NEA/NSC/DOC(2001)1NEA NUCLEAR SCIENCE COMMITTEENEA COMMITTEE ON SAFETY OF NUCLEAR INSTALLATIONSBOILING WATER REACTOR
TURBINE TRIP (TT) BENCHMARK
Volume I: Final Specifications
Revision 1 – October 2001
Corrections made to pages: 31, 32, 82, 83

byJorge Solis, Kostadin N. Ivanov and Baris Sarikaya
Nuclear Engineering Program
The Pennsylvania State University
University Park, PA, 16802 USA
Andy M. Olson and Kenneth W. Hunt
Exelon Nuclear
200 Exelon Way, KSA2-N
Kennett Square, PA, 19348 USA

NUCLEAR ENERGY AGENCY
ORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENT

FOREWORDThe OECD Nuclear Energy Agency (NEA has recently completed under US Nuclear Regulatory
Commission (NRC) sponsorship a PWR main steam line break (MSLB) benchmark against coupledsystem thermal-hydraulic and neutron kinetics codes. The benchmark was very well received
internationally. It was felt among the participants that there should be a similar benchmark against thecodes for a BWR plant transient. The turbine trip (TT) transients in a BWR are pressurisation events inwhich the coupling between core phenomena and system dynamics plays an important role. In addition,
the data made available from experiments carried out at the plant make the present benchmark very
valuable. The NEA and US NRC have approved it for the purpose of validating advanced systembest-estimate analysis codes. A small team at Pennsylvania State University (PSU) was responsible forauthoring the final specifications, and will be in charge of co-ordinating the benchmark activities,
answering the questions, analysing the solutions submitted by benchmark participants and providing
reports summarising the results for each phase. In performing these tasks the PSU team iscollaborating with Andy M. Olson and Kenneth W. Hunt from PECO Nuclear. Lance J. Agee, EPRI,
is also providing technical assistance for this international benchmark project.
Three benchmark workshops are scheduled during the course of the benchmark activities. The firstworkshop was conducted for the participants in the exercises concerning the BWR TT transient, andwas instrumental in finalising the benchmark specifications. It took place on 9-10 November 2000 in
Philadelphia and was hosted by Exelon Nuclear. The second workshop will focus on resolving issues
that may have arisen in the analyses of the first two exercises. Any topics related to the third exercise
will also be discussed. This workshop is scheduled for 15-16 October 2001 and will be hosted by the
Paul Scherrer Institut (PSI), Switzerland. The third and final workshop concerning this benchmark will
be conducted in May 2002 to resolve issues related to the third exercise, to address any outstanding
issues and to reach an agreement on the technical basis for the final reports. It is planned to be hosted
by the Institute for Safety Research, Rossendorf Research Centre, Germany.
The NEA-NRC BWR TT Benchmark will be published in four volumes as NEA and NUREG/CR
reports. CD-ROMs will also be prepared and will include the four reports and the transient boundary
conditions, decay heat values, as a function of time, cross-section libraries and supplementary tables
and graphs not published in the paper version. The transient boundary conditions, decay heat values
and the cross-section libraries can also be found at the benchmark ftp site:
Address: varna.me.psu.edu
Id: bwrtt
Password: tt2000

3

Acknowledgements
The authors would like to thank Professor J. Aragonés from UPM, Dr. T. Lefvert and
Dr. S. Langenbuch from GRS and Dr. F. Eltawila of US NRC, whose support and encouragement inestablishing this benchmark are invaluable.
This report is the sum of many efforts, the participants, the funding agencies and their staff – theUS Nuclear Regulatory Commission and the Organisation of Economic Co-operation andDevelopment. Special appreciation is due to: L. Agee from EPRI, Professor T. Downar from Purdue
University, B. Aktas from ISLINC, Dr. G. Gose and Dr. C. Peterson from CSA, Dr. A. Hotta from
TSI, Dr. P. Coddington from PSI and Dr. U. Grundmann from FZR. Their technical assistance,
comments and suggestions have been very valuable. We would like to thank them for the effort andtime involved.
Of particular note are the efforts of Dr. F. Eltawila assisted by Dr. J. Han and Dr. J. Uhle of the
US Nuclear Regulatory Commission. Through their efforts, funding is secured for the remainder ofthis project. We also thank them for their invaluable technical advice and assistance.
The authors wish to express their sincere appreciation for the outstanding support offered by
Dr. E. Sartori, who is providing efficient administration, organisation and valuable technical advice.
Finally, we are grateful to A. Costa for having devoted her competence and skills to the editing of
this report.

4

TABLE OF CONTENTS

Foreword ...........................................................................................................................................

3

Chapter 1 INTRODUCTION........................................................................................................ 11
1.1 Objectives............................................................................................................... 12
1.2 Definition of benchmark exercises......................................................................... 12
1.2.1 Exercise 1 – Power vs. time plant system simulation with fixed
axial power profile table.............................................................................. 12
1.2.2 Exercise 2 – Coupled 3-D kinetics/core thermal-hydraulicBC model and/or 1-D kinetics plant system simulation............................... 12
1.2.3 Exercise 3 – Best-estimate coupled 3-D core/T-H system modelling .......... 13
Chapter 2 CORE AND NEUTRONICS DATA .......................................................................... 15
2.1 General ................................................................................................................... 15
2.2 Core geometry and fuel assembly (FA) geometry ................................................. 15
2.3 Neutron modelling ................................................................................................. 15
2.4 Two-dimensional (2-D) assembly types and three-dimensional (3-D)
composition maps................................................................................................... 16
2.5 Cross-section library .............................................................................................. 16
2.6 Monitored point and average neutron fluxes in the reactor core............................ 17
2.7 Corrected average coolant density for feedback effects......................................... 18
Chapter 3 THERMAL-HYDRAULIC DATA............................................................................. 45
3.1 Component specifications for the full thermal-hydraulic system model................ 45
3.1.1 Reactor vessel .............................................................................................. 45
3.1.2 Reactor re-circulation system ...................................................................... 45
3.1.3 Core region .................................................................................................. 46

5

3.1.4 Steam lines ................................................................................................... 46
3.1.5 Feedwater lines............................................................................................ 46
3.2 Definition of the core thermal-hydraulic boundary conditions model ................... 47
3.3 Thermal-physical and heat transfer specifications ................................................. 47
3.3.1 Nuclear fuel (UO2-PuO2) properties ............................................................ 47
3.3.2 Gas gap conductance................................................................................... 49
3.3.3 Zircaloy cladding properties........................................................................ 49
Chapter 4 NEUTRONIC/THERMAL-HYDRAULIC COUPLING ......................................... 61
Chapter 5 TT PROBLEM ............................................................................................................. 63
5.1 Description of TT2 scenario................................................................................... 63
5.2 Initial steady state conditions ................................................................................. 64
5.3 Transient calculations............................................................................................. 64
Chapter 6 OUTPUT REQUESTED ............................................................................................. 71
6.1 Initial steady state results ....................................................................................... 71
6.2 Transient results ..................................................................................................... 72
6.3 Output format ......................................................................................................... 73
References ......................................................................................................................................... 77
Appendix A – Skeleton input deck..................................................................................................... 79
Appendix B – Sample cross-section table .......................................................................................... 87

6

List of figures
Figure 2.2.1.

Reactor core cross-sectional view............................................................................. 34

Figure 2.2.2.

PB2 initial fuel assembly lattice ............................................................................... 35

Figure 2.2.3.

PB2 reload fuel assembly lattice for 100 mil channels............................................. 36

Figure 2.2.4.

PB2 reload fuel assembly lattice for 120 mil channels............................................. 37

Figure 2.2.5.

PB2 reload fuel assembly lattice for LTA assemblies .............................................. 38

Figure 2.4.1.

PSU control rod grouping......................................................................................... 39

Figure 2.4.2.

Radial distribution of assembly types....................................................................... 40

Figure 2.5.1.

Fuel assembly orientation for ADF assignment ....................................................... 41

Figure 2.6.1.

Core orificing and TIP arrangement ......................................................................... 42

Figure 2.6.2.

Elevation of core components................................................................................... 43

Figure 3.1.1.1. PB2 RETRAN thermal-hydraulic model .................................................................. 56
Figure 3.1.2.1. Simplified TRAC-BF1 BWR jet pump model ......................................................... 57
Figure 3.2.1.

PB2 OECD/NRC TT vessel/core boundary conditions model ................................. 58

Figure 3.2.2.

PB2 reactor core thermal-hydraulic channel radial map........................................... 59

Figure 5.2.1.

PB2 TT2 initial control rod pattern........................................................................... 69

Figure 5.2.2.

PB2 HZP control rod pattern .................................................................................... 69

Figure 6.1.

Form for axial power distribution............................................................................. 74

Figure 6.2.

Form for radial power distribution............................................................................ 74

Figure A.1.

RETRAN nodalisation diagram................................................................................ 86

List of tables
Table 2.2.1.

PB2 fuel assembly data ............................................................................................... 19

Table 2.2.2.1. Assembly design 1 ...................................................................................................... 19
Table 2.2.2.2. Assembly design 2 ...................................................................................................... 20
Table 2.2.2.3. Assembly design 3 ...................................................................................................... 20

7

Table 2.2.2.4. Assembly design 4 ...................................................................................................... 20
Table 2.2.2.5. Assembly design 5 ...................................................................................................... 21
Table 2.2.2.6. Assembly design 6 ...................................................................................................... 21
Table 2.3.1.

Decay constant and fractions of delayed neutrons ...................................................... 21

Table 2.3.2.

Heavy-element decay heat constants........................................................................... 22

Table 2.4.1.1. Assembly design for Type 1 initial fuel ...................................................................... 22
Table 2.4.1.2. Assembly design for Type 2 initial fuel ...................................................................... 23
Table 2.4.1.3. Assembly design for Type 3 initial fuel ...................................................................... 24
Table 2.4.1.4. Assembly design for Type 4 8 × 8 UO2 reload ........................................................... 25
Table 2.4.1.5. Assembly design for Type 5 8 × 8 UO2 reload ........................................................... 26
Table 2.4.1.6. Assembly design for Type 6 8 × 8 UO2 reload, LTA.................................................. 27
Table 2.4.2.

Control rod data........................................................................................................... 28

Table 2.4.3.

Definition of assembly types.......................................................................................

Table 2.4.4.

Composition numbers in axial layer for each assembly type ...................................... 29

Table 2.5.1.

Range of variables ....................................................................................................... 30

Table 2.5.2.

Key to macroscopic cross-section tables..................................................................... 31

Table 2.5.3.

Macroscopic cross-section tables structure ................................................................. 31

Table 2.6.1.

Measured LPRMs for levels A, B, C and D................................................................ 33

28

Table 3.1.1.1. Reactor vessel design data........................................................................................... 50
Table 3.1.1.2. Peach Bottom 2 vessel fluid volumes.......................................................................... 51
Table 3.1.1.3. PB2 reference design information............................................................................... 52
Table 3.1.2.1. Reactor re-circulation system design characteristics................................................... 53
Table 3.1.2.2. PB2 BWR TRAC-BF1 simplified jet pump model..................................................... 54
Table 3.1.3.1. Core related hydraulic loss coefficients (inlet orifices)............................................... 54
Table 3.1.3.2. Fuel estimated loss coefficients................................................................................... 54
Table 3.1.3.3. Core related hydraulic leakage flows .......................................................................... 54

8

Table 3.1.4.1. Nuclear system safety and relief valves ...................................................................... 54
Table 3.1.4.2. Steam bypass design data............................................................................................ 55
Table 3.3.3.1. Specific heat of zircaloy versus temperature for T ≤ 1 248 K..................................... 55
Table 5.2.1.

PB2 TT2 initial conditions from process computer P1 edit ........................................ 65

Table 5.2.2.

PB2 TT2 initial core axial relative power from process computer P1 edit ................. 66

Table 5.2.3.

PB2 HZP initial conditions ......................................................................................... 66

Table 5.3.1.

TSV flow fraction vs. time .......................................................................................... 66

Table 5.3.2.

Bypass valve position vs. time .................................................................................... 67

Table 5.3.3.

Feedwater flow vs. time .............................................................................................. 67

Table 5.3.4.

PB2 TT2 scram characteristics.................................................................................... 67

Table 5.3.5.

CRD position after scram vs. time .............................................................................. 68

Table 5.3.6.

PB2 TT2 event timing (time delay in msec) ............................................................... 68

Table 5.3.7.

PB2 TT2 peak measured responses............................................................................. 68

Table 5.3.8.

TT2 test acquisition instrument time delays (in msec)................................................ 68

Table 6.3.1.

Sequence of events output........................................................................................... 75

9Chapter 1
INTRODUCTION

Incorporation of full three-dimensional (3-D) models of the reactor core into system transientcodes allows for a “best-estimate” calculation of interactions between the core behaviour and plant
dynamics. Recent progress in computer technology has made development of coupled system
thermal-hydraulic and neutron kinetics code systems feasible. Considerable efforts have been made invarious countries and organisations in this direction. To verify the capability of the coupled codes toanalyse complex transients with coupled core-plant interactions and to fully test thermal-hydrauliccoupling, appropriate light water reactor (LWR) transient benchmarks need to be developed on ahigher “best-estimate” level. The previous sets of transient benchmark problems separately addressed
system transients (designed mainly for thermal-hydraulic system codes with point kinetics models)and core transients (designed for thermal-hydraulic core boundary conditions models coupled with athree-dimensional (3-D) neutron kinetics model). The Nuclear Energy Agency (NEA) of theOrganisation for Economic Co-operation and Development (OECD) has recently completed – under
the auspices of the US Nuclear Regulatory Commission (NRC) – sponsorship of a PWR main steamline break (MSLB) benchmark [1] against coupled thermal-hydraulic and neutron kinetics codes.
A benchmark team from the Pennsylvania State University (PSU) has been responsible for developing
the benchmark specifications, assisting the participants and co-ordinating the benchmark activities.
The benchmark has been well received by the international community. The participants of the PWR
benchmark felt that there should be a similar benchmark against the codes for a BWR plant transient.
A turbine trip (TT) transient in a BWR is a pressurisation event in which the coupling between core
phenomena and system dynamics plays an important role. In addition, the available real plant
experimental data [2,3] makes the proposed benchmark problem very valuable. The NEA, OECD and
US NRC have approved a BWR TT benchmark for the purpose of validating advanced systembest-estimate analysis codes.
As a result, this benchmark project is being established to challenge the coupled system
thermal-hydraulic/neutron kinetics codes against a Peach Bottom 2 (a GE-designed BWR/4) turbine
trip transient with a sudden closure of the turbine stop valve. Three turbine trip transients at different
power levels were performed at the Peach Bottom (PB) 2 BWR/4 nuclear power plant (NPP) prior to
shutdown for refuelling at the end of Cycle 2 in April 1977. The second test is selected for thebenchmark problem to investigate the effect of the pressurisation transient (following the sudden
closure of the turbine stop valve) on the neutron flux in the reactor core. In a best-estimate manner thetest conditions approached the design basis conditions as closely as possible. The actual data werecollected, including a compilation of reactor design and operating data for Cycles 1 and 2 of PB andthe plant transient experimental data. The transient was selected for this benchmark because it is a
dynamically complex event for which neutron kinetics in the core were coupled withthermal-hydraulics in the reactor primary system.

