0318 surf 98A01 hexyc 0.0 0.0 10.55000 0319 surf 98A02 hexyc 0.0 0.0 10.80000 0320 surf 98A03 pz -160.00000 0321 surf 98A04 pz -156.00000 0322 0323 cell 98A901 98 outside 98A04 0324 0325 cell 98A002 98 fill 115 -98A00 98A03 -98A04 0326 cell 98A003 98 t91 98A00 -98A01 98A03 -98A04 0327 cell 98A004 98 lead 98A01 -98A02 98A03 -98A04 0328 cell 98A905 98 outside 98A02 98A03 -98A04 0329 0330 cell 98A906 98 outside -98A03 0331 0332 % --- --- Universe 97 --- --- Lower Axial Reflector 0333 0334 surf 97A00 hexyc 0.0 0.0 10.15000 0335 surf 97A01 hexyc 0.0 0.0 10.55000 0336 surf 97A02 hexyc 0.0 0.0 10.80000 0337 surf 97A03 pz -250.00000 0338 surf 97A04 pz -160.00000

78

0339 0340 cell 97A901 97 outside 97A04 0341 0342 cell 97A002 97 lead -97A00 97A03 -97A04 0343 cell 97A003 97 t91 97A00 -97A01 97A03 -97A04 0344 cell 97A004 97 lead 97A01 -97A02 97A03 -97A04 0345 cell 97A905 97 outside 97A02 97A03 -97A04 0346 0347 cell 97A906 97 outside -97A03 0348 0349 % --- --- Universe 96 --- --- Lower Lead 0350 0351 surf 96A00 hexyc 0.0 0.0 10.15000 0352 surf 96A01 hexyc 0.0 0.0 10.55000 0353 surf 96A02 hexyc 0.0 0.0 10.80000 0354 surf 96A03 pz -400.00000 0355 surf 96A04 pz -250.00000 0356 0357 cell 96A901 96 outside 96A04 0358 0359 cell 96A002 96 lead -96A00 96A03 -96A04 0360 cell 96A003 96 lead 96A00 -96A01 96A03 -96A04 0361 cell 96A004 96 lead 96A01 -96A02 96A03 -96A04 0362 cell 96A905 96 outside 96A02 96A03 -96A04 0363 0364 cell 96A906 96 outside -96A03 0365 0366 % --- --- Universe 1000 --- --- 0367 0368 surf A00 hexyc 0.0 0.0 10.80000 0369 surf A01 pz -400.00000 0370 surf A02 pz -250.00000 0371 surf A03 pz -160.00000 0372 surf A04 pz -156.00000 0373 surf A05 pz -60.00000 0374 surf A06 pz 60.00000 0375 surf A07 pz 84.00000 0376 surf A08 pz 90.00000 0377 surf A09 pz 130.00000 0378 surf A10 pz 280.00000 0379 0380 cell A901 1000 outside A10 0381 cell A002 1000 fill 104 -A00 A09 -A10 0382 cell A003 1000 outside A00 A09 -A10 0383 cell A004 1000 fill 103 -A00 A08 -A09 0384 cell A005 1000 outside A00 A08 -A09 0385 cell A006 1000 fill 102 -A00 A07 -A08 0386 cell A007 1000 outside A00 A07 -A08 0387 cell A008 1000 fill 101 -A00 A06 -A07 0388 cell A009 1000 outside A00 A06 -A07 0389 cell A010 1000 fill 100 -A00 A05 -A06 0390 cell A011 1000 outside A00 A05 -A06 0391 cell A012 1000 fill 99 -A00 A04 -A05 0392 cell A013 1000 outside A00 A04 -A05 0393 cell A014 1000 fill 98 -A00 A03 -A04 0394 cell A015 1000 outside A00 A03 -A04 0395 cell A016 1000 fill 97 -A00 A02 -A03 0396 cell A017 1000 outside A00 A02 -A03 0397 cell A018 1000 fill 96 -A00 A01 -A02 0398 cell A019 1000 outside A00 A01 -A02 0399 cell A920 1000 outside -A01 0400 0401 % ----------------------------------------------------------- 0402 0403 % --- Universes for fuel2 ----------------------------------- 0404 0405 % ----------------------------------------------------------- 0406 0407 % --- --- Universe 204 --- --- Upper Lead 0408 0409 surf 204B00 hexyc 0.0 0.0 10.15000 0410 surf 204B01 hexyc 0.0 0.0 10.55000 0411 surf 204B02 hexyc 0.0 0.0 10.80000 0412 surf 204B03 pz 130.00000 0413 surf 204B04 pz 280.00000 0414 0415 cell 204B901 204 outside 204B04 0416 0417 cell 204B002 204 lead -204B00 204B03 -204B04 0418 cell 204B003 204 lead 204B00 -204B01 204B03 -204B04 0419 cell 204B004 204 lead 204B01 -204B02 204B03 -204B04 0420 cell 204B905 204 outside 204B02 204B03 -204B04 0421 0422 cell 204B906 204 outside -204B03 0423 0424 % --- --- Universe 203 --- --- Upper Axial Reflector 0425 0426 surf 203B00 hexyc 0.0 0.0 10.15000 0427 surf 203B01 hexyc 0.0 0.0 10.55000 0428 surf 203B02 hexyc 0.0 0.0 10.80000 0429 surf 203B03 pz 90.00000 0430 surf 203B04 pz 130.00000 0431 0432 cell 203B901 203 outside 203B04 0433 0434 cell 203B002 203 lead -203B00 203B03 -203B04 0435 cell 203B003 203 t91 203B00 -203B01 203B03 -203B04 0436 cell 203B004 203 lead 203B01 -203B02 203B03 -203B04 0437 cell 203B905 203 outside 203B02 203B03 -203B04 0438 0439 cell 203B906 203 outside -203B03 0440 0441 % --- --- Universe 202 --- --- Top Plug 0442 0443 surf 202B00 hexyc 0.0 0.0 10.15000 0444 surf 202B01 hexyc 0.0 0.0 10.55000 0445 surf 202B02 hexyc 0.0 0.0 10.80000 0446 surf 202B03 pz 84.00000 0447 surf 202B04 pz 90.00000 0448 0449 cell 202B901 202 outside 202B04 0450 0451 cell 202B002 202 fill 115 -202B00 202B03 -202B04 0452 cell 202B003 202 t91 202B00 -202B01 202B03 -202B04 0453 cell 202B004 202 lead 202B01 -202B02 202B03 -202B04