11

1.1 Objectives
The BWR reference problem chosen for simulation is a turbine trip transient, which begins with asudden turbine stop valve (TSV) closure. The pressure oscillation generated in the main steam piping
propagates with relatively little attenuation into the reactor core. The induced core pressure oscillation
results in dramatic changes of the core void distribution and fluid flow. The magnitude of the neutron
flux transient taking place in the BWR core is strongly affected by the initial rate of pressure risecaused by pressure oscillation and has a strong spatial variation. The correct simulation of the power
response to the pressure pulse and subsequent void collapse requires a 3-D core modelling
supplemented by a one-dimensional (1-D) simulation of the remainder of the reactor coolant system.
The purpose of this proposal is to establish a BWR TT benchmark exercise based on a welldefined problem with a complete set of input specifications and reference experimental data for
qualification of the coupled 3-D neutron kinetics/thermal-hydraulic system transient codes. Since thiskind of transient is a dynamically complex event in which reactor variables change very rapidly,
it constitutes a good benchmark problem to test the coupled codes on both levels: neutronics/
thermal-hydraulic coupling and core/plant system coupling. Subsequently, the objectives of the
proposed benchmark are: comprehensive feedback testing and examination of the capability ofcoupled codes to analyse complex transients with coupled core/plant interactions through comparison
with actual experimental data.
1.2 Definition of the benchmark exercises
The benchmark consists of three separate exercises.
1.2.1 Exercise 1 – Power vs. time plant system simulation with fixed axial power profile table(obtained from experimental data)
The purpose of the first exercise is to test the thermal-hydraulic system response and to initialise
the participants’ system models. Core power response is fixed to reproduce the actual test results
utilising either power or reactivity vs. time data.
1.2.2 Exercise 2 – Coupled 3-D kinetics/core thermal-hydraulic BC model and/or 1-D kinetics plantsystem simulation
Two steady states are to be modelled for Exercise 2: hot zero power (HZP) conditions and theinitial conditions of TT2. The HZP state would provide a clean initialisation of the core neutronics
models since the thermal-hydraulic feedback is spatially uniform across the core. The description of
HZP conditions is provided in Chapter 3.
The second exercise consists of two options. Option 1 of the second exercise is to perform a
coupled 3-D kinetics/thermal-hydraulic calculation for the reactor core using the PSU-provided
boundary conditions at core inlet and exit. The core boundary conditions will be provided utilising a
combination of the calculated PSU results and test data. Option 2 of the second exercise is to perform
coupled 1-D neutron kinetics/thermal-hydraulics core boundary condition model calculation for thecore using the same boundary conditions provided for Option 1. One-dimensional cross-sections arecollapsed from the cross-section libraries generated for 3-D simulation. The participants canparticipate in either or both options.

121.2.3 Exercise 3 – Best-estimate coupled 3-D core/thermal-hydraulic system modelling
The third exercise also consists of two options. In Option 1 the participants perform a coupled
3-D core/thermal-hydraulic calculation for the core and 1-D thermal-hydraulics modelling for thebalance of the plant. In Option 2 the participants perform the calculation using a 1-D kinetics coremodel and 1-D thermal-hydraulics for the reactor primary system. This exercise combines elements ofthe first two exercises of this benchmark and is an analysis of the transient in its entirety.
Extreme versions of Exercise 3 that provide the opportunity to better test the code coupling andfeedback modelling are defined as follows:•

Turbine trip without bypass system relief opening (would increase the power peak andprovide enough pressurisation for safety/relief valve opening).

•

Turbine trip without scram (would increase the power peak and produce a second power peak
and would be a challenge to the coupled code predictions).

•

Combined extreme scenario – turbine trip with bypass system relief failure without reactor
scram. Some preliminary results indicate that this case is very close to a super-prompt criticalstate and makes a good case for code-to-code comparisons.

The initial steady state reference results will be based on those provided from the P-1 processcomputer power distribution data in the EPRI reports [2]. For the TT2 transient test [3], the dynamic
measurements were taken with high-speed digital acquisition system capable of sampling over
150 signals every 6 milliseconds. The core power distribution measurements were taken from theplant’s local in-core flux detectors. Special fast response pressure and differential pressure transducers
were installed in parallel with the existing plant instruments in the nuclear steam supply system.
The TT transient scenario is based on the TT2 test, as discussed in the reference EPRI reports. In thisTT transient, the nuclear power is driven by the increase in pressure, which causes a void collapse in
the core. The positive power response is almost immediate, but the transient is soon slowed down by
the feedback from the increased direct and conducted heat flux to the coolant, which will, in turn,produce void and provide a negative reactivity feedback. The scram is triggered at a defined power
level (as a multiple of the initial power). Since the transient is fast and of short duration, the fueltemperature rise is moderate and the Doppler effect plays a subordinate role compared to otherfeedback effects. The complete TT scenario is described along with a set of initial and boundary
conditions in Chapter 5. Transient simulations will be initiated from 0-5 seconds, and within this time
the sequence of events, core exit pressure response, total core power response and other integral
parameters will be compared to the experimental data. For the extreme versions of Exercise 3,
transient simulations should be performed for 10 seconds to capture the thermal-hydraulic response of
these cases. The radial and axial power distributions at different detector levels and positions will also
be compared. In addition there will be some code-to-code comparisons for the transient behaviour ofother key thermal-hydraulic parameters such as core average fuel temperature and core average void
fraction as well as 2-D normalised power (NP) distribution and core average axial power distribution.

13

Chapter 2
CORE AND NEUTRONICS DATA

2.1 General
The reference design for the BWR is derived from real reactor, plant and operation data for the
PB2 BWR/4 NPP and it is based on the information provided in EPRI reports and some additionalsources such as the PECO Energy Topical Report [4]. This chapter specifies the core and neutronic
data to be used in all the calculations.
2.2 Core geometry and fuel assembly (FA) geometry
The radial geometry of the reactor core is shown in Figure 2.2.1. Radially, the core is divided into
cells 15.24 cm wide, each corresponding to one fuel assembly (FA), plus a radial reflector (shaded
area of Figure 2.2.1) of the same width. There are a total of 888 assemblies, 764 FA and 124 reflector
assemblies. Axially, the reactor core is divided into 26 layers (24 core layers plus top and bottom
reflectors) with a constant height of 15.24 cm (including reflector nodes). The total active core heightis 365.76 cm. The axial nodalisation accounts for material changes in the fuel design and for exposureand history variations. Geometric data for the FA and fuel rod is provided in Table 2.2.1. Data fordifferent assembly designs is given in Tables 2.2.2.1 through 2.2.2.6. Fuel assembly lattice drawings,
including detailed dimensions, for initial fuel, reload fuel with 100 and 120 mil channels and the leadtest assemblies (LTA) are shown in Figures 2.2.2 through 2.2.5. The numbers 100 and 120 refer to thewall thickness of the channel (1 mil = 0.001 inches).
The core loading during the test was as follows: 576 fuel assemblies were the original 7 × 7 typefrom Cycle 1 (C1), and the remaining 188 were a reload of 8 × 8 fuel assemblies. One hundred andeighty-five control rods provided reactivity control. To build the participant’s given neutronic model,
these control rods can be grouped according to their initial insertion position (see Chapter 5,
Figure 5.2.1). The control rod grouping used by PSU to perform reference calculations is presented in
Figure 2.4.1.
2.3 Neutron modelling
Two prompt and six delayed neutron groups are modelled. The energy release per fission for thetwo prompt neutron groups is 0.3213 × 10–10 and 0.3206 × 10–10 W-s/fission, and this energy release isconsidered to be independent of time and space. It is assumed that 2% of fission power is released as
direct gamma heating for the in-channel coolant flow and 1.7% for the bypass flow. Table 2.3.1 shows
global core-wide decay time constants and fractions of delayed neutrons. In addition delayedparameters are provided in the cross-section library for each of the compositions shown in Table 2.4.4.
The prompt neutron lifetime is 0.45085E-04.

15

It is recommended that ANS-79 be used as a decay heat standard model. In total 71 decay heatgroups are used: 69 groups are used for the three isotopes 235U, 239Pu and 238U with the decay heatconstants defined in the 1979 ANS standard; plus, the heavy-element decay heat groups for 239U and239
Np are used with constants given in Table 2.3.2. It is recommended that the participants also use theassumption of an infinite operation at a power of 3 293 MWt. For participants who are not capable ofusing the ANS-79 decay heat standard, a file of the decay heat evolution throughout the transient isprovided on CD-ROM and at the benchmark ftp site under the directory Decay-Heat. These predictions
are obtained using the PSU coupled code results. The effective decay heat energy fraction of the total
thermal power (the relative contribution in the steady state) is equal to 0.065583.
2.4 Two-dimensional (2-D) assembly types and three-dimensional (3-D) composition maps
Nineteen assembly types are contained within the core geometry. There are 435 compositions.
The corresponding sets of cross-sections are provided. Each composition is defined by material
properties (due to changes in the fuel design) and burn-up. The burn-up dependence is a three-component
vector of variables: exposure (GWd/t), spectral history (void fraction) and control rod history.
Assembly designs are defined in Tables 2.4.1.1 through 2.4.1.6. Control rod geometry data is provided
in Table 2.4.2. The definition of assembly types is shown in Table 2.4.3. The radial distribution ofthese assembly types within the reactor geometry is shown in Figure 2.4.2. The axial locations ofcompositions for each assembly type are shown in Table 2.4.4.
2.5 Cross-section library
A complete set of diffusion coefficients, macroscopic cross-sections for scattering, absorption,and fission, assembly discontinuity factors (ADFs), as a function of the moderator density and fueltemperature is defined for each composition. The group inverse neutron velocities are also provided
for each composition. Dependence of the cross-sections on the above variables is specified through a
two-dimensional table look-up. Each composition is assigned to a cross-section set containing separate
tables for the diffusion coefficients and cross-sections, with each point in the table representing a
possible core state. The expected range of the transient is covered by the selection of an adequate
range for the independent variables shown in Table 2.5.1. Specifically, Exercise 1 was used forselecting the range of thermal-hydraulic variables. A steady state calculation was run using the
TRAC-BF1 code and initial conditions of the second turbine trip for choosing discrete values of thethermal-hydraulic variables (pressure, void fraction and coolant/moderator temperature). A transient
calculation was performed to determine the expected range of change of the above variables.
A modified linear interpolation scheme (which includes extrapolation outside the thermal-hydraulicrange) is used to obtain the appropriate total cross-sections from the tabulated ones based on the reactor
conditions being modelled. Table 2.5.2 shows the definition of a cross-section table associated with acomposition. Table 2.5.3 shows the macroscopic cross-section table structure for one cross-section set.
All cross-section sets are assembled into a cross-section library. The cross-sections are provided inseparate libraries for rodded (nemtabr) and un-rodded compositions (nemtab). The format of eachlibrary is as follows:•

The first line of data is shows the number of data points used for the independent
thermal-hydraulic parameters. The parameters used in this benchmark include fuel temperatureand moderator density.

•

Each cross-section set is in the order shown in Table 2.5.3. Each table is in the format
described in Table 2.5.2. More detailed information on this format is presented in Appendix B.
16

First, the values of the independent thermal-hydraulic parameters (fuel temperature andmoderator density) used to specify that particular set of cross-sections are listed, followed by
the values of the cross-sections* and ADFs. Since there is one-half symmetry for all theassembly designs, two ADFs per composition per energy group are provided – West (widegap) and South (narrow gap). Because the fuel assembly designs employed in PB2 core
design have one-half symmetry, it is assumed that North is equal to West and East is equal toSouth (e.g. Figure 2.5.1). Detector parameters† are included after the two-group cross-sections
followed by the delayed neutron parameters for six groups. Finally, the group inverse neutron
velocities complete the data for a given cross-section set.
•

The dependence on fuel temperature in the reflector cross-section tables is also modelled.
This is because the reflector cross-sections are generated by performing lattice physics
transport calculations, including the next fuel region. In order to simplify the reflector
feedback modelling the following assumptions are made for this benchmark: an average fueltemperature value equal to 550 K is used for the radial reflector cross-section modelling inboth the initial steady state and transient simulations, and the average coolant density for theradial reflector is equal to the inlet coolant density. For the axial reflector regions thefollowing assumptions are made: for the bottom, the fuel temperature is equal to the inlet
coolant temperature (per thermal-hydraulic channel or cell) and the coolant density is equal tothe inlet coolant density (again per channel); for the top, the fuel temperature is equal to theoutlet coolant temperature (per channel) and the coolant density is equal to the outlet coolant
density (per channel).

All cross-section data, along with a program for linear interpolation, are supplied on CD-ROM
and at the benchmark ftp site under the directory XS-Lib in the format described above.
For the generation of 1-D cross-sections, each plane is treated as a different composition and eachplanar cross-section is obtained from a 3-D coupled code steady state calculation. Since thesecross-sections are functions of thermal-hydraulic state parameters such as moderator density and fueltemperature, several 3-D calculations are performed to generate planar cross-sections at various
thermal-hydraulic states in order to cover the range of thermal-hydraulic conditions encountered under
the simulated transient. The planar cross-sections are then functionalised for the use of 1-D
calculations. Two cross-section libraries for both TRAC and RETRAN 1-D cross-section formats are
generated for performing 1-D kinetics calculations. These libraries are also located at the benchmark
site under XS-Lib directory. They are also provided on the CD-ROM.
2.6 Monitored point and average neutron fluxes in the reactor core
BWR LPRM response model
For the purpose of comparing the three-dimensional (3-D) power distribution provided
experimentally by local power range monitor (LPRM) measurements during PB2 TT2, the following
LPRM response model could be implemented in the 3-D neutronics code:
R LPRM ( x , y, z) =2

∑φglobalector( x , y, z) ⋅ φ gbundle ( x , y, z) ⋅ σ det
g
g

g =1

* Please note that the provided absorption cross-sections already take the xenon thermal cross-sections into account;however, at the participants’ request, the thermal macro and micro xenon cross-sections are listed in the cross-section sets.
†
Detector parameters are described in Section 2.6.

17

where φ global( x , y, z) is the homogeneous flux from the 3-D kinetics global solution extrapolated at thegdetector location. It could be obtained from the global core neutronics calculation by extrapolating theflux function to the detector location based on the specific code solution method.
φ gbundle ( x , y, z) is the single assembly detector factor which is the ratio between the flux in thedetector location and the average flux of the neutronic cell (from lattice CASMO calculation):
φ gbundle ( x , y, z) =φ det ector ,lattice ( x , y, z),lattice
φ avg
g

ector
where σ det
is the microscopic fission cross-section for fissile material of the fission chamber.
g

Microscopic cross-sections of the fission material and the detector factors are provided incross-section tables as described in Section 2.5. The detector responses of the surrounding four
neutronic nodes are derived independently and then averaged. The CASMO lattice calculation uses
235
U as the fission chamber fissile material. By default, the detector position is in the Southeast (SE)corner of the fuel assembly as shown below:
NW

NE

SW

SE
Detector
location

BWR fuel assembly

Experimental flux measurements
The PB2 reactor core is equipped with local neutron flux measurement instruments that are called
local power range monitors (LPRMs). There are a total of 43 instrument tubes that are located radiallyaccording to Figure 2.6.1. Within each instrument tube, the LPRMs are located at four axial levels:
Level A, Level B, Level C and Level D, which are axially located from bottom to top of the active fuellength at 18, 54, 90 and 120 inches, respectively. The axial location of the above levels is shown in
Figure 2.6.2. Co-ordinates for radial location are presented in Table 2.6.1. The pair of numbers shownin Table 2.6.1 represents the (X,Y) location in a Cartesian co-ordinate system as it is shown in
Figure 2.6.1. There were a total of 80 monitored points (20 per each axial level) during TT2 transient.
Therefore, comparisons can be performed between local experimental measured fluxes and code
predictions as the average of each axial level (A, B, C and D).
2.7 Corrected average coolant density for feedback effects
Lattice physics calculations are performed by homogenising the fuel lattice and the bypass flow
associated with it. When obtaining the average coolant density, a correction that accounts for the18

bypass channel conditions should be included since this is going to influence the feedback effect on
the cross-section calculation through the average coolant density. The following approach should beapplied:
ρ eff
act =

(

A act ρ act + A byp ρ byp − ρ sat

)

A act

where ρ eff
act is the effective average coolant density for cross-section calculation, ρbyp is the averagemoderator coolant density of the bypass channel, ρsat is the saturated moderator coolant density of the
bypass channel, Aact is flow cross-sectional area of the active heated channel and Abyp is the flowcross-sectional area of the bypass channel.
Bypass conditions should be obtained by adding a bypass channel to represent the core bypass
region in the thermal-hydraulic model.
Table 2.2.1. PB2 fuel assembly data

1
168
0
7×7
6.0
0.738
49
0
0
7
0.102
0.537
1.625

2
263
261
7×7
6.0
0.738
49
0
4
7
0.102
0.537
1.625

3
333
315
7×7
6.0
0.738
49
0
5
7
0.102
0.537
1.625

4
0
68
8×8
6.0
0.640
63
1
5
7
0.102
0.614
1.625

5
0
116
8×8
6.0
0.640
63
1
5
7
0.102
0.614
1.625

LTA
special
6
0
4
8×8
6.0
0.640
62
2
5
7
0.102
0.614
1.625

0
222.44
222.44441
212.21212.65547
212.06212.61490
207.78208.27328
208.0
208.33313
207.14207.45Initial load
Assembly typeNo. of assemblies, initial core
No. of assemblies, Cycle 2
Geometry
Assembly pitch, in
Fuel rod pitch
Fuel rods per assembly
Water rods per assembly
Burnable poison positions
No. of spacer grids
Inconel per grid, lb
Zr-4 per grid, lb
Spacer width, in
Assembly average fuel composition:
Gd2O3, g
UO2, kg
Total fuel, kg

ReloadReloadTable 2.2.2.1. Assembly design 1
Rod
type

Number of
rods

1
2
2s

31
17
01

Pellet density
UO2
UO2+Gd2O3(g/cm3)(g/cm3)
10.42
10.42
10.42

Stack
density(g/cm3)
10.34
10.34
10.34

Gd2O3
(g)

UO2
(g)

0
0
0

4 548
4 548
4 140

Pellet outer diameter = 1.23698 cm.
Cladding = Zircaloy-2, 1.43002 cm outer diameter × .08128 cm wall thickness, all rods.
Gas plenum length = 40.64 cm.

19

Stack
length(cm)
365.76365.76330.2

Table 2.2.2.2. Assembly design 2
Rod
type

Number of
rods

1
1s
2
3
4
5A
6B

25
1
12
6
1
3
1

Pellet density
UO2
UO2+Gd2O3(g/cm3)(g/cm3)
10.42
–
10.42
–
10.42
–
10.42
–
10.42
–
–
10.29
10.42
10.29

Stack
density(g/cm3)
10.32
10.32
10.32
10.32
10.32
10.19
10.27

Gd2O3
(g)

UO2
(g)

0
0
0
0
0
129
54

4 352
3 935
4 352
4 352
4 352
4 171
4 277

Stack
length(cm)
365.76330.20365.76365.76365.76365.76365.76Pellet outer diameter = 1.21158 cm.
Cladding = Zircaloy-2, 1.43002 cm outer diameter × .09398 cm wall thickness, all rods.
Gas plenum length = 40.132 cm.

Table 2.2.2.3. Assembly design 3
Rod
type

Number of
rods

1
2
3
4
5A
6C
7E
8D

26
11
6
1
2
1
1
1

Pellet density
UO2
UO2+Gd2O3
3(g/cm )
(g/cm3)
10.42
–
10.42
–
10.42
–
10.42
–
–
10.29
–
10.29
10.42
10.25
10.42
10.25

Stack
density(g/cm3)
10.32
10.32
10.32
10.32
10.19
10.19
10.28
10.19

Gd2O3
(g)

UO2
(g)

0
0
0
0
129
117
43
129

4 352
4 352
4 352
4 352
4 171
3 771
4 292
4 172

Stack
length(cm)
365.76365.76365.76365.76365.76330.20365.76365.76Pellet outer diameter = 1.21158 cm.
Cladding = Zircaloy-2, 1.43002 cm outer diameter × .09398 cm wall thickness, all rods.
Gas plenum length = 40.132 cm.

Table 2.2.2.4. Assembly design 4
Rod
type

Number of
rods

1
2
3
4
5
WS

39
14
4
1
5
1

Pellet density
UO2
UO2+Gd2O3(g/cm3)(g/cm3)
10.42
–
10.42
–
10.42
–
10.42
–
–
10.29
–
–

Stack
density(g/cm3)
10.32
10.32
10.32
10.32
10.19
–

Gd2O3
(g)

UO2
(g)

0
0
0
0
98
0

3 309
3 309
3 309
3 309
3 172
0

Pellet outer diameter = 1.05664 cm.
Cladding = Zircaloy-2, 1.25222 cm outer diameter × .08636 cm wall thickness, all rods.
Gas plenum length = 40.64 cm except water rod.
Gd2O3 in rod type 5 runs full 365.76 cm.
Water rod (WS) has holes drilled top and bottom to provide water flow and little or no boiling.
Water rod is also a spacer positioning rod.

20

Stack
length(cm)
365.76365.76365.76365.76365.76–

Table 2.2.2.5. Assembly design 5
Rod
type

Number of
rods

1
2
3
4
5
WS

39
14
4
1
5
1

Pellet density
UO2
UO2+Gd2O3(g/cm3)(g/cm3)
10.42
–
10.42
–
10.42
–
10.42
–
–
10.33
–
–

Stack
density(g/cm3)
10.32
10.32
10.32
10.32
10.23
–

Gd2O3
(g)

UO2
(g)

0
0
0
0
66
0

3 309
3 309
3 309
3 309
3 216
0

Stack
length(cm)
365.76365.76365.76365.76365.76–Pellet outer diameter = 1.05664 cm.
Cladding = Zircaloy-2, 1.25222 cm outer diameter × .08636 cm wall thickness, all rods.
Gas plenum length = 40.64 cm, except water rod.
Gd2O3 in rod type 5 runs full 365.76 cm.
Water rod (WS) has holes drilled top and bottom to provide water flow and little or no boiling.
Water rod is also a spacer positioning rod.

Table 2.2.2.6. Assembly design 6
Rod
type

Number of
rods

1
2
3
4
5
WR,WS
ENDS

38
14
4
1
5
2
62

Pellet density
UO2
UO2+Gd2O3(g/cm3)(g/cm3)
10.42
–
10.42
–
10.42
–
10.42
–
–
10.33
–
–
10.42
–

Stack
density(g/cm3)
10.32
10.32
10.32
10.32
10.23
–
10.32

Gd2O3
(g)

UO2
(g)

0
0
0
0
63
0
0

3 125
3 125
3 125
3 125
3 037
0
223

Pellet outer diameter = 1.0414 cm.
Cladding = Zircaloy-2, 1.22682 cm outer diameter × .08128 cm wall thickness, all fuelled rods.
= Zircaloy-2, 1.50114 cm outer diameter × .07620 cm wall thickness, water rods.
Gas plenum length = 24.0792 cm.
Gd2O3 in rod type 5 runs full 355.6 cm.
Water rod (WS) has holes drilled top and bottom to provide water flow and little or no boiling.
Water rod is also a spacer positioning rod.

Table 2.3.1. Decay constant and fractions of delayed neutrons
Group

Decay constant (s–1)

1
2
3
4
5
6

0.012813
0.031536
0.124703
0.328273
1.405280
3.844728

Relative fraction ofdelayed neutrons in %0.01670.11340.10220.21520.08370.0214

Total fraction of delayed neutrons: 0.5526%.

21

Stack
length
(cm)
355.6
355.6
355.6
355.6
355.6
–
25.4

Table 2.3.2. Heavy-element decay heat constants
Group no.
(isotope)
70 (239U)
71 (239Np)

Decay constant(s–1)
4.91 × 10–4
3.41 × 10–6

Available energy froma single atom (MeV)
0.474
0.419

Table 2.4.1.1. Assembly design for Type 1 initial fuelRod type
1
2

23

U (wt.%)
1.33
0.71

Gd2O3 (wt.%)
0022

No. of rods
31
18

Table 2.4.1.2. Assembly design for Type 2 initial fuelRod type
1
2
3
4
5A
6B

235

U (wt.%)
2.93
1.94
1.69
1.33
2.93
2.93

Gd2O3 (wt.%)
0
0
0
0
3.0
3.0

23

No. of rods
26
12
6
1
3
1

Table 2.4.1.3. Assembly design for Type 3 initial fuelRod type
1
2
3
4
5A
6C
7E
8D

235

U (wt.%)
2.93
1.94
1.69
1.33
2.93
2.93
2.93
1.94

Gd2O3 (wt.%)
0
0
0
0
3.0
3.0
4.0
4.0

24

No. of rods
26
11
6
1
2
1
1
1

Table 2.4.1.4. Assembly design for Type 4 8 × 8 UO2 reload
Rod type
1
2
3
4
5
WS

235

U (wt.%)
3.01
2.22
1.87
1.45
3.01
–

Gd2O3 (wt.%)
0
0
0
0
3.0
0

WS – Spacer positioning water rod.
G – Gadolinium rods.

25

No. of rods
39
14
4
1
5
1

Table 2.4.1.5. Assembly design for Type 5 8 × 8 UO2 reload
Rod type
1
2
3
4
5
WS

235

U (wt.%)
3.01
2.22
1.87
1.45
3.01
–

Gd2O3 (wt.%)
0
0
0
0
2.0
0

WS – Spacer positioning water rod.
G – Gadolinium rods.

26

No. of rods
39
14
4
1
5
1

Table 2.4.1.6. Assembly design for Type 6 8 × 8 UO2 reload, LTA
Rod type
1
2
3
4
5
WS
WR

235

U (wt.%)
3.01
2.22
1.87
1.45
3.01
–
–

Gd2O3 (wt.%)
0
0
0
0
2.0
0
0

WS – Spacer positioning water rod.
WR – Water rod.
G – Gadolinium rods.

27

No. of rods
38
14
4
1
5
1
1

Table 2.4.2. Control rod data
Movable control rods

Shape
Pitch, cm
Stroke, cm
Control length, cm
Control material
Material density
Number of control material tubes per rod
Tube dimensions
Control blade half span, cm
Control blade full thickness, cm
Control blade tip radius, cm
Sheath thickness, cm
Central structure wing length, cm
Blank tubes per wing

Cruciform
30.48
365.76363.22B4C granules in Type-304, stainless steel tubes and sheath
70% of theoretical
84.47752 cm outer diameter by .0635 cm wall
12.3825.79248.39624.14224
1.98501
None

Table 2.4.3. Definition of assembly types
Assembly type
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19

Assembly design(see Tables 2.4.1.1 through 2.4.1.6)
5
4
5
6
2
2
2
2
2
2
3
2
3
2
3
2
3
2
Reflector

28

29

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26

1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19
433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433
1 25 49 73 97 121 145 169 193 217 241 265 289 313 337 361 385 409 435
2 26 50 74 98 122 146 170 194 218 242 266 290 314 338 362 386 410 435
3 27 51 75 99 123 147 171 195 219 243 267 291 315 339 363 387 411 435
4 28 52 76 100 124 148 172 196 220 244 268 292 316 340 364 388 412 435
5 29 53 77 101 125 149 173 197 221 245 269 293 317 341 365 389 413 435
6 30 54 78 102 126 150 174 198 222 246 270 294 318 342 366 390 414 435
7 31 55 79 103 127 151 175 199 223 247 271 295 319 343 367 391 415 435
8 32 56 80 104 128 152 176 200 224 248 272 296 320 344 368 392 416 435
9 33 57 81 105 129 153 177 201 225 249 273 297 321 345 369 393 417 435
10 34 58 82 106 130 154 178 202 226 250 274 298 322 346 370 394 418 435
11 35 59 83 107 131 155 179 203 227 251 275 299 323 347 371 395 419 435
12 36 60 84 108 132 156 180 204 228 252 276 300 324 348 372 396 420 435
13 37 61 85 109 133 157 181 205 229 253 277 301 325 349 373 397 421 435
14 38 62 86 110 134 158 182 206 230 254 278 302 326 350 374 398 422 435
15 39 63 87 111 135 159 183 207 231 255 279 303 327 351 375 399 423 435
16 40 64 88 112 136 160 184 208 232 256 280 304 328 352 376 400 424 435
17 41 65 89 113 137 161 185 209 233 257 281 305 329 353 377 401 425 435
18 42 66 90 114 138 162 186 210 234 258 282 306 330 354 378 402 426 435
19 43 67 91 115 139 163 187 211 235 259 283 307 331 355 379 403 427 435
20 44 68 92 116 140 164 188 212 236 260 284 308 332 356 380 404 428 435
21 45 69 93 117 141 165 189 213 237 261 285 309 333 357 381 405 429 435
22 46 70 94 118 142 166 190 214 238 262 286 310 334 358 382 406 430 435
23 47 71 95 119 143 167 191 215 239 263 287 311 335 359 383 407 431 435
24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 435
434 434 434 434 434 434 434 434 434 434 434 434 434 434 434 434 434 434 434

Table 2.4.4. Composition numbers in axial layer for each assembly type

Table 2.5.1. Range of variables
T Fuel
(°K)
400.0
800.0
1 200.0
1 600.0
2 000.0
2 400.0
400.0
800.0
1 200.0
1 600.0
2 000.0
2 400.0
400.0
800.0
1 200.0
1 600.0
2 000.0
2 400.0
400.0
800.0
1 200.0
1 600.0
2 000.0
2 400.0
400.0
800.0
1 200.0
1 600.0
2 000.0
2 400.0
400.0
800.0
1 200.0
1 600.0
2 000.0
2 400.0

Rho M.
(kg/m3)141.595
141.595
141.595
141.595
141.595
141.595
226.154226.154226.154226.154226.154226.154299.645299.645299.645299.645299.645299.645435.045435.045435.045435.045435.045435.045599.172599.172599.172599.172599.172599.172779.405
779.405
779.405
779.405
779.405
779.405

30

Table 2.5.2. Key to macroscopic cross-section tables
Tf1

Tf2

Tf3

Tf4

Tf5

Tf6

ρm1

ρm2

ρm3

ρm4

ρm5

ρm6

Σ1

Σ2

...
...