79

0454 cell 202B905 202 outside 202B02 202B03 -202B04 0455 0456 cell 202B906 202 outside -202B03 0457 0458 % --- --- Universe 201 --- --- Upper FGP 0459 0460 surf 201B00 hexyc 0.0 0.0 10.15000 0461 surf 201B01 hexyc 0.0 0.0 10.55000 0462 surf 201B02 hexyc 0.0 0.0 10.80000 0463 surf 201B03 pz 60.00000 0464 surf 201B04 pz 84.00000 0465 0466 cell 201B901 201 outside 201B04 0467 0468 cell 201B002 201 fill 114 -201B00 201B03 -201B04 0469 cell 201B003 201 t91 201B00 -201B01 201B03 -201B04 0470 cell 201B004 201 lead 201B01 -201B02 201B03 -201B04 0471 cell 201B905 201 outside 201B02 201B03 -201B04 0472 0473 cell 201B906 201 outside -201B03 0474 0475 % --- --- Universe 200 --- --- Central Fuel Region 0476 0477 surf 200B00 hexyc 0.0 0.0 10.15000 0478 surf 200B01 hexyc 0.0 0.0 10.55000 0479 surf 200B02 hexyc 0.0 0.0 10.80000 0480 surf 200B03 pz -60.00000 0481 surf 200B04 pz 60.00000 0482 0483 cell 200B901 200 outside 200B04 0484 0485 cell 200B002 200 fill 112 -200B00 200B03 -200B04 0486 cell 200B003 200 t91 200B00 -200B01 200B03 -200B04 0487 cell 200B004 200 lead 200B01 -200B02 200B03 -200B04 0488 cell 200B905 200 outside 200B02 200B03 -200B04 0489 0490 cell 200B906 200 outside -200B03 0491 0492 % --- --- Universe 199 --- --- Lower FGP 0493 0494 surf 199B00 hexyc 0.0 0.0 10.15000 0495 surf 199B01 hexyc 0.0 0.0 10.55000 0496 surf 199B02 hexyc 0.0 0.0 10.80000 0497 surf 199B03 pz -156.00000 0498 surf 199B04 pz -60.00000 0499 0500 cell 199B901 199 outside 199B04 0501 0502 cell 199B002 199 fill 114 -199B00 199B03 -199B04 0503 cell 199B003 199 t91 199B00 -199B01 199B03 -199B04 0504 cell 199B004 199 lead 199B01 -199B02 199B03 -199B04 0505 cell 199B905 199 outside 199B02 199B03 -199B04 0506 0507 cell 199B906 199 outside -199B03 0508 0509 % --- --- Universe 198 --- --- Bottom Plug 0510 0511 surf 198B00 hexyc 0.0 0.0 10.15000 0512 surf 198B01 hexyc 0.0 0.0 10.55000 0513 surf 198B02 hexyc 0.0 0.0 10.80000 0514 surf 198B03 pz -160.00000 0515 surf 198B04 pz -156.00000 0516 0517 cell 198B901 198 outside 198B04 0518 0519 cell 198B002 198 fill 115 -198B00 198B03 -198B04 0520 cell 198B003 198 t91 198B00 -198B01 198B03 -198B04 0521 cell 198B004 198 lead 198B01 -198B02 198B03 -198B04 0522 cell 198B905 198 outside 198B02 198B03 -198B04 0523 0524 cell 198B906 198 outside -198B03 0525 0526 % --- --- Universe 197 --- --- Lower Axial Reflector 0527 0528 surf 197B00 hexyc 0.0 0.0 10.15000 0529 surf 197B01 hexyc 0.0 0.0 10.55000 0530 surf 197B02 hexyc 0.0 0.0 10.80000 0531 surf 197B03 pz -250.00000 0532 surf 197B04 pz -160.00000 0533 0534 cell 197B901 197 outside 197B04 0535 0536 cell 197B002 197 lead -197B00 197B03 -197B04 0537 cell 197B003 197 t91 197B00 -197B01 197B03 -197B04 0538 cell 197B004 197 lead 197B01 -197B02 197B03 -197B04 0539 cell 197B905 197 outside 197B02 197B03 -197B04 0540 0541 cell 197B906 197 outside -197B03 0542 0543 % --- --- Universe 196 --- --- Lower Lead 0544 0545 surf 196B00 hexyc 0.0 0.0 10.15000 0546 surf 196B01 hexyc 0.0 0.0 10.55000 0547 surf 196B02 hexyc 0.0 0.0 10.80000 0548 surf 196B03 pz -400.00000 0549 surf 196B04 pz -250.00000 0550 0551 cell 196B901 196 outside 196B04 0552 0553 cell 196B002 196 lead -196B00 196B03 -196B04 0554 cell 196B003 196 lead 196B00 -196B01 196B03 -196B04 0555 cell 196B004 196 lead 196B01 -196B02 196B03 -196B04 0556 cell 196B905 196 outside 196B02 196B03 -196B04 0557 0558 cell 196B906 196 outside -196B03 0559 0560 % --- --- Universe 2000 --- --- 0561 0562 surf B00 hexyc 0.0 0.0 10.80000 0563 surf B01 pz -400.00000 0564 surf B02 pz -250.00000 0565 surf B03 pz -160.00000 0566 surf B04 pz -156.00000 0567 surf B05 pz -60.00000 0568 surf B06 pz 60.00000