Where:– Tf is the Doppler (fuel) temperature (°K)– ρm is the moderator density (kg/m3)

Σ34

Σ35

Σ36

Macroscopic cross-sections are in units of cm–1

Table 2.5.3. Macroscopic cross-section tables structure*************************************************************************
Cross-Section Table Input**
T FuelRho Mod.
66************ X-Section Set ##*************************************************************************
Group No. 1************** Diffusion Coefficient Table************** Absorption X-Section Table************** Fission X-Section Table************** Nu-Fission X-Section Table************** Scattering From Group 1 to 2 X-Section Table************** Assembly Disc. Factor Table - W************** Assembly Disc. Factor Table - S************** Detector Flux Ratio Table************** Detector Microscopic Fission X-Section Table*31

*************************************************************************
Group No. 2************** Diffusion Coefficient Table************** Absorption X-Section Table************** Fission X-Section Table************** Nu-Fission X-Section Table************** Xe Macroscopic X-Section Table************** Xe Microscopic X-Section Table************** Assembly Disc. Factor Table - W************** Assembly Disc. Factor Table - S************** Detector Flux Ratio Table************** Detector Microscopic Fission X-Section Table************** Detector Flux Ratio Table (not energy group dependent)************** Detector Microscopic Fission X-Section Table (not energy group dependent)************** Effective Delayed Neutron Yield in Six Groups************** Decay Constants for Delayed Neutron Groups************** Inv. Neutron Velocities*

32

Table 2.6.1. Measured LPRMs for levels A, B, C and D
Co-ordinates for radial location (see Figure 5.4.2)
08-17
08-25
08-33
08-49
16-33
16-49
16-57
24-17
24-25
24-41
32-09
32-33
32-41
32-57
40-33
40-41
48-25
48-49
56-25
56-33

33

Figure 2.2.1. Reactor core cross-sectional view34

Figure 2.2.2. PB2 initial fuel assembly latticeDim. ID
A
B
C
Dim. (in) 12.00 c5.27800 0.3750
Dim. (cm) 30.48 13.40612 0.9525
Dim. ID
K
L
M
Dim. (in)0.18700
Dim. (cm)
0.47498

D

N

E
F
G
H
0.0800 0.1750 0.14350 0.73800
0.2032 0.4445 0.36449 1.87452
O
P
Q
R

35

I

S
0.38000.9652

J

Figure 2.2.3. PB2 reload fuel assembly lattice for 100 mil channels

Dim. ID
A
B
C
Dim. (in) 12.00 05.27800 0.3550
Dim. (cm) 30.48 13.40612 0.9017
Dim. ID
K
L
M
Dim. (in)0.16700
Dim. (cm)0.42418

D

N

E
F
G
0.100 0.14700 0.15300
0.254 0.37338 0.38862
O
P
Q

36

H
0.64001.6256R

I

S
0.38000.9652

J

Figure 2.2.4. PB2 reload fuel assembly lattice for 120 mil channels

Dim. ID
A
B
C
Dim. (in) 12.00 05.27800 0.3550
Dim. (cm) 30.48 13.40612 0.8509
Dim. ID
K
L
M
Dim. (in)0.14700
Dim. (cm)0.42418

D

N

E
F
G
0.1200 0.14700 0.15300
0.3048 0.37338 0.38862
O
P
Q

37

H
0.64001.6256R

I

S
0.38000.9652

J

Figure 2.2.5. PB2 reload fuel assembly lattice for LTA assemblies

Dim. ID
A
B
C
Dim. (in) 12.00 05.27800 0.3550
Dim. (cm) 30.48 13.40612 0.9017
Dim. ID
K
L
M
Dim. (in)0.16700
Dim. (cm)0.42418

D

N

E
F
G
0.100 0.15700 0.15800
0.254 0.39878 0.40132
O
P
Q

38

H
0.64001.6256R

I

S
0.38000.9652

J

39

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0

0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0

0
0
1
1
1
1
4
4
1
1
3
3
1
1
4
4
1
1
1
1
0
0

0
0
0
1
1
1
1
4
4
1
1
3
3
1
1
4
4
1
1
1
1
0
0
0

0
0
0
1
1
1
1
8
8
1
1
6
6
1
1
6
6
1
1
8
8
1
1
1
1
0
0
0

0
0
0
1
1
1
1
8
8
1
1
6
6
1
1
6
6
1
1
8
8
1
1
1
1
0
0
0

0
0
1
1
1
1
2
2
1
1
3
3
1
1
5
5
1
1
3
3
1
1
2
2
1
1
1
1
0
0

0
0
0
1
1
1
1
2
2
1
1
3
3
1
1
5
5
1
1
3
3
1
1
2
2
1
1
1
1
0
0
0

0
1
1
1
1
8
8
1
1
6
6
1
1
7
7
1
1
7
7
1
1
6
6
1
1
8
8
1
1
1
1
0

0
1
1
1
1
8
8
1
1
6
6
1
1
7
7
1
1
7
7
1
1
6
6
1
1
8
8
1
1
1
1
0

0
1
1
4
4
1
1
3
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
3
1
1
4
4
1
1
0

0
1
1
4
4
1
1
3
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
3
1
1
4
4
1
1
0

0
1
1
1
1
6
6
1
1
7
7
1
1
5
5
1
1
5
5
1
1
7
7
1
1
6
6
1
1
1
1
0

0
1
1
1
1
6
6
1
1
7
7
1
1
5
5
1
1
5
5
1
1
7
7
1
1
6
6
1
1
1
1
0

0
1
1
3
3
1
1
5
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
5
1
1
3
3
1
1
0

0
1
1
3
3
1
1
5
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
5
1
1
3
3
1
1
0

0
1
1
1
1
6
6
1
1
7
7
1
1
5
5
1
1
5
5
1
1
7
7
1
1
6
6
1
1
1
1
0

0
1
1
1
1
6
6
1
1
7
7
1
1
5
5
1
1
5
5
1
1
7
7
1
1
6
6
1
1
1
1
0

0
1
1
4
4
1
1
3
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
3
1
1
4
4
1
1
0

0
1
1
4
4
1
1
3
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
3
1
1
4
4
1
1
0

Figure 2.4.1. PSU control rod grouping
0
1
1
1
1
8
8
1
1
6
6
1
1
7
7
1
1
7
7
1
1
6
6
1
1
8
8
1
1
1
1
0

0
1
1
1
1
8
8
1
1
6
6
1
1
7
7
1
1
7
7
1
1
6
6
1
1
8
8
1
1
1
1
0

0
0
0
1
1
1
1
2
2
1
1
3
3
1
1
5
5
1
1
3
3
1
1
2
2
1
1
1
1
0
0
0
0
0
1
1
1
1
2
2
1
1
3
3
1
1
5
5
1
1
3
3
1
1
2
2
1
1
1
1
0
0
0
0
0
1
1
1
1
8
8
1
1
6
6
1
1
6
6
1
1
8
8
1
1
1
1
0
0
0

0
0
0
1
1
1
1
8
8
1
1
6
6
1
1
6
6
1
1
8
8
1
1
1
1
0
0
0
0
0
0
1
1
1
1
4
4
1
1
3
3
1
1
4
4
1
1
1
1
0
0
0
0
0
1
1
1
1
4
4
1
1
3
3
1
1
4
4
1
1
1
1
0
0

0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

40

19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19
19 19 11 5 6 5 6 6 6 6 6 6 6 5 5 11 19 19
19 19 19 6 6 1 5 1 6 1 1 1 1 5 1 6 1 6 6 19 19 19
19 7 13 13 1 10 1 10 1 10 12 14 10 1 9 1 10 1 15 13 8 19
19 19 6 7 1 14 12 14 15 16 15 15 16 17 15 16 15 10 15 1 7 6 19 19
19 19 19 13 10 1 16 1 15 3 15 1 15 2 2 17 1 15 3 15 1 15 1 10 13 19 19 19
19 8 6 9 1 15 10 15 14 15 14 17 14 17 17 18 17 14 15 14 17 10 15 1 10 6 8 19
19 19 12 7 1 15 4 15 3 17 3 15 2 15 15 14 17 2 15 3 17 3 16 4 15 1 7 13 19 19
19 19 6 13 1 16 10 17 15 17 17 15 15 17 14 17 17 15 15 14 17 13 17 14 16 10 15 1 13 7 19 19
19 11 6 1 16 1 15 3 17 2 15 2 15 2 15 2 2 17 2 15 2 17 2 15 3 17 1 15 1 6 11 19
19 5 1 10 10 15 12 17 16 15 14 17 15 15 14 17 17 13 17 15 15 15 17 14 15 14 15 10 10 1 5 19
19 6 6 1 16 3 17 3 15 2 15 2 17 2 17 17 15 17 2 17 2 15 2 15 3 17 3 15 1 6 5 19
19 6 1 9 16 17 14 16 15 15 14 16 15 17 17 17 17 15 17 14 17 15 15 14 15 14 16 16 9 1 6 19
19 7 5 1 17 3 15 2 15 2 15 2 17 2 17 2 2 17 2 17 2 15 2 15 2 17 1 15 1 5 6 19
19 6 1 10 15 16 15 15 15 17 15 17 17 17 15 15 17 15 17 15 17 13 15 17 15 14 15 16 10 1 6 19
19 6 1 12 16 2 16 13 16 2 17 15 17 2 15 15 15 15 2 17 15 15 2 17 13 17 2 15 14 1 6 19
19 7 1 12 15 2 17 15 15 2 15 15 15 2 16 17 15 15 2 17 15 17 2 17 13 16 2 17 12 1 6 19
19 6 1 10 16 17 15 15 15 17 14 17 15 17 15 16 15 17 17 15 17 13 15 15 16 13 15 15 10 1 6 19
19 6 6 1 15 1 17 2 15 2 15 2 17 2 17 2 2 17 2 17 2 17 2 15 2 17 1 15 1 5 6 19
19 6 1 9 16 17 12 16 15 15 14 17 14 17 14 17 17 15 17 16 17 14 15 15 15 14 16 17 9 1 6 19
19 6 6 1 16 3 17 3 15 2 15 2 17 2 17 16 15 17 2 17 2 15 2 15 3 15 3 15 1 6 6 19
19 5 1 10 10 17 14 15 14 17 15 15 15 17 14 15 17 15 17 14 15 14 15 14 15 14 15 10 10 1 5 19
19 11 5 1 16 1 17 3 15 2 17 2 15 2 17 2 2 15 2 17 2 15 2 15 3 17 1 14 1 5 10 19
19 19 7 13 1 16 10 15 14 15 15 15 15 17 16 17 18 14 17 15 15 15 17 14 17 10 16 1 14 6 19 19
19 19 13 7 1 15 4 15 3 15 3 15 2 17 14 14 17 2 17 3 17 3 17 4 15 1 7 13 19 19
19 8 6 10 1 17 10 17 12 15 14 17 13 17 17 13 16 14 15 12 15 10 15 1 10 6 8 19
19 19 19 13 10 1 16 1 17 3 17 1 17 2 2 17 3 15 3 16 1 16 1 9 13 19 19 19
19 19 6 7 1 16 10 16 16 18 18 15 16 17 18 16 16 10 16 1 7 6 19 19
19 7 11 15 1 10 1 9 1 10 10 10 10 1 10 1 10 1 15 13 7 19
19 19 19 6 6 1 6 1 6 1 1 1 1 6 1 5 1 6 6 19 19 19
19 19 11 5 6 6 7 6 6 6 6 7 6 6 5 11 19 19
19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19

Figure 2.4.2. Radial distribution of assembly types

Figure 2.5.1. Fuel assembly orientation for ADF assignment
Wide
G
a
p

North

West
East

G
a
p
South
Narrow

41

Figure 2.6.1. Core orificing and TIP system arrangement

42Figure 2.6.2. Elevation of core components

43Chapter 3
THERMAL-HYDRAULIC DATAA PB2 RETRAN [4] thermal-hydraulic skeleton input deck, as well as the PB2 RETRAN model
nodalisation and steam line nodalisation diagrams, are provided in Appendix A. English units are usedin this skeleton deck (e.g. ft, ft2, etc.). The detailed plant drawings are provided in Ref. [2].
3.1 Component specifications for the full thermal-hydraulic system model
3.1.1 Reactor vessel
The following tables provide all of the necessary data about the PB2 reactor vessel. Table 3.1.1.1
contains the design data, and Table 3.1.1.2 contains the volume data. Table 3.1.1.3 contains important
PB2 reference design information. Please note that the volumes and elevations in the skeleton input
deck, given in Appendix A, are based on the nodalisation used for that deck as shown in Figure 3.1.1.1.
These volumes and elevations involve combining different physical regions. In contrast, the values
given in the tables are the actual physical volumetric data obtained from the actual vessel dimensions.
See Figure 3.1.1.1 for the way in which the core regions are defined in the RETRAN skeleton input
deck. Figure 3.1.1.1 also shows the flow paths of the reactor vessel, reactor re-circulation system andsteam lines. As can be seen in Figure 3.1.1.1, a single volume (Volume 7) is used to model the steam
space above the steam separators. The downcomer region is divided into three volumes. The upper
downcomer (Volume 8) models the region surrounding the steam separators and includes the normal
steam-water interface. The middle downcomer (Volume 9) models the region surrounding thestandpipes and is the volume where the feedwater flow and the liquid flow from the steam separators
mixes. The lower downcomer models the region surrounding the core shroud and jet pumps. Flow to
the re-circulation loops and jet pump suctions are from this volume.
A single volume (Volume 1) is used to model the fluid region below the core support plate (lower
plenum). The upper plenum region above the upper guide plate and the standpipes are both modelled
as single volumes (Volumes 4 and 5). Two-sided, passive heat conductors are used to model thematerial of the shroud head and the standpipes. A single volume is used to model the internal volumeof the 211 steam separators. Since the liquid flow from the separators, which includes any steam
carry-under, enters the subcooled middle downcomer, the effects of carry-under can be ascertained
without introducing steam bubbles into the liquid downcomer.
3.1.2 Reactor re-circulation system
This section provides the participants with the data for the reactor re-circulation system (RRS).
Table 3.1.2.1 summarises the basic RRS parameters. The two re-circulation loops are modelled
separately. Each re-circulation loop is modelled with three fluid volumes: suction, pump and discharge(Volumes 11, 12, 13, 14, 15 and 16). Each loop drives ten jet pumps lumped as one. Actual pump data45

is used to input pump performance parameters in the normal operating quadrants based on built-in
curves for a pump of similar specific speed. Rated values for pump flow, head and torque are based on
actual pump data, as is the pump moment of inertia.
The included jet pump model corresponds to the simplified TRAC-BF1 JETP component model.
The main features and geometric characteristics of the jet pump are captured in this model and it isshown in Figure 3.1.2.1. Table 3.1.2.2 provides the geometric characteristics. To better understandhow the model is built, please refer to Figure 3.1.2.1 and Table 3.1.2.2. Note that the information
provided in Table 3.1.2.2 corresponds to a single jet pump. For the participants whose codes do notinclude a jet pump model capability, a write-up containing a jet pump model can be found on thebenchmark side under the directory Specifications. The name of the file is jet-pump.doc.
3.1.3 Core region
Twenty-four fluid volumes (Volumes 101-124) are used to model the active (i.e. fuelled) regionof the core. Additionally, single volumes are used to model an unheated core inlet region and coreoutlet region (Volumes 2 and 125). The entire core bypass region is modelled with one fluid volume(Volume 3).
Loss coefficients for the central and peripheral core inlet orifice are provided in Table 3.1.3.1.
Table 3.1.3.2 presents the fuel region loss coefficients for each of the fuel types present in the PB2
reactor core at end cycle (EOC) 2. Table 3.1.3.3 provides hydraulic leakage characteristics for the
7 × 7 and 8 × 8 fuel designs.
3.1.4 Steam lines
The four main steam lines are lumped into one line, which is divided into six volumes (Volumes 50,
51, 52, 53, 54 and 55). Two of the volumes (50 and 51) model the steam lines inboard of the main
steam isolation valves (MSIVs). The second inboard volume is connected to the junctions representing
the safety/relief valves (SRVs). Table 3.1.4.1 summarises the safety relief valve reference design
information. Note that no safety/relief valves are actuated during the actual TT2 test. The remaining
four volumes (Volumes 52, 53, 54 and 55) model the steam lines from the MSIVs to the turbine
stop/control valves.
The steam bypass system is modelled up to and including the condenser (Volumes 200, 201, 202
and 500. The condenser is modelled as a boundary condition. Important junction parameters such as
flow areas and flow pressure loss coefficients are based on steam bypass system design data. Steam
bypass system reference design data is provided in Table 3.1.4.2.
3.1.5 Feedwater lines
The feedwater lines are not modelled as fluid volumes. Instead, a fill junction is used to specify
the feedwater mass flow as a boundary condition. Time-dependent feedwater flow is provided later in
Chapter 5 (Table 5.3.3).

46

3.2 Definition of the core thermal-hydraulic boundary conditions model
The PB2 thermal-hydraulic model can be converted to a core thermal-hydraulic boundary
condition model by defining inlet and outlet thermal-hydraulic boundary conditions. The developedmodel for performing the 3-D core thermal-hydraulic boundary condition calculation (Option 1 of
Exercise 2) was built based on different TRAC-BF1 thermal-hydraulic components as follows.
A 33-channel thermal-hydraulic core boundary condition model was obtained from the PB2 TT2
TRAC-BF1 system model. Bottom and top boundary conditions are specified in this model using the
FILL and BREAK TRAC-BF1 components. The developed model is illustrated in Figure 3.2.1.
Figure 3.2.2 shows the thermal-hydraulic radial mapping scheme used to represent the PB2 reactor
core. The 33 thermal-hydraulic channels shown in this figure are coupled to the neutronic code modelin the radial plane as was shown in Figure 2.4.1 of Chapter 2. Thermal-hydraulic channels identified
with zeroes are treated as reflector regions. This mapping scheme follows the spatial mesh overlays
developed for the PB2 TRAC-BF1/NEM 3-D neutron kinetics/thermal-hydraulic model. The coreboundary condition model using 1-D kinetics (Option 2 of Exercise 2) could use the system
thermal-hydraulic model developed for Exercises 1 and 3 or just use one average channel for
representing the whole core plus the bypass channel.
There are several files of data available at the ftp site and on the CD-ROM that are used for
definition of the core thermal-hydraulic boundary condition model. This data is taken from a
combination of the best-estimate core plant system code calculations performed and test data.
The boundary conditions provided to the participants are both steady state and time dependent. They areprovided for the bottom and top regions adjacent to the inlet and outlet region of the core region. These
values are obtained from the lower and upper region of the vessel component of the TRAC-BF1 model.
The types of boundary conditions that are provided to the participants are:•At the inlet of the channels: mass flows (kg/s) and temperatures (K) from 0 s to 5 s. Thirty-three
files are provided since the model used to obtain these variables contains 33 thermal-hydraulicchannels. Also, a single file containing core mass flow and core inlet temperature vs. time isprovided to participants whose thermal-hydraulic models consist of a single average channel.