80

0569 surf B07 pz 84.00000 0570 surf B08 pz 90.00000 0571 surf B09 pz 130.00000 0572 surf B10 pz 280.00000 0573 0574 cell B901 2000 outside B10 0575 cell B002 2000 fill 204 -B00 B09 -B10 0576 cell B003 2000 outside B00 B09 -B10 0577 cell B004 2000 fill 203 -B00 B08 -B09 0578 cell B005 2000 outside B00 B08 -B09 0579 cell B006 2000 fill 202 -B00 B07 -B08 0580 cell B007 2000 outside B00 B07 -B08 0581 cell B008 2000 fill 201 -B00 B06 -B07 0582 cell B009 2000 outside B00 B06 -B07 0583 cell B010 2000 fill 200 -B00 B05 -B06 0584 cell B011 2000 outside B00 B05 -B06 0585 cell B012 2000 fill 199 -B00 B04 -B05 0586 cell B013 2000 outside B00 B04 -B05 0587 cell B014 2000 fill 198 -B00 B03 -B04 0588 cell B015 2000 outside B00 B03 -B04 0589 cell B016 2000 fill 197 -B00 B02 -B03 0590 cell B017 2000 outside B00 B02 -B03 0591 cell B018 2000 fill 196 -B00 B01 -B02 0592 cell B019 2000 outside B00 B01 -B02 0593 cell B920 2000 outside -B01 0594 0595 % ----------------------------------------------------------- 0596 0597 % --- Universes for fuel3 ----------------------------------- 0598 0599 % ----------------------------------------------------------- 0600 0601 % --- --- Universe 304 --- --- 0602 0603 surf 304C00 hexyc 0.0 0.0 10.15000 0604 surf 304C01 hexyc 0.0 0.0 10.55000 0605 surf 304C02 hexyc 0.0 0.0 10.80000 0606 surf 304C03 pz 130.00000 0607 surf 304C04 pz 280.00000 0608 0609 cell 304C901 304 outside 304C04 0610 0611 cell 304C002 304 lead -304C00 304C03 -304C04 0612 cell 304C003 304 lead 304C00 -304C01 304C03 -304C04 0613 cell 304C004 304 lead 304C01 -304C02 304C03 -304C04 0614 cell 304C905 304 outside 304C02 304C03 -304C04 0615 0616 cell 304C906 304 outside -304C03 0617 0618 % --- --- Universe 303 --- --- 0619 0620 surf 303C00 hexyc 0.0 0.0 10.15000 0621 surf 303C01 hexyc 0.0 0.0 10.55000 0622 surf 303C02 hexyc 0.0 0.0 10.80000 0623 surf 303C03 pz 90.00000 0624 surf 303C04 pz 130.00000 0625 0626 cell 303C901 303 outside 303C04 0627 0628 cell 303C002 303 lead -303C00 303C03 -303C04 0629 cell 303C003 303 t91 303C00 -303C01 303C03 -303C04 0630 cell 303C004 303 lead 303C01 -303C02 303C03 -303C04 0631 cell 303C905 303 outside 303C02 303C03 -303C04 0632 0633 cell 303C906 303 outside -303C03 0634 0635 % --- --- Universe 302 --- --- 0636 0637 surf 302C00 hexyc 0.0 0.0 10.15000 0638 surf 302C01 hexyc 0.0 0.0 10.55000 0639 surf 302C02 hexyc 0.0 0.0 10.80000 0640 surf 302C03 pz 84.00000 0641 surf 302C04 pz 90.00000 0642 0643 cell 302C901 302 outside 302C04 0644 0645 cell 302C002 302 fill 115 -302C00 302C03 -302C04 0646 cell 302C003 302 t91 302C00 -302C01 302C03 -302C04 0647 cell 302C004 302 lead 302C01 -302C02 302C03 -302C04 0648 cell 302C905 302 outside 302C02 302C03 -302C04 0649 0650 cell 302C906 302 outside -302C03 0651 0652 % --- --- Universe 301 --- --- 0653 0654 surf 301C00 hexyc 0.0 0.0 10.15000 0655 surf 301C01 hexyc 0.0 0.0 10.55000 0656 surf 301C02 hexyc 0.0 0.0 10.80000 0657 surf 301C03 pz 60.00000 0658 surf 301C04 pz 84.00000 0659 0660 cell 301C901 301 outside 301C04 0661 0662 cell 301C002 301 fill 114 -301C00 301C03 -301C04 0663 cell 301C003 301 t91 301C00 -301C01 301C03 -301C04 0664 cell 301C004 301 lead 301C01 -301C02 301C03 -301C04 0665 cell 301C905 301 outside 301C02 301C03 -301C04 0666 0667 cell 301C906 301 outside -301C03 0668 0669 % --- --- Universe 300 --- --- 0670 0671 surf 300C00 hexyc 0.0 0.0 10.15000 0672 surf 300C01 hexyc 0.0 0.0 10.55000 0673 surf 300C02 hexyc 0.0 0.0 10.80000 0674 surf 300C03 pz -60.00000 0675 surf 300C04 pz 60.00000 0676 0677 cell 300C901 300 outside 300C04 0678 0679 cell 300C002 300 fill 113 -300C00 300C03 -300C04 0680 cell 300C003 300 t91 300C00 -300C01 300C03 -300C04 0681 cell 300C004 300 lead 300C01 -300C02 300C03 -300C04 0682 cell 300C905 300 outside 300C02 300C03 -300C04 0683