•

At the outlet of the thermal-hydraulic channels: pressure (Pa) from 0 s to 5 s. Since all thechannels have a common plenum, pressure is constant radially. Therefore, a single filecontaining pressure vs. time information is provided.

3.3 Thermal-physical and heat transfer specifications
3.3.1 Nuclear fuel (UO2-PuO2) properties
Doppler temperature
The average fuel temperature is used for feedback purposes. This value should be obtained fromthe fuel rod model of each code.
Density[()ρ = f TD 1 − f PuO 2 ρ UO2 + f PuO2 ρ PuO 2]

where fTD is the fraction of theoretical density (0.95), fPuO2 is the weight fraction of PuO2 in fuel(default = 0.0), ρUO2 equals 1.097E4 kg/m3 and ρPuO2 equals 1.146E4 kg/m3.
47

Specific heatb
 b1b 24 exp 4 
 − b 5 
b3b5
T 



C p = 15.496
exp
+ 2b 2 T +
2
2
b
T
b
T
6




b
6


 T 2 exp 4  − 1   T  

where Cp is the specific heat capacity (J/kgK) and T is the fuel temperature (K). For the values of b1
through b6, see the following table.

b1
b2
b3
b4
b5
b6

UO2
19.145
7.8473E–04
5.6437E+06
535.285
37 694.6
1.987

UO2-PuO2
19.53
9.25E–04
6.02E+06
539.0
40 100.0
1.987

Thermal conductivity
For Tc < T1: c1

k = c
+ c 3 exp(c 4 Tc ) in W/m-K
 c 2 + Tc


For Tc > T:k = c[c 5 + c 3 exp(c 4 Tc )] in W/m-K

where Tc is the temperature (oC) and fTD is the fraction of theoretical density.
1 − β(1 − f TD ) c = 100.0  = 100.0, for f TD = 0.95
 1 − 0.05β 

where β = c6 + c7Tc. For additional values, see the following table.

c1
c2
c3
c4
c5
c6
c7
T1

UO2
40.4
464.0
1.216E–04
1.867E–03
0.0191
2.58-5.8E–04
1 650.0

48

UO2-PuO2
33.3
375.0
1.54E–04
1.71E–03
0.01711.43
0.0
1 550.0

3.3.2 Gas gap conductance
All participants should use the following constant value:
K gap = 4542.56

BTU 
W 
 800

hr − ft 2 − F m −K2

3.3.3 Zircaloy cladding properties
Density
A constant value is used: ρ = 6 551.4 kg/m3.
Specific heat
For T > 1 248 K, Cp = 356 J/kgK. For T ≤ 1 248 K, use Table 3.3.3.1.
Thermal conductivity
The following expression is used to calculate cladding thermal conductivity:k = a 0 + a 1T + a 2 T 2 + a 3 T 3

where k is the thermal conductivity (W/m-K) and T is the temperature (K). For the remaining values,
see the following table.

a1
a2
a3
a4

Zr
7.51
2.09E–02-1.45E–05
7.67E–09

ZrO2
1.96-2.41E–04
6.43E–07-1.95E–10

Expansion effects of fuel and cladding will not be considered in this benchmark. The heat transfer
coefficient between cladding and moderator, as well as heat transfer across the pellet-clad gap, has tobe calculated using code specific correlations.

49

Table 3.1.1.1. Reactor vessel design data
Item

Data

Reactor vessel
575/574.82
Operating temperature (°F/°K)
Inside length (in/m)
875.125/22.228
Design pressure (psig/Pa)
1 250/8 719 771
Vessel nozzles (number – size, in/cm)
2 – 28/71.12
Re-circulation outlet
4 – 26/66.04
Steam outlet
10 – 12/30.48
Re-circulation inlet
6 – 12/30.48
Feedwater inlet
2 – 10/25.4
Core spray inlet
2 – 6/15.24
Instrument (one of these is head spray)
185 – 6/15.24
CRD
2 – 4/10.16
Jet pump instrumentation
1 – 4/10.16
Vent
2 – 6/15.24
Instrumentation
1 – 4/10.16
CRD hydraulic system return1 – 2/5.08
Core differential pressure and liquid control
1 – 2/5.08
Drain
55 – 2/5.08
In-core flux instrumentation2 – 1/2.54
Head seal leak detection
Weights (lb/kg)
Bottom head
207 500/94 120.4
Vessel shell
842 300/382 061
Vessel flange
105 800/47 990.1
Support skirt
28 200/12 791
Other vessel components
65 000/29 484
Total vessel without top head
1 248 800/566 446.2
Top head252 200/114 396
Total vessel
1 501 000/680 842.1

50

Table 3.1.1.2. Peach Bottom 2 vessel fluid volumes1
Height above vessel bottom
inm
1.29540
51.00000
3.04480
119.8740
4.85460
191.1260
5.28583
208.1035
5.49436216.3134
8.05546
317.1441
9.15196360.3134
9.62980
379.1260
10.4553
411.6260
11.2427442.6251
13.3985527.5000
14.9098587.0000
16.1290635.000018.9230745.0000
22.1107870.5000
1

Vessel fluid volume
in3
m3
11.89100
7.255888E+05
56.75600
3.463251E+06
104.4010
6.370549E+06
114.8187
7.006237E+06
118.7613
7.246815E+06
158.8763
9.694632E+06
176.9395
1.079685E+07
183.4396
1.119348E+07
208.6850
1.273396E+07
237.3600
1.448371E+07
304.9000
1.860500E+07
323.8791
1.976310E+07
365.2703
2.228879E+07
450.1402
2.746756E+07
517.9812
3.160721E+07

Jet pump volumes excluded51

Table 3.1.1.3. PB2 reference design information
Parameter

Value

Rated core thermal power, MWt
Rated core total flow rate, (Mlb/hr)/(kg/s)
Bypass flow rate, fraction of total core flow
Fraction of core thermal power passing through fuel cladding
Approximate bypass coolant total power fraction
Approximate active coolant total power fraction
Approximate channel wall direct heating fraction
Design minimum critical power ratio for 7 × 7 assemblies (Cycle 2)
Design minimum critical power ratio for 8 × 8 assemblies (Cycle 2)
Design overpower for turbine-generator system
Turbine inlet pressure, psia/Pa
Rated reactor dome pressure, psia/Pa
Rated steam flow rate, (Mlb/hr)/(kg/s)
Steam moisture content, fraction
Rate steam dryer and separator pressure drop, psia/Pa
Rated core pressure, psia/Pa
Core pressure drop at rated conditions, psia/Pa
Approximate core inlet pressure, psia/Pa
Core inlet enthalpy, (Btu/lb)/(J/kg)
Enthalpy rise across core, (Btu/lb)/(J/kg) (average)
Core support plate pressure drop, psi/Pa
Core orifice and lower tie plate pressure drop, Pa
Fuel bundle pressure drop
Reactor average exit quality at rated conditions
Design hot channel active coolant exit quality
Design bypass coolant exit quality
Total feedwater flow rate, (Mlb/hr)/(kg/s)
Feedwater temperature, °F/°K
Control rod drive flow rate, (lb/hr)/(kg/s)
Control rod drive flow temperature, °F/°K
Clean-up demineraliser flow rate, (lb/hr)/(kg/s)
Clean-up demineraliser inlet temperature, °F/°K
Clean-up demineraliser outlet temperature, °F/°K
Location of demineralised water returnJet pump design M ratio
Jet pump design N ratio
Number of re-circulation pumps
Re-circulation pump typeRe-circulation pump rated flow, (Mlb/hr)/(kg/s)
Total developed pump head, ft/m
Re-circulation pump efficiency, per centHead loss from vessel re-circulation outlet to vessel inlet, ft/m
Head loss from vessel re-circulation inlet to jet pump 180° bend entrance, ft/m

3 293
102.5/12 915
Ref. [2], Figs. 54-55
.96
.02
.02
.0075
≥1.28
≥1.31
105% rated steam
965/6.653E06
1 020/7.033E06
13.381/1 685.98.001
15/103 421
1 035/7.1361E06
22/151 685
1 060/7.3084E06
521.3/1.2125E06
109.6/2.5491E05
18/1.24105E05
Ref. [2], Figs. 48-53
Ref. [2], Figs. 44-47
.129
.25
.0
13.331/1 679.7
376.1/464.32
50 000/6.2999
80/299.82
133 300/16.7958
528/548.7
431/494.82
Feedwater line
1.96
.16
2
Centrifugal
17.1/2 154.56
710/216.41
87
59/17.98
11/3.353

52

Table 3.1.2.1. Reactor re-circulation system design characteristics
Item

Data

External loops
Number of loops
Pipe sizes (nominal OD)
Pump suction, in/cm
Pump discharge, in/cm
Discharge manifold, in/cm
Re-circulation inlet line, in/cm
Cross-tie line, in/cm
Design pressure (psig/Pa), design temperature (°F/°K)
Suction piping
Discharge piping
Pumps
Operation at rated conditions
Re-circulation pump
Flow gpm/(m3/s) (approximate)
Flow, (lb/hr)/(kg/s)
Total developed head, ft/m
Suction pressure (static), psia/Pa
Available NPSH* (min.), hp/W
Water temperature (max.). °F/°K
Pump hydraulic HP (min.), hp/W
Flow velocity at pump suction, fps/(m/s) (approximate)
Drive motor and power supply
Frequency (at rated), Hz
Frequency (operating range), Hz
Total required power to M-G sets
KW/set
KW/total
Jet pumps
NumberTotal jet pump flow, (lb/h)/(kg/s)
Throat ID, in/cm
Diffuser ID, in/cm
Nozzle ID, in/cm (representative)
Differ exit velocity, fps/(m/s)
Jet pump head, ft/m

53

2
28/71.12
28/72.12
22/55.88
12/30.48
22/55.88
1 148/8 016 506, 562/567.59
1 326/9 243 773, 562/567.59
1 500/1.044346E07, 575/574.82

45 200/2.851677
1.71E07/2 154.56
710/216.408
1 032/7 115 389
500/373 000
528/548.71
6 130/4 572 980
27.5/8.382
56
11.5-57.5
6 730
13 46020
1.025E08/12 915
8.18/20.7772
19.0/48.26
3.14/7.9756
15.3/4.6634
76.1/23.195

Table 3.1.2.2. PB2 BWR TRAC-BF1 simplified jet pump model
Primary tube (four thermal-hydraulic cells)
Inner radius of the primary tube wall, m
0.14009
Wall thickness of the primary tube wall, m 0.00635
Cell lengths, mCell volumes, m3
Cell edge flow areas, m2
Hydraulic diameters, m

2.5766, 0.30531, 1.8865, 0.24232
0.091159, 0.013037, 0.20718, 0.044325
0.070412, 0.03538, 0.050468, 0.018292, 0.018292
0.2286, 0.21224, 0.25349, 0.4826, 0.4826
Side tube (two thermal-hydraulic cells)
0.080772
Inner radius of the side tube wall, m
0.00635
Wall thickness of the side tube wall, m
0.39675, 0.41893
0.007811, 0.01275
0.0052537, 0.030434, 0.030434
0.081788, 0.19685, 0.19685

Cell lengths, mCell volumes, m3
Cell edge flow areas, m2
Hydraulic diameters, m

Table 3.1.3.1. Core related hydraulic loss coefficients (inlet orifices) (K/A2)
Central core inlet orifice, in–-4/cm–4
Peripheral core inlet orifice, in–4/cm–4

0.1293/0.003106
0.7916/0.01902

Table 3.1.3.2. Fuel estimated loss coefficients (K/A2)–4–4

Fuel lower tie plate, in /cm
Fuel spacers, in–4/cm–4
Fuel upper tie plate, in–4/cm–4

7 × 7 fuel type0.0320/0.000769
0.00450/0.000108
0.00490/0.000118

8 × 8 fuel type0.0344/0.000826
0.00502/0.000121
0.00510/0.000123

Table 3.1.3.3. Core related hydraulic leakage flows
7 × 7 bundle leakage (central, per assembly), lbm/hr/kg/s
7 × 7 bundle leakage (peripheral, per assembly), lbm/hr/kg/s
8 × 8 bundle leakage (central, per assembly), lbm/hr/kg/s
8 × 8 water rod (central, per assembly), lbm/hr/kg/s
Core plate leakage, Mlbm/hr/kg/s
Total leakage, Mlbm/hr/kg/s

4 600/0.5796
1 150/0.1449
10 860/1.36836
920/0.11592
2.14/269.64
6.68/841.68

Table 3.1.4.1. Nuclear system safety and relief valves
Number of valves
Relief valves
Total*
Safety valves443
11 (5)
2

Set pressure(psig/Pa)
1 105/7.720E06
1 115/7.789E06
1 125/7.858E06

Capacity at 103% of set
pressure (each), (lb/h)/(kg/s)
819 000/103.19
827 000/104.20
834 000/105.08

1 230/8.582E06

939 858/118.40* The number in parentheses indicates the number of relief valves which serve in the automatic depressurisation capacity.

54

Table 3.1.4.2. Steam bypass design data
Number of valves
Design flow (per valve), lbm/hr/kg/s
Design inlet pressure, psia/Pa
Design outlet pressure (downstream of valves, psia/Pa
Pressure at entrance to condenser, psia/Pa

9390 000/49.13
965/6 653 675
724/4 991 980
250/1 723 750

Table 3.3.3.1. Specific heat of zircaloy versus temperature for T ≤ 1 248 K
T (K)
300
400
640
1 090
1 093
1 113
1 133
1 153
1 173
1 193
1 213
1 233
1 248

Cp (J/kgK)
281
302
331
375
502
590
615
719
816
770
619
469
356

55

Figure 3.1.1.1. PB2 RETRAN thermal-hydraulic model

56

Figure 3.1.2.1. Simplified TRAC-BF1 BWR jet pump model

57

Figure 3.2.1. PB2 OECD/NRC TT vessel/core boundary conditions model

58

59

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 18 17 17 17 17 17 17 17 17 17 17 17 17 18 0 0
0 0 0 33 14 15 14 15 14 15 15 15 15 14 15 14 15 14 33 0 0 0
0 33 18 16 15 14 15 14 15 14 14 14 14 15 14 15 14 15 16 18 33 0
0 0 33 14 15 13 13 13 13 13 11 13 13 11 13 13 13 13 13 15 14 33 0 0
0 0 0 18 14 15 13 12 13 12 11 12 11 10 10 11 12 11 12 13 12 13 15 14 18 0 0 0
0 33 33 29 26 11 13 11 13 11 13 13 11 11 11 11 13 13 11 13 11 13 11 26 29 33 33 0
0 0 18 29 30 27 26 11 12 11 12 7 6 7 8 8 7 6 7 12 11 12 11 26 27 30 29 18 0 0
0 0 33 29 30 13 13 27 25 7 7 7 7 7 8 8 8 8 7 7 7 7 7 25 27 13 13 30 29 33 0
0 17 29 30 13 28 27 28 22 31 7 31 7 6 7 6 6 7 6 7 31 7 31 22 28 27 28 13 30 29 17
0 17 30 29 13 27 13 27 24 22 23 7 8 3 3 3 3 3 3 8 7 23 22 24 27 13 27 13 29 30 17
0 17 29 30 27 28 27 28 22 31 22 4 3 4 3 3 3 3 4 3 4 22 31 22 28 27 28 27 30 29 17
0 17 30 29 27 13 13 22 22 22 24 21 5 3 3 3 3 3 3 5 21 24 22 22 22 13 13 27 29 30 17
0 17 29 30 27 28 27 32 22 32 21 4 21 4 19 2 2 19 4 21 4 21 32 22 32 27 28 27 30 29 17
0 17 30 29 27 27 27 24 22 22 20 20 20 19 19 1 1 19 19 20 20 20 22 22 24 27 27 27 29 30 17
0 17 30 29 27 10 9 22 22 32 20 20 20 2 1 1 1 1 2 20 20 20 32 22 22 9 10 27 29 30 17
0 17 30 29 27 10 9 22 22 32 20 20 20 2 1 1 1 1 2 20 20 20 32 22 22 9 10 27 29 30 17
0 17 30 29 27 27 27 24 22 22 20 20 20 19 19 1 1 19 19 20 20 20 22 22 24 27 27 27 29 30 17
0 17 29 30 27 28 27 32 22 32 21 4 21 4 19 2 2 19 4 21 4 21 32 22 32 27 28 27 30 29 17
0 17 30 29 27 13 13 22 22 22 24 21 5 3 3 3 3 3 3 5 21 24 22 22 22 13 13 27 29 30 17
0 17 29 30 27 28 27 28 22 31 22 4 3 4 3 3 3 3 4 3 4 22 31 22 28 27 28 27 30 29 17
0 17 30 29 13 27 13 27 24 22 23 7 8 3 3 3 3 3 3 8 7 23 22 24 27 13 27 13 29 30 17
0 17 29 30 13 28 27 28 22 31 7 31 7 6 7 6 6 7 6 7 31 7 31 22 28 27 28 13 30 29 17
0 0 33 29 30 13 13 27 25 7 7 7 7 7 8 8 8 8 7 7 7 7 7 25 27 13 13 30 29 33 0
0 0 18 29 30 27 26 11 12 11 12 7 6 7 8 8 7 6 7 12 11 12 11 26 27 30 29 18 0 0
0 33 33 29 26 11 13 11 13 11 13 13 11 11 11 11 13 13 11 13 11 13 11 26 29 33 33 0
0 0 0 18 14 15 13 12 13 12 11 12 11 10 10 11 12 11 12 13 12 13 15 14 18 0 0 0
0 0 33 14 15 13 13 13 13 13 11 13 13 11 13 13 13 13 13 15 14 33 0 0
0 33 18 16 15 14 15 14 15 14 14 14 14 15 14 15 14 15 16 18 33 0
0 0 0 33 14 15 14 15 14 15 15 15 15 14 15 14 15 14 33 0 0 0
0 0 18 17 17 17 17 17 17 17 17 17 17 17 17 18 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Figure 3.2.2. PB2 reactor core thermal-hydraulic channel radial map

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Chapter 4
NEUTRONIC/THERMAL-HYDRAULIC COUPLING

The feedback, or coupling, between neutronics and thermal-hydraulics can be characterised bychoosing user supplied mapping schemes (spatial mesh overlays) in the radial and axial core planes.
Some of the inlet perturbations (inlet disturbances of both temperature and flow rate) are
specified as a fraction of the position across the core inlet. This requires either a 3-D modelling of thevessel, or some type of a multi-channel model. The PSU developed core multi-channel model consistsof 33 channels to represent the 764 fuel assemblies of the PB2 reactor core. The above core
thermal-hydraulic model was built according to different criteria. First, the fuel assemblies are ranked
according to the inlet orifice characteristics. A second criterion is the fuel assembly type (e.g. 7 × 7 or
8 × 8). Finally, thermal-hydraulic conditions are also considered (e.g. fuel assembly power, mass flow,etc.).
For the purposes of this benchmark (Exercises 2 and 3), it is recommended that an assembly flow
area of 15.535 in2 (1.0023E–02 m2) for fuel assemblies with 7 × 7 fuel rod arrays, and 15.5277 in2(1.0017E–02 m2) for fuel assemblies with 8 × 8 fuel rod arrays be used in the core thermal-hydraulicmulti-channel models. There are 764 fuel assemblies in the PB2 reactor core. At EOC 2, there are
576 fuel assemblies of 7 × 7 type, and 188 of the 8 × 8 type. The radial distribution of assembly types
is shown in Figure 2.4.2 in which the assembly types from 1 to 4 identify a fuel assembly with 8 × 8
fuel arrays and the assembly types from 5 to 18 identify a fuel assembly with 7 × 7 fuel rod arrays.
The core hydraulic characteristics (e.g. core pressure drop) can be found in Ref. [2].

61Chapter 5
TT PROBLEM

5.1 Description of TT2 scenario
A turbine trip (TT) is characterised by a sudden closure of the turbine stop valve (TSV). It can beinitiated by a number of turbine or nuclear system malfunctions. An initiating signal could be a highlevel of condensates in the separators and heaters drain, high vibrations, TSV closure carried out by
the reactor operator, condenser low-vacuum and reactor high liquid level. TSV closure causes asudden reduction of steam flow, which results in a nuclear system pressure increase. The systempressure increase due to the TT is mitigated by the reactor protection system functions. At high power
levels, a TSV closure produces a reactor scram, a turbine bypass valve (BPV) opening and, on someplants, a prompt re-circulation pump trip (prompt RPT). At lower initial power levels, the scram
initiated by the TSV closure is bypassed if the measured power level indicates the transient can behandled by the turbine bypass system. The safety and relief valves (SRVs) and the BPVs help in
releasing the steam production and in limiting the nuclear system pressure increase. On plants whichhave prompt RPT or if the anticipated transient without scram (ATWS-RPT) set point is reached, theincrease of the reactor water level, because of the RPT, can reach the high water level trip set point
and trip the feedwater system. Following the feedwater system trip, the reactor water level will drop to
the low water level set point, which will initiate the high-pressure emergency systems.
A TT transient in a BWR type reactor is considered one of the most complex events to beanalysed because it involves the reactor core, the high pressure coolant boundary, associated valvesand piping in highly complex interactions with variables changing very rapidly.
As mentioned earlier, the transient begins with a sudden TSV closure that initiates a pressure
wave in the main steam system, which is quickly transmitted to the reactor pressure vessel. While theTSVs are closing, the bypass system valves are designed to open, allowing a steam release andtherefore a pressure relief. SRVs can begin to open at pre-established set points, providing additionalpressure relief. The pressure wave requires a detailed nodal modelling of the steam system and its
associated valves to assure that timing effects and pressure wave magnitude can be accurately
determined. This assures the availability of a pressure history in each valve allowing an adequate
modelling of steam flow through each valve.
As the steam pressure increase reaches the reactor pressure vessel, its path must be modelled fromthe steam dome through the dryers and steam separators, and through the downcomer region to there-circulation system and jet pumps. Accurate representation assures that the induced core pressure
oscillations affect the core voids and the core fluid flow in the correct way. Modelling each of theabove regions requires special care to assure an adequate simulation of the pressure increase during
the transient. Adequate modelling of the pressure increase assures that the correct core response iscalculated.

63

5.2 Initial steady state conditions
TT2 initial conditions
The initial steady state reference data are based on those provided in EPRI reports [2,3]. For the
TT2 transient test, the dynamic measurements were taken with a high-speed digital acquisition systemcapable of sampling over 150 signals every 6 milliseconds. The core power distribution measurements
were taken from the plant’s local in-core flux detectors. Special fast response pressure and differential
pressure transducers were installed in parallel with the existing plant instruments in the nuclear steam
supply system. Table 5.2.1 provides the reactor initial conditions for performing steady statecalculations. Figure 5.2.1 shows the PB2 EOC2 TT2 initial control rod pattern. The units of thenumbers shown in the control rod map are called notches. One notch equals a length of 3 inches.
Table 5.2.2 provides the process computer P1 edit for initial core axial relative power distribution in
Exercise 1, and for comparison purposes for Exercises 2 and 3.
Initial water level above vessel zero (AVZ) is equal to 557 inches (14.1478 m). This measured
level is the actual level inside the steam dryer shroud. The initial level AVZ is equal to 564 inches(14.3256 m) for the narrow range measurement outside steam dryer shroud. AVZ is the lowest interior
elevation of the vessel (bottom of lower plenum).
HZP initial conditions
The initial conditions for performing PB2 hot zero power (HZP) core calculations are given in
Table 5.2.3. The fixed thermal-hydraulic variables should be equally distributed through the wholecore. The initial power corresponds to 1% of the PB2 nominal power. Figure 5.2.2 shows the HZP
control rod pattern that should be used for the analysis of this calculation. The initial conditions
presented in Table 5.2.3 along with the control rod pattern shown in Figure 5.2.2 should produce a
critical or very near to critical reactor core. A similar control rod grouping approach as shown in
Figure 2.4.1 could be used to set up the control rod mapping scheme for just two control rod groups.
5.3 Transient calculations
Most of the important phenomena of interest during TT2 occurred in the first five seconds.
Therefore, the transient will be simulated for this time period. This approach simplifies the number ofcomponents required for performing the analysis of TT2. TSV closure characteristics are presented inTable 5.3.1. Basically, the transient begins with the closure of the TSV. At some point in time, theturbine BPV begins to open. Table 5.3.2 shows the BPV characteristics during the transient. The onlyboundary conditions imposed in the analysis should be limited to the opening and closure of the above
valves. Also, if the opening set points of the SRVs are reached, these valves should be included in themodel. Feedwater system behaviour during the transient is shown in Table 5.3.3. The normalised
relative fission power vs. time data for performing Exercise 1 is available at the benchmark ftp site
under the directory Specifications. The file name is nfpower_exercise1.
According to Tables 3-6 of Ref. [3], the actual average planar range monitor (APRM) high flux
scram set point should be set to 95% of rated power or 3 128.35 MWt. Table 5.3.4 shows the scram
initiation time and the delay time that should be used for performing Exercises 2 and 3. Table 5.3.5
shows the average control rod density (CRD) position during reactor scram. This table can be used forthe 1-D neutronic calculation of the transient. An average velocity can be obtained from Table 5.3.5
for the scram modelling in the 3-D kinetics case. An approximate value obtained from the above table64is 2.34 ft/s (0.713 m/s) for the first 0.04 seconds and 4.67 ft/s (1.423 m/s) thereafter. Table 5.3.6 shows
the time delays between the initiation of the TSV motion and the pressure responses along the steamline and in the reactor vessel. These values can be used to evaluate the steam line models used in the
different code system simulations. Some available TT2 transient test peak measured values arepresented in Table 5.3.7. Some TT2 test data acquisition instrument time delays are given in
Table 5.3.8.
The neutronics and thermal-hydraulic information presented in Chapters 1-5 suffices for
performing Exercises 1, 2 and 3. In addition, extreme versions of Exercise 3 are defined as follows:
1. Turbine trip without bypass system relief opening (would increase the power peak andprovide enough pressurisation for safety/relief valve opening).
To perform this exercise, the participants should inactivate the BPV opening in their
thermal-hydraulic modelling. Everything else should remain the same as for Exercise 3.
2. Turbine trip without scram (would increase the power peak and produce a second power peak
and would be a challenge to the coupled code predictions).
No credit for scram is taken during this exercise. To perform this calculation, the participants
should inactivate the reactor scram by simply specifying a large number for scram initiation.
Everything else should remain the same as for Exercise 3.
3. Combined extreme scenario – turbine trip with bypass system relief failure and without
reactor scram. Some preliminary results indicated that this case is very close to a super-prompt
critical state and makes a good case for code-to-code comparisons).
To perform this exercise, both reactor scram and BPV opening should be inactivated.
Everything else should remain the same as for Exercise 3.
Table 5.2.1. PB2 TT2 initial conditions from process computer P1 edit
Core thermal power, MWt
Initial power level, % of rated
Gross power output, MWe
Feedwater flow, kg/s
Reactor pressure, Pa
Total core flow, kg/s
Core inlet subcooling, J/kg
Feedwater temperature, K
Core pressure drop (calculated), Pa
Core pressure drop (measured), Pa
Jet pump driving flow, kg/s
Core average exit quality, fraction
Core average void fraction, fraction
Core average power density, kW/lControl density, fraction* Corrected for calibration and conversion errors

65

2 030
61.65
625.1
980.26
6 798 470.0
10 445.0
48 005.291
442.31
113 560.7
83 567.4
2 871.24*
0.097
0.304
31.28
0.159

Table 5.2.2. PB2 TT2 initial core axial relative power from process computer P1 edit
Node number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24

Axial location (cm)
7.62
22.86
38.1
53.34
68.58
83.82
99.06
114.3
129.54144.78160.02
175.26190.5
205.74220.98236.22251.46266.7
281.94297.18312.42327.66342.9
358.14

Relative power
0.308051
0.616103
0.707754
0.773947
0.814681
0.880874
0.972526
1.066723
1.163467
1.260211.356953
1.407871
1.412963
1.402779
1.37732
1.328949
1.257664
1.188925
1.122733
1.031081
0.913971
0.763764
0.580460.29023

Table 5.2.3. PB2 HZP initial conditions
Fuel temperature, K
3
Average coolant density, kg/m
Reactor power, MW

552.833
753.9777
32.93

Table 5.3.1. TSV flow fraction vs. time
Time (sec)
0.000
0.010
0.020
0.030
0.040
0.050
0.054
0.061
0.066
0.068
0.078
0.086
0.096
1.00
5.00

Flow (fraction)
1.00000.99950.99850.99700.99500.99300.99000.95000.86000.76000.32000.14500.0000
0.000
0.000

66

Table 5.3.2. Bypass valve position vs. time
Time (sec)
0.000
0.054
0.060
0.072
0.090
0.102
0.138
0.162
0.222
0.300
0.504
0.672
0.732
0.846
5.000

Position (%)
0.00000.00000.00000.41000.71002.35008.97008.970015.72029.49062.76088.17091.430100.00100.00

Table 5.3.3. Feedwater flow vs. time
Time (sec)
0.0
0.4
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0

Flow (lbm/sec)
2 171.0
2 171.0
2 165.0
2 005.0
2 000.0
1 920.0
1 900.0
1 950.0
2 030.0
2 220.0
2 485.0
2 760.0

Table 5.3.4. PB2 TT2 scram characteristics
APRM high flux scram set-point, % rated
Time delay prior to rod motion, msec
Time of scram initiation, sec
Initiates CR insertion, sec

67

95 (3 128.35 MWt)
120
0.63
0.75

Table 5.3.5. CRD position after scram vs. time
Time (sec)
0.000
0.120
0.160
0.247
0.354
0.457
2.500
3.080
5.000

Position (ft)0.00000.00000.09350.50001.00001.500010.20012.00012.000

Table 5.3.6. PB2 TT2 event timing (time delay in msec)
TSV begin to close
TSV closed
Begin bypass opening
Bypass full open
Turbine pressure initial response
A. Steam line
B. Steam line
Steam line pressure initial response
A. Steam line
D. Steam line
Vessel pressure initial responseCore exit pressure initial response

000
096
060
846
102
126
348
378
432
486

Table 5.3.7. PB2 TT2 peak measured responses
Average neutron flux, % rated
Core exit pressure, psia
Reactor vessel pressure, psia

00279
1 034
1 038

Table 5.3.8. TT2 test acquisition instrument time delays (in msec)
Core upper plenum
Steam dome
Turbine inlet

68

60
50
45

Figure 5.2.1. PB2 TT2 initial control rod pattern(48 – full withdrawn, 0 – full insertion)

59
55
51
47
43
39
35
31
27
23
19
15
11
07
03

48
48
48
48
48
48
48

48
48
34
48
36
48
34
48
48

48
48
0
48
26
48
26
48
0
48
48

48
48
40
48
36
48
32
48
36
48
40
48
48

02

06

10

14

48
48
0
48
26
48
4
48
4
48
26
48
0
48
48

48
34
48
36
48
48
48
48
48
48
48
36
48
34
48

48
48
26
48
4
48
32
48
32
48
4
48
26
48
48

48
36
48
32
48
48
48
48
48
48
48
32
48
36
48

48
48
26
48
4
48
32
48
32
48
4
48
26
48
48

48
34
48
36
48
48
48
48
48
48
48
36
48
34
48

48
48
0
48
26
48
4
48
4
48
26
48
0
48
48

48
48
40
48
36
48
32
48
36
48
40
48
48

48
48
0
48
26
48
26
48
0
48
48

48
48
34
48
36
48
34
48
48

48
48
48
48
48
48
48

18

22

26

30

34

38

42

46

50

54

58

Figure 5.2.2. PB2 HZP control rod pattern(48 – full withdrawn, 0 – full insertion)

59
55
51
47
43
39
35
31
27
23
19
15
11
07
03

0
48
0
48
0
48
0

0
48
0
48
0
48
0
48
0

0
48
0
48
0
48
0
48
0
48
0

0
48
0
48
0
48
0
48
0
48
0
48
0

02

06

10

14

0
48
0
48
0
48
0
48
0
48
0
48
0
48
0

48
0
48
0
48
0
48
0
48
0
48
0
48
0
48

0
48
0
48
0
48
0
48
0
48
0
48
0
48
0

48
0
48
0
48
0
48
0
48
0
48
0
48
0
48

0
48
0
48
0
48
0
48
0
48
0
48
0
48
0

48
0
48
0
48
0
48
0
48
0
48
0
48
0
48

0
48
0
48
0
48
0
48
0
48
0
48
0
48
0

0
48
0
48
0
48
0
48
0
48
0
48
0

0
48
0
48
0
48
0
48
0
48
0

0
48
0
48
0
48
0
48
0

0
48
0
48
0
48
0

18

22

26

30

34

38

42

46

50

54

58

69

Chapter 6
OUTPUT REQUESTED•

Results should be presented on paper and electronic format (diskette, CD, etc).