81

0684 cell 300C906 300 outside -300C03 0685 0686 % --- --- Universe 299 --- --- 0687 0688 surf 299C00 hexyc 0.0 0.0 10.15000 0689 surf 299C01 hexyc 0.0 0.0 10.55000 0690 surf 299C02 hexyc 0.0 0.0 10.80000 0691 surf 299C03 pz -156.00000 0692 surf 299C04 pz -60.00000 0693 0694 cell 299C901 299 outside 299C04 0695 0696 cell 299C002 299 fill 114 -299C00 299C03 -299C04 0697 cell 299C003 299 t91 299C00 -299C01 299C03 -299C04 0698 cell 299C004 299 lead 299C01 -299C02 299C03 -299C04 0699 cell 299C905 299 outside 299C02 299C03 -299C04 0700 0701 cell 299C906 299 outside -299C03 0702 0703 % --- --- Universe 298 --- --- 0704 0705 surf 298C00 hexyc 0.0 0.0 10.15000 0706 surf 298C01 hexyc 0.0 0.0 10.55000 0707 surf 298C02 hexyc 0.0 0.0 10.80000 0708 surf 298C03 pz -160.00000 0709 surf 298C04 pz -156.00000 0710 0711 cell 298C901 298 outside 298C04 0712 0713 cell 298C002 298 fill 115 -298C00 298C03 -298C04 0714 cell 298C003 298 t91 298C00 -298C01 298C03 -298C04 0715 cell 298C004 298 lead 298C01 -298C02 298C03 -298C04 0716 cell 298C905 298 outside 298C02 298C03 -298C04 0717 0718 cell 298C906 298 outside -298C03 0719 0720 % --- --- Universe 297 --- --- 0721 0722 surf 297C00 hexyc 0.0 0.0 10.15000 0723 surf 297C01 hexyc 0.0 0.0 10.55000 0724 surf 297C02 hexyc 0.0 0.0 10.80000 0725 surf 297C03 pz -250.00000 0726 surf 297C04 pz -160.00000 0727 0728 cell 297C901 297 outside 297C04 0729 0730 cell 297C002 297 lead -297C00 297C03 -297C04 0731 cell 297C003 297 t91 297C00 -297C01 297C03 -297C04 0732 cell 297C004 297 lead 297C01 -297C02 297C03 -297C04 0733 cell 297C905 297 outside 297C02 297C03 -297C04 0734 0735 cell 297C906 297 outside -297C03 0736 0737 % --- --- Universe 296 --- --- 0738 0739 surf 296C00 hexyc 0.0 0.0 10.15000 0740 surf 296C01 hexyc 0.0 0.0 10.55000 0741 surf 296C02 hexyc 0.0 0.0 10.80000 0742 surf 296C03 pz -400.00000 0743 surf 296C04 pz -250.00000 0744 0745 cell 296C901 296 outside 296C04 0746 0747 cell 296C002 296 lead -296C00 296C03 -296C04 0748 cell 296C003 296 lead 296C00 -296C01 296C03 -296C04 0749 cell 296C004 296 lead 296C01 -296C02 296C03 -296C04 0750 cell 296C905 296 outside 296C02 296C03 -296C04 0751 0752 cell 296C906 296 outside -296C03 0753 0754 % --- --- Universe 3000 --- --- 0755 0756 surf C00 hexyc 0.0 0.0 10.80000 0757 surf C01 pz -400.00000 0758 surf C02 pz -250.00000 0759 surf C03 pz -160.00000 0760 surf C04 pz -156.00000 0761 surf C05 pz -60.00000 0762 surf C06 pz 60.00000 0763 surf C07 pz 84.00000 0764 surf C08 pz 90.00000 0765 surf C09 pz 130.00000 0766 surf C10 pz 280.00000 0767 0768 cell C901 3000 outside C10 0769 cell C002 3000 fill 304 -C00 C09 -C10 0770 cell C003 3000 outside C00 C09 -C10 0771 cell C004 3000 fill 303 -C00 C08 -C09 0772 cell C005 3000 outside C00 C08 -C09 0773 cell C006 3000 fill 302 -C00 C07 -C08 0774 cell C007 3000 outside C00 C07 -C08 0775 cell C008 3000 fill 301 -C00 C06 -C07 0776 cell C009 3000 outside C00 C06 -C07 0777 cell C010 3000 fill 300 -C00 C05 -C06 0778 cell C011 3000 outside C00 C05 -C06 0779 cell C012 3000 fill 299 -C00 C04 -C05 0780 cell C013 3000 outside C00 C04 -C05 0781 cell C014 3000 fill 298 -C00 C03 -C04 0782 cell C015 3000 outside C00 C03 -C04 0783 cell C016 3000 fill 297 -C00 C02 -C03 0784 cell C017 3000 outside C00 C02 -C03 0785 cell C018 3000 fill 296 -C00 C01 -C02 0786 cell C019 3000 outside C00 C01 -C02 0787 cell C920 3000 outside -C01 0788 0789 0790 % ----------------------------------------------------------- 0791 0792 % --- Universes for CSD ------------------------------------ 0793 0794 % ----------------------------------------------------------- 0795 0796 % --- CSD pins 0797 0798 pin 4

82

0799 0800 lead 0801 0802 pin 30 0803 0804 b4c2 1.60 %0.900 % b4c Nat 0805 heg 1.64 %1.000 % heg 0806 t91 1.74 %1.100 % cladding 0807 lead %fills the rest of the universe 0808 0809 % ---CSD Pin Lattice (type = 2, pin pitch = 2.03831 cm): 0810 0811 lat 606 2 0.0 0.0 9 9 3.8 0812 0813 4 4 4 4 4 4 4 4 4 0814 4 4 4 4 4 4 4 4 4 0815 4 4 4 4 30 30 30 4 4 0816 4 4 4 30 30 30 30 4 4 0817 4 4 30 30 4 30 30 4 4 0818 4 4 30 30 30 30 4 4 4 0819 4 4 30 30 30 4 4 4 4 0820 4 4 4 4 4 4 4 4 4 0821 4 4 4 4 4 4 4 4 4 0822 0823 % --- --- Universe 61 --- --- 0824 0825 surf 61D00 hexyc 0.0 0.0 10.15000 0826 surf 61D01 hexyc 0.0 0.0 10.55000 0827 surf 61D02 hexyc 0.0 0.0 10.80000 0828 surf 61D03 pz 200.00000 0829 surf 61D04 pz 280.00000 0830 0831 cell 61D901 61 outside 61D04 0832 0833 cell 61D002 61 lead -61D00 61D03 -61D04 0834 cell 61D003 61 lead 61D00 -61D01 61D03 -61D04 0835 cell 61D004 61 lead 61D01 -61D02 61D03 -61D04 0836 cell 61D905 61 outside 61D02 61D03 -61D04 0837 0838 cell 61D906 61 outside -61D03 0839 0840 % --- --- Universe 60 --- --- 0841 0842 surf 60D00 hexyc 0.0 0.0 10.15000 0843 surf 60D01 hexyc 0.0 0.0 10.55000 0844 surf 60D02 hexyc 0.0 0.0 10.80000 0845 surf 60D03 pz 60.00000 0846 surf 60D04 pz 200.00000 0847 0848 cell 60D901 60 outside 60D04 0849 0850 cell 60D002 60 fill 606 -60D00 60D03 -60D04 0851 cell 60D003 60 t91 60D00 -60D01 60D03 -60D04 0852 cell 60D004 60 lead 60D01 -60D02 60D03 -60D04 0853 cell 60D905 60 outside 60D02 60D03 -60D04 0854 0855 cell 60D906 60 outside -60D03 0856 0857 % --- --- Universe 59 --- --- 0858 0859 surf 59D00 hexyc 0.0 0.0 10.15000 0860 surf 59D01 hexyc 0.0 0.0 10.55000 0861 surf 59D02 hexyc 0.0 0.0 10.80000 0862 surf 59D03 pz -400.00000 0863 surf 59D04 pz 60.00000 0864 0865 cell 59D901 59 outside 59D04 0866 0867 cell 59D002 59 lead -59D00 59D03 -59D04 0868 cell 59D003 59 t91 59D00 -59D01 59D03 -59D04 0869 cell 59D004 59 lead 59D01 -59D02 59D03 -59D04 0870 cell 59D905 59 outside 59D02 59D03 -59D04 0871 0872 cell 59D906 59 outside -59D03 0873 0874 % --- --- Universe 600 --- --- 0875 0876 surf D00 hexyc 0.0 0.0 10.80000 0877 surf D01 pz -400.00000 0878 surf D02 pz 60.00000 0879 surf D03 pz 200.00000 0880 surf D04 pz 280.00000 0881 0882 cell D901 600 outside D04 0883 0884 cell D002 600 fill 61 -D00 D03 -D04 0885 cell D003 600 outside D00 D03 -D04 0886 cell D004 600 fill 60 -D00 D02 -D03 0887 cell D005 600 outside D00 D02 -D03 0888 cell D006 600 fill 59 -D00 D01 -D02 0889 cell D007 600 outside D00 D01 -D02 0890 0891 cell D908 600 outside -D01 0892 0893 % ----------------------------------------------------------- 0894 0895 % --- Universe 50 for Radial Reflector ---------------------- 0896 0897 % ----------------------------------------------------------- 0898 0899 pin 6 0900 0901 lead 0902 0903 % --- Fuel pin :1 0904 0905 pin 5 0906 0907 ref 0.700 0908 heg 0.738 0909 t91 0.788 0910 lead %fills the rest of the universe 0911 0912 % --- Lattice 55: Reflector Lattice 0913

83

0914 lat 55 2 0.0 0.0 15 15 1.7 0915 0916 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 0917 6 6 6 6 6 6 6 5 5 5 5 5 5 5 6 0918 6 6 6 6 6 6 5 5 5 5 5 5 5 5 6 0919 6 6 6 6 6 5 5 5 5 5 5 5 5 5 6 0920 6 6 6 6 5 5 5 5 5 5 5 5 5 5 6 0921 6 6 6 5 5 5 5 5 5 5 5 5 5 5 6 0922 6 6 5 5 5 5 5 5 5 5 5 5 5 5 6 0923 6 5 5 5 5 5 5 5 5 5 5 5 5 5 6 0924 6 5 5 5 5 5 5 5 5 5 5 5 5 6 6 0925 6 5 5 5 5 5 5 5 5 5 5 5 6 6 6 0926 6 5 5 5 5 5 5 5 5 5 5 6 6 6 6 0927 6 5 5 5 5 5 5 5 5 5 6 6 6 6 6 0928 6 5 5 5 5 5 5 5 5 6 6 6 6 6 6 0929 6 5 5 5 5 5 5 5 6 6 6 6 6 6 6 0930 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 0931 0932 % --- --- Universe 50 --- --- 0933 0934 surf R00 hexyc 0.0 0.0 10.15000 0935 surf R01 hexyc 0.0 0.0 10.55000 0936 surf R02 hexyc 0.0 0.0 10.80000 0937 surf R03 pz -400.00000 0938 surf R04 pz 280.00000 0939 0940 cell R901 50 outside R04 0941 0942 cell R002 50 fill 55 -R00 R03 -R04 0943 cell R003 50 t91 R00 -R01 R03 -R04 0944 cell R004 50 lead R01 -R02 R03 -R04 0945 cell R905 50 outside R02 R03 -R04 0946 0947 cell R906 50 outside -R03 0948 0949 0950 % ----------------------------------------------------------- 0951 0952 % --- Universe 7 for Empty Assembly ------------------------- 0953 0954 % ----------------------------------------------------------- 0955 0956 surf E00 hexyc 0.0 0.0 10.80000 0957 surf E01 pz -400.00000 0958 surf E02 pz 280.00000 0959 0960 cell E901 7 outside E02 0961 cell E002 7 lead -E00 E01 -E02 0962 cell E003 7 outside E00 E01 -E02 0963 cell E904 7 outside -E01 0964 0965 0966 % ----------------------------------------------------------- 0967 0968 % --- Universe for full LFR Core ---------------------------- 0969 0970 % ----------------------------------------------------------- 0971 0972 % --- Core lattice 0973 0974 lat 710 3 0.0 0.0 31 31 21.60000 0975 0976 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 0977 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 50 50 7 7 7 7 7 0978 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 50 50 50 50 50 50 50 50 50 7 7 7 0979 7 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 50 3000 3000 3000 3000 3000 3000 3000 3000 3000 50 50 50 7 7 0980 7 7 7 7 7 7 7 7 7 7 7 7 7 50 50 3000 3000 3000 3000 3000 600 600 3000 3000 3000 3000 3000 50 50 7 7 0981 7 7 7 7 7 7 7 7 7 7 7 50 50 3000 3000 600 3000 3000 3000 3000 3000 3000 3000 3000 3000 600 3000 3000 50 50 7 0982 7 7 7 7 7 7 7 7 7 7 50 50 3000 3000 3000 3000 2000 2000 2000 2000 2000 2000 2000 2000 3000 3000 3000 3000 50 50 7 0983 7 7 7 7 7 7 7 7 7 50 50 3000 3000 3000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 3000 3000 3000 50 50 7 0984 7 7 7 7 7 7 7 7 50 50 3000 3000 3000 2000 2000 2000 1000 1000 1000 1000 1000 1000 2000 2000 2000 3000 3000 3000 50 50 7 0985 7 7 7 7 7 7 7 50 50 3000 600 3000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 3000 600 3000 50 50 7 0986 7 7 7 7 7 7 50 50 3000 600 3000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 3000 600 3000 50 50 7 0987 7 7 7 7 7 50 50 3000 3000 3000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 3000 3000 3000 50 50 7 0988 7 7 7 7 7 50 3000 3000 3000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 3000 3000 3000 50 7 7 0989 7 7 7 7 50 3000 3000 3000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 3000 3000 3000 50 7 7 0990 7 7 7 50 50 3000 3000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 3000 3000 50 50 7 7 0991 7 7 7 50 3000 600 3000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 3000 600 3000 50 7 7 7 0992 7 7 50 50 3000 3000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 3000 3000 50 50 7 7 7 0993 7 7 50 3000 3000 3000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 3000 3000 3000 50 7 7 7 7 0994 7 7 50 3000 3000 3000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 3000 3000 3000 50 7 7 7 7 7 0995 7 50 50 3000 3000 3000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 3000 3000 3000 50 50 7 7 7 7 7 0996 7 50 50 3000 600 3000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 3000 600 3000 50 50 7 7 7 7 7 7 0997 7 50 50 3000 600 3000 2000 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 2000 3000 600 3000 50 50 7 7 7 7 7 7 7 0998 7 50 50 3000 3000 3000 2000 2000 2000 1000 1000 1000 1000 1000 1000 2000 2000 2000 3000 3000 3000 50 50 7 7 7 7 7 7 7 7 0999 7 50 50 3000 3000 3000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 3000 3000 3000 50 50 7 7 7 7 7 7 7 7 7 1000 7 50 50 3000 3000 3000 3000 2000 2000 2000 2000 2000 2000 2000 2000 3000 3000 3000 3000 50 50 7 7 7 7 7 7 7 7 7 7 1001 7 50 50 3000 3000 600 3000 3000 3000 3000 3000 3000 3000 3000 3000 600 3000 3000 50 50 7 7 7 7 7 7 7 7 7 7 7 1002 7 7 50 50 3000 3000 3000 3000 3000 600 600 3000 3000 3000 3000 3000 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 1003 7 7 50 50 50 3000 3000 3000 3000 3000 3000 3000 3000 3000 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 7 1004 7 7 7 50 50 50 50 50 50 50 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 1005 7 7 7 7 7 50 50 50 50 50 50 50 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 1006 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