•

All data should be in SI units (kg, m, s).

•

For time histories, data should be at 0.006 seconds intervals (for code-to-data comparison).

•

For time histories, data should be at 0.05 seconds intervals (for code-to-code comparison).

6.1 Initial steady state results
The following steady state results will be compared for Exercises 1 and 3:•

Core average axial void fraction distribution.

•

Core axial pressure drop.

•Core inlet enthalpy.

The following results will be compared for the initial test conditions (Exercises 2 and 3) and for
the HZP state (Exercise 2):•

Core averaged relative axial power distribution.

•

Core averaged axial void fraction distribution (excluding the HZP state).

•

Radial power distribution – two-dimensional assembly normalised power distribution (for the
3-D kinetics options).

•

Keff.

•

Relative power distributions for fuel assemblies 75 (rodded bundle) and 367 (un-rodded
bundle) – numbering the core fuel region from top to bottom and from left to right (see fuelregion on Figure 2.2.1).

71

6.2 Transient results
Exercise 1, 2 and 3•

Sequence of events:− Turbine stop valve closed, s.
− Bypass valve begins opening, s.
− Bypass full open, ms.
− Vessel (dome) pressure initial response, s.
− Core exit pressure initial response, s.
− Safety/relief valve opening, s.
− Safety/relief valve closing, s.

•Time histories:− Total reactor core fission power.
− Dome pressure.
− Core exit pressure.
− Total jet pump flow.

Exercises 2 and 3 (3-D kinetics version)
For Exercises 2 and Exercise 3 (3-D kinetics option), a comparison against LPRM measurements
is performed. The participants are provided with an LPRM response model, which is described in
Chapter 2. The necessary neutronic data is included in the 3-D cross-section library as it is describedin Chapter 2. For comparison purposes, only the averaged time history values are requested from theparticipants at the four different levels: A, B, C and D.
•

Transient peaked measured response:− Averaged neutron flux, % rated.
− Core exit pressure, Mpa.
− Reactor vessel (dome) pressure, Mpa.
− Maximum power after reactor scram.

72•Transient snapshots (radial and axial normalised core power distributions) plus relative power
distributions at the specified bundle locations (75 and 367):− At time of maximum power before reactor scram.
− At time of maximum power after reactor scram.
− At the end of the transient (5 seconds for normal Exercises, 10 seconds for extreme
versions of Exercise 3).

6.3 Output format
Results may be sent via e-mail to kni1@psu.edu or on diskette to Kostadin N. Ivanov, Nuclear
Engineering Program, 230 Reber Building, University Park, PA, 16802, USA.
Diskettes should be in PC 3.5" (720 KB or 1.44 MB) format, containing one text (ASCII) file foreach exercise, named RESULTS.A, RESULTS.B and RESULTS.C respectively. Contents should betyped as close as possible to sample format.
Remarks•

Time histories consist of data records (time, value, value), one per line, starting at 0 seconds
up to 5 seconds (10 seconds for the extreme versions of Exercise 3). Please provide the units
on the first line.

•

Radial and axial profiles should be given according to the form shown in Figures 6.1 and 6.2.

•

Please do not use tabs in the data files.

•

Start each line in column one and end each line with a carriage return <CR>.

73

Figure 6.1. Form for axial power distribution

Figure 6.2. Form for radial power distribution
Bottom
1

2

3

4

5

6

7

8

9 10 11 12

13 14 15 16 17 18 19 20 21 22 23 24
Top74

Output sample
1

PEACH BOTTOM TURBINE TRIP BENCHMARK RESULTS FROM CODE “XXXXXXXX”,
EXERCISE 3

2

STEADY STATE RESULTS
2.1 Keff = 1.00000
2.2 Radial power distribution (full core) – start each line in column one, leave a blank space inbetween each number, and use a total of six spaces per number:
0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9999 0.9999 0.9999 0.9999

2.3 Axial power distribution – place all data starting in column one, leave a blank in between
each number, and use a total of six spaces per number:
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

2.4 Core averaged axial void fraction distribution – use the same format as for the axial power
distribution.
3

SEQUENCE OF EVENTS
Table 6.3.1. Sequence of events output
Event description

Time (seconds)

Turbine stop valve closed
Bypass valve begins opening
Bypass full open
Vessel (dome) pressure initial responseCore exit pressure initial response
Safety/relief valve opening (extreme cases of Exercise 3)
Safety/relief valve closing (extreme cases of Exercise 3
High flux set point reached75

4TRANSIENT TIME HISTORIESThe first column of numbers should be the time covering a time interval from 0 to 5 seconds, withdata taken every 0.006 seconds. The second, third, fourth and fifth column should be core power,
dome pressure, core exit pressure and total jet pump flow respectively; at that time, with a space
between the columns. Time histories for the extreme cases of Exercise 3 should cover a timeinterval from 0 to 10 seconds, with data taken every 0.05 seconds. The same column format as
above should be used for the time history variables.

76

REFERENCES[1]

K. Ivanov, et al., “PWR Main Steam Line Break (MSLB) Benchmark. Volume 1: Final
Specifications”, NEA/NSC/DOC(99)8, April 1999.

[2]

N.H. Larsen, “Core Design and Operating Data for Cycles 1 and 2 of Peach Bottom 2”, EPRI
NP-563, June 1978.

[3]

L.A. Carmichael and R.O. Niemi, “Transient and Stability Tests at Peach Bottom Atomic Power
Station Unit 2 at End of Cycle 2”, EPRI NP-564, June 1978.

[4]

A.M. Olson, Topical Report PECo-FMS-0004-A, “Methods for Performing BWR System
Transient Analysis”, Philadelphia Electric Company (1988).

77

APENDIX A
Skeleton Input Deck

79

SKELETON INPUT DECK
NVOL – 53, NJUN – 66

Volumes
No. volume
Description
001
LOWER PLENUM – LPM
002
CORE INLET VOLUME – CIV
003
CORE BYPASS
004
UPPER CORE PLENUM –UPM
005
STANDPIPES
006
STEAM SEPARATORS – SS
007
STEAM DOME
008
UPPER DOWNCOMER – UDC
009
MIDDLE DOWNCOMER – MDC
010
LOWER DOWNCOME – LDC
011
RECIRC SUCCTION 'A'
012
RECIRC SUCCTION 'B'
013
RECIRC PUMP 'A'
014
RECIRC PUMP 'B'
015
RECIRC DISCHARGE 'A'
016
RECIRC DISCHARGE 'B'
017
JET PUMP 'A'
018
JET PUMP 'B'
050
MAIN STEAM LINE 1
051
MAIN STEAM LINE 2
052
MAIN STEAM LINE 3053
MAIN STEAM LINE 4054
MAIN STEAM LINE 5055
MAIN STEAM LINE 6
101
CORE 1
102
CORE 2
103
CORE 3

No. volume
Description
104
CORE 4105
CORE 5
106
CORE 6107
CORE 7108
CORE 8109
CORE 9110
CORE 10111
CORE 11112
CORE 12113
CORE 13114
CORE 14115
CORE 15116
CORE 16
117
CORE 17118
CORE 18
119
CORE 19120
CORE 20
121
CORE 21
122
CORE 22123
CORE 23
124
CORE 24
125
CORE EXIT VOLUME
200
STEAM BYPASS CHEST
201
STEAM BYPASS LINES
202
STEAM BYPASS ORIFICE
500
CONDENSER

81

#
001
002
003
004
005
006
007
008
009
010
017
018
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125

Volume2 064.951
106.0898
965.9736
953.0751
377.5064
681.5879
6 292.622
1 919.922
1 721.338
2 241.127
125.6451
125.6451
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
41.97954
142.1182

Reactor vessel
ZVolume FlowA
DiamV
17.28125 119.49084 0.791085
1.196067 88.698869 0.372351
14.475 69.055861 0.170615
5190.61502 15.5788
8.9177 42.332261 0.505417
6.166667 91.669802 0.74375
22.31771 281.95647 18.94725
9.083333 204.79822 1.091352
9.963541 238.70411 2.11053
24.34896 92.042004 2.791474
16.43333 7.6457436 1.00E+20
16.43333 7.6457436 1.00E+20
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
0.5
83.959069 0.044608
1.692708 83.959069 0.044608

#
11
12
13
14
15
16

Volume233.9687
233.9687
49.67949
49.67949
306.8175
306.8175

Re-circulation loops
ZVolume FlowA
DiamV
42.05208 3.6502301 2.155833
42.05208 3.6502301 2.155833
3.077917 3.6502301 2.155833
3.077917 3.6502301 2.155833
51.08117 2.8411115 0.524994
51.08117 2.8411115 0.524994

82

Elev
0
16.9625
17.2812531.71875
35.540633
44.458333
50.62541.541667
34.494792
10.145833
9.9583333
9.9583333
18.026042
18.526042
19.026042
19.526042
20.026042
20.526042
21.026042
21.526042
22.026042
22.526042
23.026042
23.526042
24.026042
24.526042
25.026042
25.526042
26.026042
26.526042
27.026042
27.526042
28.026042
28.526042
29.026042
29.526042
30.02604

Elev-27.0313-27.0313-23.5833-23.5833-22.6125-22.6125

#
050
051
052
053
054
055
200
201
202
500

Steam lines and steam bypass system
Volume ZVolume FlowA
DiamV
634.0143 46.51042 12.199428 1.970583
594.8101 18.41667 12.199428 1.970583
1 064.168 17.54871 12.199428 1.970583
964.0202 2.220583 12.199428 1.970583
901.7411 2.220583 12.199428 1.970583
1 163.289 2.720583 12.199428 1.970583
216.2789
5.25
2.9781592 1.323024
484.4076 37.91146 2.8539713 0.635417
16.71875 0.88182 5.4965753 0.88182
1.00E+2050
1.00E+09 1.00E+09

Elev-8.364583-10.0521-10.9801
4.264783
4.014784
3.264708
4.25-32.224-32.6649-50

JunctionsNo.
Description
junction001
JET PUMP ’A’ DISCHARGE
002
JET PUMP ’B’ DISCHARGE
003
LPM TO CORE INLET VOL.
004
LOWER PLENUM TO BYPASS
005
CORE INLET TO BYPASS
006
BYPASS TO UPPER PLENUM
007
UPPER PLENUM TI STANDPIPES
008
STANDPIPES TO SS
009
SS TO STEAM DOME
010
SS TO MDC
011
UDC TO STEAM DOME
012
UDC TO MDC
013
MDC TO LDC
014
JET PUMP ’B’ SUCTION’015
JET PUMP ’A’ SUCTION’
016
RECIRC ’B’ SUCTION
017
RECIRC ’A’ SUCTION
018
PUMP ’B’ SUCTION
019
PUMP ’A’ SUCTION
020
PUMP ’B’ DISCHARGE
021
PUMP ’A’ DISCHARGE
022
JET PUMP ’B’ DRIVE
023
JET PUMP ’A’ DRIVE
050
STEAM DOME TO MN STM L1051
MN STM L1 TO MN STM L2052
MN STM L2 TO MN STM L3053
MN STM L3 TO MN STM L4054
MN STM L4 TO MN STM L5055
MN STM L5 TO MN STM L6056
MS STM L6 TO STM BYPASS
057
MAIN STOP VALVES
060
SAFETY VALVES
070
SAFETY RELIEF VALVE GRP 1

No.
junction
071
072
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
200
201
202
300
400

83

Description
SAFETY RELIEF VALVE GRP 2
SAFETY RELIEF VALVE GRP 3
CORE INLET TO CORE 1
CORE 1 TO CORE 2
CORE 2 TO CORE 3
CORE 3 TO CORE 4
CORE 4 TO CORE 5
CORE 5 TO CORE 6
CORE 6 TO CORE 7
CORE 7 TO CORE 8
CORE 8 TO CORE 9
CORE 9 TO CORE 10
CORE 10 TO CORE 11
CORE 11 TO CORE 12
CORE 12 TO CORE 13
CORE 13 TO CORE 14
CORE 14 TO CORE 15
CORE 15 TO CORE 16
CORE 16 TO CORE 17
CORE 17 TO CORE 18
CORE 18 TO CORE 19
CORE 19 TO CORE 20
CORE 20 TO CORE 21
CORE 21 TO CORE 22
CORE 22 TO CORE 23
CORE 23 TO CORE 24
CORE 24 TO CORE EXIT
CORE EXT TO UPM
STEAM BYPASS VALVESSTEAM BYPASS ORIFICESTEAM BYPASS TO CONDENSER
FEEDWATER NFILL
HPCI

#
001
002
003
004
005
006
007
008
009
010
011
012
013
014
015
018
019
020
021
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125

Frm
017
018
001
001
002
003
004
005
006
006
008
008
009
010
010
012
011
014
013
002
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125

Reactor vessel
To
JnArea001 21.81662
001 21.81662
002 19.00019
003
0.29
003
1.71
004 44.12424
005 42.33226
006 42.33226
007 60.49032
009 136.5707
007 283.1268
009 156.5359
010
79.6361
018
2.7
017
2.7
014
3.65023013
3.65023016
3.65023015
3.65023
101 83.95907
102 83.95907
103 83.95907
104 83.95907
105 83.95907
106 83.95907
107 83.95907
108 83.95907
109 83.95907
110 83.95907
111 83.95907
112 83.95907
113 83.95907
114 83.95907
115 83.95907
116 83.95907
117 83.95907
118 83.95907
119 83.95907
120 83.95907
121 83.95907
122 83.95907
123 83.95907
124 83.95907
125 83.95907
004 83.95907

84

JnElev
9.958333
9.958333
16.9625
17.2812518
31.71875
35.54063
44.45833
50.62544.45833
50.62541.54167
34.49479
26.39167
26.39167-23.5833-23.5833-20.5054-20.5054
18.02604
18.52604
19.02604
19.52604
20.02604
20.52604
21.02604
21.52604
22.02604
22.52604
23.02604
23.52604
24.02604
24.52604
25.02604
25.52604
26.02604
26.52604
27.02604
27.52604
28.02604
28.52604
29.02604
29.52604
30.02604
31.71875