1007 1008 1009 1010 % --- Surfaces: REACTOR CORE 1011 1012 surf F00 cyl 0.0 0.0 285.00000 1013 surf F01 cyl 0.0 0.0 290.00000 1014 surf F02 pz -400.00000 1015 surf F03 pz 280.00000 1016 1017 cell F901 0 outside F03 1018 1019 cell F002 0 fill 710 -F00 F02 -F03 1020 cell F003 0 t91 F00 -F01 F02 -F03 1021 cell F904 0 outside F01 F02 -F03 1022 1023 cell F905 0 outside -F02 1024 1025 % ----------------------------------------------------------- 1026 1027 %% ---Materials for ELSY--- %% 1028 1029 % % fuel1 % fuel2 % fuel3 1030 % % Pu 14.6% % Pu 15.5% % Pu 18.5% 1031 % % % % 1032 % U234 % 0.002562 % 0.002535 % 0.002445 1033 % U235 % 0.349286 % 0.345605 % 0.333335 1034 % U236 % 0.00854 % 0.00845 % 0.00815 1035 % U238 % 85.039612 % 84.14341 % 81.15607 1036 % PU238 % 0.342808 % 0.36394 % 0.43438 1037 % PU239 % 8.32419 % 8.837325 % 10.547775 1038 % PU240 % 3.934846 % 4.177405 % 4.985935 1039 % PU241 % 0.886074 % 0.940695 % 1.122765 1040 % PU242 % 1.111936 % 1.18048 % 1.40896 1041

84

1042 % --- inner MOX fuel 1043 1044 mat fuel1 -11.0049 1045 1046 92234.12c 0.000009 1047 92235.12c 0.001176 1048 92236.12c 0.000029 1049 92238.12c 0.286329 1050 94238.12c 0.001154 1051 94239.12c 0.028028 1052 94240.12c 0.013249 1053 94241.12c 0.002983 1054 94242.12c 0.003744 1055 8016.12c 0.663300 1056 1057 % --- central MOX fuel 1058 1059 mat fuel2 -11.0092 1060 1061 92234.12c 0.000009 1062 92235.12c 0.001164 1063 92236.12c 0.000028 1064 92238.12c 0.283311 1065 94238.12c 0.001225 1066 94239.12c 0.029755 1067 94240.12c 0.014065 1068 94241.12c 0.003167 1069 94242.12c 0.003975 1070 8016.12c 0.663300 1071 1072 % --- outer MOX fuel 1073 1074 mat fuel3 -11.0236 1075 1076 92234.12c 0.000008 1077 92235.12c 0.001122 1078 92236.12c 0.000027 1079 92238.12c 0.273253 1080 94238.12c 0.001463 1081 94239.12c 0.035514 1082 94240.12c 0.016788 1083 94241.12c 0.003780 1084 94242.12c 0.004744 1085 8016.12c 0.663300 1086 1087 % --- Reflector 1088 1089 mat ref -6.0 1090 1091 40090.06c -0.361436 % Zr-90 1092 40091.06c -0.078821 % Zr-91 1093 40092.06c -0.120479 % Zr-92 1094 40094.06c -0.122095 % Zr-94 1095 40096.06c -0.019670 % Zr-96 1096 39089.06c -0.040200 % Y-89 1097 8016.06c -0.257300 % O-16 1098 1099 % --- FMST91 1100 1101 mat t91 -7.7 1102 1103 26054.06c -0.051272 % Fe-54 1104 26056.06c -0.810805 % Fe-56 1105 26057.06c -0.019448 % Fe-57 1106 26058.06c -0.002475 % Fe-58 1107 24050.06c -0.003906 % Cr-50 1108 24052.06c -0.075429 % Cr-52 1109 24053.06c -0.008541 % Cr-53 1110 24054.06c -0.002124 % Cr-54 1111 28058.06c -0.001365 % Ni-58 1112 28060.06c -0.000522 % Ni-60 1113 28061.06c -0.000023 % Ni-61 1114 28062.06c -0.000072 % Ni-62 1115 28064.06c -0.000018 % Ni-64 1116 42092.06c -0.001484 % Mo-92 1117 42094.06c -0.000925 % Mo-94 1118 42095.06c -0.001592 % Mo-95 1119 42096.06c -0.001668 % Mo-96 1120 42097.06c -0.000955 % Mo-97 1121 42098.06c -0.002413 % Mo-98 1122 42100.06c -0.000963 % Mo-100 1123 23051.06c -0.002000 % V-51 1124 41093.06c -0.001000 % Nb-93 1125 25055.06c -0.006000 % Mn-55 1126 14028.06c -0.004612 % Si-28 1127 14029.06c -0.000234 % Si-29 1128 14030.06c -0.000155 % Si-30 1129 1130 % --- Lead 1131 1132 mat lead -11.37 1133 1134 82204.06c 0.014000 % Pb-204 1135 82206.06c 0.241000 % Pb-206 1136 82207.06c 0.221000 % Pb-207 1137 82208.06c 0.524000 % Pb-208 1138 1139 1140 % --- CSD Natural B4C: 1141 1142 mat b4c1 -2.418 1143 1144 5010.06c -0.14419 % B-10 1145 5011.06c -0.63843 % B-11 1146 6000.06c -0.21738 % C-nat 1147 1148 % ---DSD Enriched B4C: 1149 1150 mat b4c2 -2.296 1151 1152 5010.06c -0.68702 % B-10 1153 5011.06c -0.08397 % B-11 1154 6000.06c -0.22901 % C-nat 1155 1156 % --- Helium: heg

85

1157 1158 mat heg -0.00159 1159 1160 2004.06c 1 % He4

86

G. GFR

This appendix summarizes the studies performed within the scope of the preliminary

design of a pin fuelled core with silicon-carbide ceramic cladding for the 2400 MWth

Gas-cooled Fast Reactor (GFR), which was provided to the GoFastR (Gas-cooled Fast

Reactor) project by CEA [16]. General core design parameters of GFR are given in

Table 8. Safety coefficients of GFR core, which were calculated with the Serpent MC

code, are given in Table 9. A Serpent input file which was used to calculate these safety

coefficients is not reported in this document to due copyright concerns. A modified core

design, which in a way reflects the original GFR core is presented in a form of Serpent

input in Appendix E.

Table 8: GFR core parameters.

Reactor thermal power (MWth) 2400 Primary coolant He Fuel (U,Pu)C Core volume (m3) 23.6 Core Radius/Hight (cm) 213.4/165 Power density (W/cm3) 90 CSD / DSD 18 / 13 Number of I/O FA 264 / 252 PuC content in I/O FA (wt%) 14.10/17.63 Fuel residence time (EFPD) 1443

Table 9: Safety coefficients and their relative deviations calculated with Serpent MC.

Safety coefficients Units Doppler constant pcm -1073±20 Axial Fuel expansion coefficient pcm/K -0.2295±0.01 Core Radial expansion coefficient pcm/K -0.65±0.01 Axial Clad expansion coefficient pcm/K 0.03895±0.008 Control Rod Worth pcm 7205±10

87

H. ELSY

This appendix summarizes the studies performed for European Lead Fast Reactor, which

is being developed in the frame of the EU-FP6-ELSY project. The ELSY (European Lead-

cooled SYstem) reference design was simulated with the Serpent MC code. General core

design parameters are given in Table 10. A more detailed description of the

implemented design can be found here [17]. Safety coefficients of ELSY core, which

were calculated with the Serpent MC code, are shown in Table 11. A modified core

design, which in a way reflects the ELSY core, reported in [17] is presented in a form of

Serpent input in Appendix F.

Table 10: ELSY core parameters.

Reactor thermal power (MWth) 1500 Primary coolant Pb Fuel (U,Pu)O2 Core Radius/Hight (cm) 290/120 Control Rods 18 Number of I/C/O FA†† 163/102/168 PuO2 content in I/C/O FA (wt%) 14.6/15.5/18.5 Fuel residence time (EFPD) 1825

Table 11: Safety coefficients and their relative deviations calculated with Serpent MC.

Safety coefficients Units Doppler constant pcm -1020±21 Axial Fuel expansion coefficient pcm/K -0.18±0.01 Core Radial expansion coefficient pcm/K -0.68±0.01 Axial Clad expansion coefficient pcm/K 0.063±0.008 Control Rod Worth pcm 2503±10

†† I/C/O FA- Inner, Central and Outer Fuel Assemblies

88

I. Shannon Entropy

In information theory Shannon entropy is a measure of uncertainty of a variable and is

defined as

2log ( )i ii

H p p= −∑

where H is the entropy of a message, ip is the probability of the i -th character in the

message and can be calculated as

ii

NpN

=

where iN is the number of times i -th character appears in the message of length N .

Calculated in this way, entropy H gives the average number of bits per character

necessary to transfer the message.

For example for a string of length 52 which contains 26 A’s and 26 J’s the entropy is

equal to2

2 2 2 2 21

log ( ) log ( ) log ( ) 2 log ( ) 2 0.5 log (0.5) 1i i A A J J A Ai

H p p p p p p p p=

= − = − − = − = − × × =∑

where 26 0.552

JA J

Np pN

= = = = .

This is an example of low entropy. For higher entropy let us use the string

“abcdefghijklmnopqrstuvwyzabcdefghijklmnopqrstuvwyz” of length 52 with 26 different

characters. In this case the Shannon entropy is equal to

26

2 2 21

1 1log ( ) 26 log ( ) 26 log ( ) 4.7026 26i i A A

iH p p p p

=

= − = − = − × × =∑

where 2 1...52 26A B Zp p p= = = = =

It follows that one needs an average of 4.7 bits/character to encode the message, and

the message cannot be compressed to fewer than 4.7 52 244.4× = bits.

89

In this example Shannon entropy shows the possible compression limit of a message

[16].

Unlike the entropy concept in information theory, the Shannon entropy in

Monte Carlo simulations is used to characterize convergence of the fission source

distribution. It provides a measure of “spread” in the distribution.