#
16
17
18
19
20
21
22
23

Re-circulation loops
Frm ToJnAreaJnElev
10 12
7.669904
13.45833
10 11
7.669904
13.45833
12 143.65023-23.5833
11 13
3.65023-23.5833
14 163.65023-20.5054
13 15
3.65023-20.5054
16 18
0.46
26.39167
15 17
0.46
26.39167# Frm
050 007051 050052 051053 052054 053055 054056 055057 000
060 000
070 000
071 000
072 000
200 200
201 201
202 202
300 000
400 000

Steam lines
To
JnArea050 12.19943
051 12.19943
052 12.19943
053 12.19943
054 12.19943
055 12.19943
200 3.408846
055
1
051
0.27053051 0.532404
051 0.532404
051 0.399303
2011
202 0.659611
500 1.884505
009
1
009
1

85

JnElev
54.8758.364583-10.0521
4.264708
4.264708
5
4.25
4.25
8
8
8
8
5.6875-31.9375-31.9375
41.54167
41.54167

Figure A.1. RETRAN nodalisation diagram86

APPENDIX B
Sample Cross-section Table

87

*
*
*
*

NEM-Cross Section Table Input
T Fuel6

Rho Mod.
6********
X-Section set #1**
Group No. 1**************** Diffusion Coefficient Table*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .2007900E+01 .2014100E+01.2026000E+01 .2029000E+01 .2037700E+01 .1897700E+01.1909700E+01 .1915600E+01 .1918500E+01 .1927200E+01.1816700E+01 .1822600E+01 .1828400E+01 .1831300E+01.1668800E+01 .1674600E+01 .1680300E+01 .1686000E+01.1697200E+01 .1522700E+01 .1528300E+01 .1533800E+01.1542000E+01 .1550100E+01 .1383400E+01 .1388600E+01.1399000E+01 .1401600E+01 .1409300E+01**************** Absorption X-Section Table*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .5733400E-02 .5842800E-02.5997400E-02 .6028100E-02 .6107000E-02 .6023500E-02.6240400E-02 .6318300E-02 .6352700E-02 .6441400E-02.6366900E-02 .6469400E-02 .6553700E-02 .6590900E-02.6535600E-02 .6679800E-02 .6792600E-02 .6885600E-02.7033400E-02 .6807400E-02 .6961600E-02 .7082700E-02.7227000E-02 .7342100E-02 .7043900E-02 .7206500E-02.7440400E-02 .7487500E-02 .7609700E-02**************** Fission X-Section Table*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .1694519E-02 .1687392E-02.1673479E-02 .1670099E-02 .1660123E-02 .1760207E-02.1744963E-02 .1737541E-02 .1733871E-02 .1723065E-02.1798795E-02 .1790994E-02 .1783276E-02 .1779438E-02.1875604E-02 .1867335E-02 .1859149E-02 .1851046E-02.1835163E-02 .1938822E-02 .1930488E-02 .1922119E-02.1909647E-02 .1897342E-02 .1995480E-02 .1986965E-02.1969863E-02 .1965628E-02 .1952890E-02**************** Nu-Fission X-Section Table*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .4226300E-02 .4209200E-02.4176000E-02 .4167900E-02 .4144000E-02 .4384500E-02.4348100E-02 .4330300E-02 .4321500E-02 .4295600E-02.4477200E-02 .4458500E-02 .4440000E-02 .4430800E-02.4660500E-02 .4640700E-02 .4621100E-02 .4601700E-02.4563500E-02 .4810800E-02 .4790700E-02 .4770700E-02.4740700E-02 .4711100E-02 .4944200E-02 .4923700E-02.4882700E-02 .4872400E-02 .4841800E-02**************** Scattering X-Section Table*****
From group 1 to 2
.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .7693100E-02 .7633900E-02.7539000E-02 .7518200E-02 .7460300E-02 .9287200E-02.9147500E-02 .9089500E-02 .9062200E-02 .8986000E-02.1060500E-01 .1052800E-01 .1045900E-01 .1042600E-01

89.1800000E+04.4350457E+03.2020100E+01.1903800E+01.1810700E+01.1839900E+01.1688800E+01.1539200E+01.1393800E+01.1800000E+04.4350457E+03.5927800E-02.6145400E-02.6235400E-02.6687000E-02.6926700E-02.7182600E-02.7334500E-02.1800000E+04.4350457E+03.1680321E-02.1752468E-02.1806831E-02.1768199E-02.1847036E-02.1913830E-02.1978453E-02.1800000E+04.4350457E+03.4192400E-02.4366100E-02.4496300E-02.4403700E-02.4592100E-02.4750700E-02.4903200E-02.1800000E+04.4350457E+03.7583700E-02.9212100E-02.1069300E-01.1033500E-01

.1333700E-01.1288000E-01.1619500E-01.1999900E-01.1322600E-01.1661200E-01.1604500E-01.1993500E-01.1312900E-01.1647700E-01.2043400E-01.1975300E-01.1304100E-01.1635800E-01.2027500E-01**************** Assembly Disc. Factor Table - W*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .9337490E+00 .9346120E+00.9358790E+00 .9361360E+00 .9368150E+00 .9289820E+00.9305890E+00 .9311670E+00 .9314380E+00 .9321550E+00.9257670E+00 .9264880E+00 .9270990E+00 .9273760E+00.9173030E+00 .9181880E+00 .9188970E+00 .9195280E+00.9205860E+00 .9077700E+00 .9086590E+00 .9093830E+00.9103000E+00 .9110590E+00 .8938700E+00 .8947480E+00.8961440E+00 .8964430E+00 .8972790E+00**************** Assembly Disc. Factor Table - S*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .9848210E+00 .9851320E+00.9855810E+00 .9856740E+00 .9859130E+00 .9825030E+00.9830770E+00 .9833260E+00 .9834270E+00 .9836950E+00.9812700E+00 .9815420E+00 .9817760E+00 .9818830E+00.9785220E+00 .9788640E+00 .9791600E+00 .9793880E+00.9797790E+00 .9762050E+00 .9765230E+00 .9767930E+00.9771300E+00 .9774450E+00 .9735190E+00 .9738470E+00.9743250E+00 .9744300E+00 .9746920E+00*****************
Detector Flux Ratio Table*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .9891800E+00 .9897800E+00.9906670E+00 .9908580E+00 .9913620E+00 .9857230E+00.9867780E+00 .9872670E+00 .9874640E+00 .9880020E+00.9841210E+00 .9846150E+00 .9850500E+00 .9852510E+00.9804520E+00 .9810280E+00 .9815250E+00 .9819210E+00.9826270E+00 .9779290E+00 .9784330E+00 .9788730E+00.9794350E+00 .9799850E+00 .9753380E+00 .9758340E+00.9765660E+00 .9767320E+00 .9771570E+00**************** Detector Microscopic X-Section Table*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .9736330E+01 .9693220E+01.9628930E+01 .9615600E+01 .9579910E+01 .9930880E+01.9860290E+01 .9833590E+01 .9821320E+01 .9788490E+01.1000980E+02 .9980860E+01 .9956060E+01 .9944770E+01.1018720E+02 .1015710E+02 .1013180E+02 .1011080E+02.1007540E+02 .1029050E+02 .1026600E+02 .1024590E+02.1022080E+02 .1020060E+02 .1038040E+02 .1036040E+02.1033020E+02 .1032390E+02 .1030700E+02**
Group No. 2**************** Diffusion Coefficient Table*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .5900800E+00 .5923100E+00.5968800E+00 .5980400E+00 .6015400E+00 .5378600E+00.5418900E+00 .5439600E+00 .5450000E+00 .5481600E+00.5004600E+00 .5023300E+00 .5042600E+00 .5052300E+00.4381900E+00 .4398700E+00 .4415800E+00 .4433100E+00.4468400E+00 .3802700E+00 .3817900E+00 .3833400E+00.3857000E+00 .3881000E+00 .3252600E+00 .3266200E+00.3294000E+00 .3301000E+00 .3322400E+00

90.1299900E-01.1624800E-01.2013200E-01.1800000E+04.4350457E+03.9353030E+00.9298700E+00.9247810E+00.9280960E+00.9198200E+00.9100110E+00.8954810E+00.1800000E+04.4350457E+03.9853740E+00.9828240E+00.9810430E+00.9821880E+00.9794880E+00.9770250E+00.9741160E+00.1800000E+04.4350457E+03.9902490E+00.9863100E+00.9837410E+00.9858490E+00.9820960E+00.9792580E+00.9762490E+00.1800000E+04.4350457E+03.9658420E+01.9891880E+01.1004490E+02.9914680E+01.1010120E+02.1022860E+02.1034410E+02.1800000E+04.4350457E+03.5945800E+00.5398500E+00.4986100E+00.5081700E+00.4441900E+00.3849100E+00.3280000E+00

**************** Absorption X-Section Table*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .5089000E-01 .5057300E-01.4996700E-01 .4982000E-01 .4939000E-01 .5237200E-01.5174400E-01 .5144300E-01 .5129500E-01 .5086200E-01.5320900E-01 .5289500E-01 .5259300E-01 .5244400E-01.5542800E-01 .5510600E-01 .5479300E-01 .5448800E-01.5389800E-01 .5744400E-01 .5711600E-01 .5679900E-01.5633800E-01 .5589200E-01 .5972300E-01 .5938600E-01.5874000E-01 .5858300E-01 .5812200E-01**************** Fission X-Section Table*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .2736097E-01 .2715214E-01.2675363E-01 .2665772E-01 .2637649E-01 .2805652E-01.2763665E-01 .2743720E-01 .2733911E-01 .2705215E-01.2836320E-01 .2815297E-01 .2795044E-01 .2785100E-01.2938063E-01 .2916184E-01 .2895035E-01 .2874416E-01.2834761E-01 .3015435E-01 .2993270E-01 .2971797E-01.2940705E-01 .2910713E-01 .3092586E-01 .3069935E-01.3026466E-01 .3016016E-01 .2985157E-01**************** Nu-Fission X-Section Table*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .6824100E-01 .6773100E-01.6676100E-01 .6652700E-01 .6584100E-01 .6988600E-01.6886500E-01 .6837900E-01 .6814000E-01 .6744100E-01.7059600E-01 .7008400E-01 .6959100E-01 .6934900E-01.7300500E-01 .7247300E-01 .7195900E-01 .7145800E-01.7049200E-01 .7482200E-01 .7428100E-01 .7376000E-01.7300300E-01 .7227300E-01 .7662500E-01 .7607300E-01.7501700E-01 .7476100E-01 .7401100E-01**************** Xe Macroscopic X-Section Table*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .1664600E-02 .1649500E-02.1619700E-02 .1612400E-02 .1590700E-02 .1670900E-02.1642200E-02 .1628100E-02 .1621100E-02 .1600400E-02.1663000E-02 .1649000E-02 .1635200E-02 .1628500E-02.1687400E-02 .1673800E-02 .1660400E-02 .1647100E-02.1621200E-02 .1699200E-02 .1685900E-02 .1672800E-02.1653500E-02 .1634700E-02 .1717500E-02 .1704300E-02.1678500E-02 .1672100E-02 .1653500E-02**************** Xe Microscopic X-Section Table*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .9948900E+06 .9852900E+06.9664200E+06 .9618000E+06 .9481500E+06 .1035600E+07.1017700E+07 .1008900E+07 .1004600E+07 .9917300E+06.1058400E+07 .1049800E+07 .1041400E+07 .1037200E+07.1115800E+07 .1107600E+07 .1099600E+07 .1091600E+07.1076000E+07 .1163900E+07 .1156100E+07 .1148400E+07.1137100E+07 .1126100E+07 .1215100E+07 .1207700E+07.1193100E+07 .1189500E+07 .1178900E+07**************** Assembly Disc. Factor Table - W*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03.5991722E+03 .7794058E+03 .2000240E+01 .2000220E+01

91.1800000E+04.4350457E+03.5026600E-01.5205300E-01.5353000E-01.5200800E-01.5433800E-01.5649000E-01.5905900E-01.1800000E+04.4350457E+03.2694950E-01.2784258E-01.2858027E-01.2756113E-01.2864291E-01.2950973E-01.3047976E-01.1800000E+04.4350457E+03.6723900E-01.6936700E-01.7112200E-01.6864100E-01.7121200E-01.7325200E-01.7553800E-01.1800000E+04.4350457E+03.1634600E-02.1656500E-02.1677000E-02.1608400E-02.1640600E-02.1659900E-02.1691300E-02.1800000E+04.4350457E+03.9757900E+06.1026600E+07.1067000E+07.1024800E+07.1087700E+07.1140900E+07.1200300E+07.1800000E+04.4350457E+03.1999820E+01

.1999190E+01.1938250E+01.1893060E+01.1825310E+01.1829460E+01.1769360E+01.1737660E+01.1998830E+01.1938130E+01.1894070E+01.1826650E+01.1764750E+01.1770510E+01.1738240E+01.1997670E+01.1938050E+01.1894390E+01.1827580E+01.1766590E+01.1733150E+01.1739930E+01.1937410E+01.1937650E+01.1894490E+01.1828350E+01.1767840E+01.1734930E+01.1938040E+01.1891960E+01.1894540E+01.1828700E+01.1768890E+01.1736380E+01**************** Assembly Disc. Factor Table - S*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04 .1800000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03 .4350457E+03.5991722E+03 .7794058E+03 .1224460E+01 .1222540E+01 .1220880E+01.1219410E+01 .1218730E+01 .1216800E+01 .1233010E+01 .1231280E+01.1229780E+01 .1228520E+01 .1227890E+01 .1226150E+01 .1239920E+01.1238310E+01 .1236610E+01 .1235410E+01 .1234850E+01 .1233340E+01.1250150E+01 .1249030E+01 .1248070E+01 .1247110E+01 .1246640E+01.1245400E+01 .1261390E+01 .1260380E+01 .1259660E+01 .1259000E+01.1258680E+01 .1257860E+01 .1281000E+01 .1280490E+01 .1280010E+01.1279550E+01 .1279330E+01 .1278640E+01**************** Detector Flux Ratio Table*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04 .1800000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03 .4350457E+03.5991722E+03 .7794058E+03 .9891800E+00 .9897800E+00 .9902490E+00.9906670E+00 .9908580E+00 .9913620E+00 .9857230E+00 .9863100E+00.9867780E+00 .9872670E+00 .9874640E+00 .9880020E+00 .9837410E+00.9841210E+00 .9846150E+00 .9850500E+00 .9852510E+00 .9858490E+00.9804520E+00 .9810280E+00 .9815250E+00 .9819210E+00 .9820960E+00.9826270E+00 .9779290E+00 .9784330E+00 .9788730E+00 .9792580E+00.9794350E+00 .9799850E+00 .9753380E+00 .9758340E+00 .9762490E+00.9765660E+00 .9767320E+00 .9771570E+00**************** Detector Microscopic X-Section Table*.4000000E+03 .8000000E+03 .1200000E+04 .1600000E+04 .1800000E+04.2400000E+04 .1415950E+03 .2261546E+03 .2996453E+03 .4350457E+03.5991722E+03 .7794058E+03 .1342130E+01 .1338480E+01 .1335320E+01.1332550E+01 .1331270E+01 .1327590E+01 .1355250E+01 .1351980E+01.1349130E+01 .1346820E+01 .1345640E+01 .1342370E+01 .1364460E+01.1361380E+01 .1357840E+01 .1355570E+01 .1354500E+01 .1351690E+01.1376000E+01 .1373870E+01 .1371990E+01 .1370120E+01 .1369200E+01.1366820E+01 .1387590E+01 .1385490E+01 .1384050E+01 .1382700E+01.1382050E+01 .1380400E+01 .1414840E+01 .1413680E+01 .1412610E+01.1411580E+01 .1411090E+01 .1409530E+01**************** Effective Delayed Neutron Yield in 6 Groups*.1703595E-03 .1021614E-02 .9344275E-03 .2033880E-02 .7323374E-03
03**************** Decay Constants for Delayed Neutron Groups*.9571060E-02 .2381817E-01 .9017845E-01 .2398291E+00 .1049847E+01.2932571E+01**************** Inv. Neutron Velocities*.5767301E-07 .2513322E-05*

92.1772451E-