It has been proven that k-effective can converge before the fission source

distribution in Monte Carlo simulations. To perform correct calculation one needs to

assess the convergence of both k-effective and the fission source distribution. To this

end, Shannon entropy is an important method to characterize the convergence of

fission source. Overall, line-plots of Shannon entropy vs. number of cycles (Figure 17)

are easier to interpret than the source distribution plots.

The entropy of the fission source is defined as

21

log ( )N

Source J JJ

H P P=

= −∑

where N is the number of meshes in the superimposed 3D grid which encapsulates all

of the fissionable regions.

Number of source sites in -th mesh after certain cycle , 1,...,

Total number of source sites in the geometryJ SJP J N= =

The variation of the Shannon entropy is within the range of 2[0, log ]N , where 0 is the

value for point source distribution, and 2log N for uniform distribution [18].

90

References

[1] D. G. Cacuci, Handbook of Nuclear Engineering: Vol. 1: Nuclear Engineering Fundamentals. Springer, 2010.

[2] L. Ghasabyan, K. Mikityuk, J. Krepel, and S. Pelloni, “Use of Serpent Monte-Carlo code for development of 3D full-core models of Gen-IV fast spectrum reactors and preparation of safety parameters/cross-section data for transient analysis with FAST code system,” in Proceedings of the International Conference on Fast Reactors and Related Fuel Cycles: Safe Technologies and Sustainable Scenarios (FR13), Paris, France.

[3] J. Leppänen, “Performance of Woodcock delta-tracking in lattice physics applications using the Serpent Monte Carlo reactor physics burnup calculation code,” Annals of Nuclear Energy, vol. 37, no. 5, pp. 715–722, May 2010.

[4] J. Leppänen, “Two practical methods for unionized energy grid construction in continuous-energy Monte Carlo neutron transport calculation,” Annals of Nuclear Energy, vol. 36, no. 7, pp. 878–885, Jul. 2009.

[5] J. Leppänen, “Development of a New Monte Carlo Reactor Physics Code,” Thesis, Helsinki,Finland, 2007.

[6] “SerpentXS: Automated Cross Section Generation for Serpent.” [Online]. Available: http://canes.github.com/SerpentXS/. [Accessed: 12-Jan-2013].

[6] B. R. Herman, E. Shwageraus, and B. Forget, “Cross Section Generation strategy for high conversion Light Water Reactors,”[Online]. MIT, 2011.

[8] T. Downar, “PARCS v2.7 U.S. NRC Core Neutronics Simulator USER MANUAL.” Aug-2006.

[9] K. Mikityuk, S. Pelloni, P. Coddington, E. Bubelis, and R. Chawla, “FAST: An advanced code system for fast reactor transient analysis,” Annals of Nuclear Energy, vol. 32, no. 15, pp. 1613–1631, Oct. 2005.

[10] “NRC: Computer Codes: TRACE.” [Online]. Available: http://www.nrc.gov/about-nrc/regulatory/research/comp-codes.html. [Accessed: 19-Oct-2012].

[11] Aurelia Chenu, “Single- and two-phase flow modeling for coupled neutronics/thermal-hydraulics transient analysis of Advanced Sodium-Cooled Fast Reactors,” PhD thesis, EPFL, Switzerland, 2011.

[12] K. Mikityuk, J. Krepel, S. Pelloni, A. Chenu, P. Petkevich, and R. Chawla, “FAST Code System: Review of Recent Developments and Near-Future Plans,” Journal of Engineering for Gas Turbines and Power, vol. 132, no. 10, p. 102915, 2010.

[13] A. E. Waltar, D. R. Todd, and P. V. Tsvetkov, Fast Spectrum Reactors. Springer, 2011.

[14] G. L. Fiorini and A. Vasile, “European Commission – 7th Framework Programme: The Collaborative Project on European Sodium Fast Reactor (CP ESFR),” Nuclear Engineering and Design, vol. 241, no. 9, pp. 3461–3469, Sep. 2011.

91

[15] E. Fridman and E. Shwageraus, “Modeling of SFR cores with Serpent–DYN3D codes sequence,” Annals of Nuclear Energy, vol. 53, no. 0, pp. 354–363, Mar. 2013.

[16] P. Richard, Y. Péneliau, and M. Zabiégo, “Reference GFR 2400 MWth core definition at start of GOFASTR,” Commissariat à l’Energie Atomique, Cadarache, Reference CEA/DEN/CAD/DER/SESI/LC4G DO2 26/03/10 Version 0, Mar. 2010.

[17] A. Alemberti, J. Carlsson, E. Malambu, A. Orden, D. Struwe, P. Agostini, and S. Monti, “European lead fast reactor—ELSY,” Nuclear Engineering and Design, vol. 241, no. 9, pp. 3470–3480, Sep. 2011.

[18] F. Brown, “On the use of Shannon entropy of the fission distribution for assessing convergence of Monte Carlo criticality calculations,” presented at the Physor, Vancouver, BC, Canada, 2006.

92

List of Abbreviations

C

CA Control Assembly · 19, 20

CP Collaborative Project · 14

CR Control Rod · 20

CRF Control Rod Follower · 20

CSD Control and Shutdown Device · 15, 16, 17, 86

CZP Cold Zero Power · 22, 30

D

DSD Diverse Shutdown Device · 14, 15, 16, 17, 86, 87

E

EFPD equivalent full power days · 15, 86, 87

ELSY European Lead-cooled SYstem · 13

ESFR European Sodium-cooled Fast Reactor · 13, 14

EUROATOM EURopean ATOMic energy community · 14

F

FA Fuel Assembly · 15, 86, 87

G

GFR Gas-cooled Fast Reactor · 13, 68, 72, 73, 86

I

I/O Inner/Outer · 15, 86, 87

L

LFR Lead-cooled Fast Reactor · 75

P

PSI Paul Scherrer Institute · 6

R

RA Reflector Assembly · 19

S

S2P Serpent to PARCS · 9, 27

SFR Sodium-cooled Fast Reactor · 55

X

XS Cross Section · 4

XSEC Cross Section Card · 4

93

ISSN 0280-316X

TRITA-FYS 2013:02

KTH/FYS/--13:02—SE

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